From 7b391eab61e8f0f0e43dd8ba3c6c5aa9f5a9c6b5 Mon Sep 17 00:00:00 2001 From: Kyle Niemeyer Date: Wed, 4 Mar 2020 09:58:48 -0800 Subject: [PATCH] more work on elliptic pdes --- _build/images/2d-ghost-node.png | Bin 0 -> 40936 bytes _build/images/heat-equation-grid.png | Bin 85674 -> 54438 bytes _build/images/pdes/elliptic_11_0.png | Bin 0 -> 36343 bytes _build/images/pdes/elliptic_13_0.png | Bin 0 -> 54734 bytes _build/images/pdes/elliptic_15_1.png | Bin 0 -> 56411 bytes _build/images/pdes/elliptic_16_1.png | Bin 0 -> 56367 bytes _build/images/pdes/elliptic_7_0.png | Bin 0 -> 26442 bytes _build/images/row-major.png | Bin 0 -> 142946 bytes _build/pdes/elliptic.html | 765 ++++++++++++++++++++++++-- content/images/2d-ghost-node.png | Bin 0 -> 40936 bytes content/images/heat-equation-grid.png | Bin 85674 -> 54438 bytes content/images/row-major.png | Bin 0 -> 142946 bytes content/pdes/elliptic.ipynb | 655 ++++++++++++++++++++-- 13 files changed, 1351 insertions(+), 69 deletions(-) create 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Example: heat transfer in a sq u_{i+1,j} + u_{i,j+1} + u_{i-1,j} + u_{i,j-1} - 4 u_{i,j} = 0 \;. \end{equation}

Consider a case where the square has sides of length $L$, and the boundary conditions are that the temperature is fixed at 100 on the left, right, and bottom sides, and fixed at 0 on the top. -For now, we'll use three segments to discretize the domain in both directions. +For now, we'll use two segments to discretize the domain in each directions, giving us nine total points in the grid. The following figures show the example problem, and the grid of points we'll use.

-
@@ -90,36 +90,42 @@

Example: heat transfer in a sq

- 4x4 grid -
Figure: Simple 4x4 grid of points
+ 3x3 grid of points +
Figure: Simple 3x3 grid of points

Using the above recursion formula, we can write an equation for each of the four unknown points (in the interior, not the boundary points): +

Using the above recursion formula, we can write an equation for each of the nine unknown points (in the interior, not the boundary points): \begin{align} -\text{for } u_{1,1}: \quad u_{2,1} + u_{1,2} + u_{0,1} + u_{1,0} - 4u_{1,1} &= 0 \\ -\text{for } u_{2,1}: \quad u_{3,1} + u_{2,2} + u_{1,1} + u_{2,0} - 4u_{2,1} &= 0 \\ -\text{for } u_{1,2}: \quad u_{2,2} + u_{1,3} + u_{0,2} + u_{1,1} - 4u_{1,2} &= 0 \\ -\text{for } u_{2,2}: \quad u_{3,2} + u_{2,3} + u_{1,2} + u_{2,1} - 4u_{2,2} &= 0 +u_{1,1} &= 100 \\ +u_{2,1} &= 100 \\ +u_{3,1} &= 100 \\ +u_{1,2} &= 100 \\ +\text{for } u_{2,2}: \quad u_{3,2} + u_{2,3} + u_{1,2} + u_{2,1} - 4u_{2,2} &= 0 \\ +u_{3,2} &= 100 \\ +u_{1,3} &= 100 \\ +u_{2,3} &= 0 \\ +u_{3,3} &= 100 \end{align} -where $u_{1,1}$, $u_{2,1}$, $u_{1,2}$, and $u_{2,2}$ are the unknowns, and $u_{0,j}$, $u_{3,j}$, $u_{i,0}$, and $u_{i,3}$ are known boundary values.

-

Let's rearrange this system of equations slightly, to move all the constant terms to the right-hand side. These constants come from our boundary conditions, where $u_{1,0} = u_{2,0} = 100$, $u_{0,1} = u_{0,2} = 100$, $u_{3,1} = u_{3,2} = 100$, and $u_{1,3} = u_{2,3} = 0$. (The points in the corners do not play a role here.) +where $u_{i,j}$ are the unknowns. Note that in this we used the side boundary condition values for the corner points $u_{1,3}$ and $u_{3,3}$, rather than the top value. (In reality this would represent a discontinuity in temperature, so these aren't very realistic boundary conditions.)

+

This is a system of linear equations, that we can represent as a matrix-vector product: \begin{align} --4u_{1,1} + u_{2,1} + u_{1,2} &= -200 \\ -u_{1,1} - 4u_{2,1} + u_{2,2} &= -200 \\ -u_{1,1} - 4u_{1,2} + u_{2,2} &= -100 \\ -u_{2,1} + u_{1,2} - 4u_{2,2} &= -100 -\end{align} -This is a system of linear equations, that we can represent as a matrix-vector product: -\begin{align} -\begin{bmatrix} -4 & 1 & 1 & 0 \\ -1 & -4 & 0 & 1 \\ -1 & 0 & -4 & 1 \\ -0 & 1 & 1 & -4 \end{bmatrix} -\begin{bmatrix} u_{1,1} \\ u_{2,1} \\ u_{1,2} \\ u_{2,2} \end{bmatrix} &= -\begin{bmatrix} -200 \\ -200 \\ -100 \\ -100 \end{bmatrix} \\ +\begin{bmatrix} +1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ +0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ +0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ +0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ +0 & 1 & 0 & 1 & -4 & 1 & 0 & 1 & 0 \\ +0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ +0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ +0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ +0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\end{bmatrix} +\begin{bmatrix} u_{1,1} \\ u_{2,1} \\ u_{3,1} \\ u_{1,2} \\ u_{2,2} \\ u_{3,2} \\ u_{1,3} \\ u_{2,3} \\ u_{3,3} \end{bmatrix} &= +\begin{bmatrix} 100 \\ 100 \\ 100 \\ +100 \\ 0 \\ 100 \\ +100 \\ 0 \\ 100 \end{bmatrix} \\ \text{or} \quad A \mathbf{u} &= \mathbf{b} \end{align} -where $A$ is a $4\times 4$ coefficient matrix, $\mathbf{u}$ is a four-element vector of unknown variables, and $\mathbf{b}$ is a four-element right-hand side vector. +where $A$ is a $9\times 9$ coefficient matrix, $\mathbf{u}$ is a nine-element vector of unknown variables, and $\mathbf{b}$ is a nine-element right-hand side vector. For $\mathbf{u}$, we had to take variables that physically represent points in a two-dimensional space and combine them in some order to form a one-dimensional column vector. Here, we used a row-major mapping, where we started with the point in the first row and first column, then added the remaining points in that row, before moving to the next row and repeating. We'll discuss this a bit more later.

If we set this up in Matlab, we can solve with u = A \ b:

@@ -137,12 +143,19 @@

Example: heat transfer in a sq
clear all; clc
 
-A = [-4  1  1  0; 
-      1 -4  0  1;
-      1  0 -4  1;
-      0  1  1 -4];
-b = [-200; -200; -100; -100];
+A = [
+1 0 0 0  0 0 0 0 0;
+0 1 0 0  0 0 0 0 0;
+0 0 1 0  0 0 0 0 0;
+0 0 0 1  0 0 0 0 0;
+0 1 0 1 -4 1 0 1 0;
+0 0 0 0  0 1 0 0 0;
+0 0 0 0  0 0 1 0 0;
+0 0 0 0  0 0 0 1 0;
+0 0 0 0  0 0 0 0 1];
+b = [100; 100; 100; 100; 0; 100; 100; 0; 100];
 
+% solve system of linear equations
 u = A \ b;
 
 disp(u)
@@ -159,10 +172,140 @@ 

Example: heat transfer in a sq
-
   87.5000
-   87.5000
-   62.5000
-   62.5000
+
   100
+   100
+   100
+   100
+    75
+   100
+   100
+     0
+   100
+
+
+
+
+

+
+ + + + + +
+ +
+
+

This gives us the values for temperature at each of the nine points. In this example, we really only have one unknown temperature: $u_{2,2}$, located in the middle. Does the value given make sense? We can check by rearranging the recursion formula for Laplace's equation: +\begin{equation} +u_{i,j} = \frac{u_{i+1,j} + u_{i,j+1} + u_{i-1,j} + u_{i,j-1}}{4} \;, +\end{equation} +which shows that in such problems the value of the middle point should be the average of the four surrounding points. This matches the value of 75 found above.

+

We can use a contour plot to visualize the results, though we'll need to convert the one-dimensional solution array into a two-dimensional matrix to plot. The Matlab reshape() function can help us here: it reshapes an array into a matrix, by specifying the target number of desired columns and rows:

+ +
+
+
+
+ +
+ +
+
+ +
+
+
% Example of using the reshape function, with a simple array going from 1 to 10
+
+% We want to convert it into a matrix with 5 columns and 2 rows.
+% The expected output is:
+% [1 2 3 4 5; 
+%  6 7 8 9 10]
+
+b = (1 : 10)';
+A = reshape(b, [5, 2]);
+disp('b array:')
+disp(b)
+disp('A matrix:')
+disp(A)
+
+ +
+
+
+ +
+
+ +
+
+ +
+
b array:
+     1
+     2
+     3
+     4
+     5
+     6
+     7
+     8
+     9
+    10
+
+A matrix:
+     1     6
+     2     7
+     3     8
+     4     9
+     5    10
+
+
+
+
+
+
+
+ +
+
+ +
+ +
+
+

This behavior may be a bit unexpected, because reshape() uses a column-major mapping. We can fix this by taking the transpose of the resulting matrix:

+ +
+
+
+
+ +
+ +
+
+ +
+
+
disp('transpose of output matrix:')
+disp(A')
+
+ +
+
+
+ +
+
+ +
+
+ +
+
transpose of output matrix:
+     1     2     3     4     5
+     6     7     8     9    10
 
 
@@ -176,12 +319,564 @@

Example: heat transfer in a sq
+
+
+ +
+
+
% We can use the reshape function to convert the calculated temperatures
+% into a 3x3 matrix:
+
+n = 3; m = 3;
+u_square = reshape(u, [n, m]);
+
+contourf(u_square')
+colorbar
+
+ +
+
+
+ +
+
+ +
+
+ + + +
+ +
+ +
+
+
+
+ +
+
+ +
+ +
+
+

Overall that looks correct: the boundary conditions are right, and we see that the center is the average of the boundaries.

+

But, clearly only using nine points (with eight of those being boundary conditions) doesn't give us a very good solution. To make this more accurate, we'll need to use more points, which also means we need to automate the construction of the system of equations.

+ +
+
+
+
+ +
+ +
+
+

Row-major mapping

For a two-dimensional elliptic PDE like Laplace's equation, we can generate a general recursion formula, but we need a way to take a grid of points where location is defined by row and column index and map these into a one-dimensional column vector, which has its own index.

+

The following figure shows a general 2D grid of points, with $n$ number of columns in the $x$ direction (using index $i$) and $m$ number of rows in the $y$ direction (using index $j$):

+
+
+ 2D grid of points +
Figure: 2D grid of points with n columns and m columns.
+
+

We want to convert the rows and columns of $u_{i,j}$ points defined by column and row index into a single column array using a different index, $k$ (this choice is arbitrary): +\begin{equation} +\begin{bmatrix} u_{1,1} \\ u_{2,1} \\ u_{3,1} \\ \vdots \\ u_{n,1} \\ +u_{1,2} \\ u_{2,2} \\ u_{3,2} \\ \vdots \\ u_{n, 2} \\ u_{1,3} \\ \vdots \\ +u_{1,m} \\ u_{2,m} \\ \vdots \\ u_{n,m} +\end{bmatrix} +\end{equation} +where $k$ refers to the index used in that array.

+

To do this mapping, we can use this formula: +\begin{equation} +k_{i,j} = (j-1)n + i +\end{equation} +where $k_{i,j}$ refers to the 1D index $k$ mapped from the 2D indices $i$ and $j$.

+
+ 3x3 grid of points +
Figure: Simple 3x3 grid of points
+

For example, in this $3\times 3$ grid, where $n=3$ and $m=3$, consider the point where $i=2$ and $j=2$ (the point right in the center). Using our formula, +\begin{equation} +k_{2,2} = (2-1)3 + 2 = 5 +\end{equation} +which matches what we can visually confirm.

+

Using that mapping, we can also identify the 1D indices associated with the points surrounding location $(i,j)$: +\begin{align} +k_{i-1,j} &= (j-1)n + i - 1 \\ +k_{i+1,j} &= (j-1)n + i + 1 \\ +k_{i,j-1} &= (j-2)n + i \\ +k_{i,j+1} &= j n + i +\end{align} +which we can use to determine the appropriate locations to place values in the coefficient and right-hand side matrices.

+ +
+
+
+
+ +
+ +
+
+

Example: heat transfer in a square plate (redux)

Let's return to the example of steady-state heat transfer in a square plate—but this time we'll set the solution up more generally so we can vary the step size $h = \Delta x = \Delta y$.

+ +
+
+
+
+ +
+ +
+
+ +
+
+
clear; clc; close all
+
+h = 0.1;
+x = [0 : h : 1]; n = length(x);
+y = [0 : h : 1]; m = length(y);
+
+% The coefficient matrix A is now m*n by m*n, since that is the total number of points.
+% The right-hand side vector b is m*n by 1.
+A = zeros(m*n, m*n);
+b = zeros(m*n, 1);
+
+u_left = 100;
+u_right = 100;
+u_bottom = 100;
+u_top = 0;
+
+for j = 1 : m
+    for i = 1 : n
+        % for convenience we calculate all the indices once
+        kij = (j-1)*n + i;
+        kim1j = (j-1)*n + i - 1;
+        kip1j = (j-1)*n + i + 1;
+        kijm1 = (j-2)*n + i;
+        kijp1 = j*n + i;
+        
+        if i == 1 
+            % this is the left boundary
+            A(kij, kij) = 1;
+            b(kij) = u_left;
+        elseif i == n 
+            % right boundary
+            A(kij, kij) = 1;
+            b(kij) = u_right;
+        elseif j == 1 
+            % bottom boundary
+            A(kij, kij) = 1;
+            b(kij) = u_bottom;
+        elseif j == m 
+            % top boundary
+            A(kij, kij) = 1;
+            b(kij) = u_top;
+        else
+            % these are the coefficients for the interior points,
+            % based on the recursion formula
+            A(kij, kim1j) = 1;
+            A(kij, kip1j) = 1;
+            A(kij, kijm1) = 1;
+            A(kij, kijp1) = 1;
+            A(kij, kij) = -4;
+        end
+    end
+end
+u = A \ b;
+
+u_square = reshape(u, [n, m]);
+contourf(x, y, u_square')
+c = colorbar;
+c.Label.String = 'Temperature';
+
+ +
+
+
+ +
+
+ +
+
+ + + +
+ +
+ +
+
+
+
+ +
+
+ +
+ +
+
+

Neumann (derivative) boundary conditions

So far, we have only discussed cases where we have Dirichlet boundary conditions; in other words, when we have all fixed values at the boundary. Frequently we also encounter Neumann-style boundary conditions, where we have the derivative specified at the boundary.

+

We can handle this in the same way we do for one-dimensional boundary value problems: either with a forward or backward difference (both of which are first-order accurate), or with a central difference using an imaginary point/ghost node (which is second-order accurate). Let's focus on using the central difference, since it is more accurate.

+
+
+ ghost node at boundary +
Figure: Ghost/imaginary node beyond an upper boundary
+
+

For example, let's say that at the upper boundary, the derivative of temperature is zero: +\begin{equation} +\left. \frac{\partial u}{\partial y} \right|_{\text{boundary}} = 0 +\end{equation}

+

Let's consider this boundary condition applied at the point shown, $u_{2,3}$. +We can approximate this derivative using a central difference: +\begin{align} +\frac{u_{2,3}}{\partial y} \approx \frac{u_{2,4} - u_{2,2}}{\Delta x} &= 0 \\ +u_{2,4} &= u_{2,2} +\end{align} +This tells us the value of the point above the boundary, $u_{2,4}$; however, this point is a "ghost" or imaginary point located outside the boundary, so we don't really care about its value. Instead, we can use this relationship to give us a usable equation for the boundary point, by incorporating it into the normal recursion formula for Laplace's equation: +\begin{align} +u_{1,3} + u_{3,3} + u_{2,4} + u_{2,2} - 4u_{2,3} &= 0 \\ +u_{1,3} + u_{3,3} + u_{2,2} + u_{2,2} - 4u_{2,3} &= 0 \\ +\rightarrow u_{1,3} + u_{3,3} + 2 u_{2,2} - 4u_{2,3} &= 0 +\end{align}

+

The recursion formula for points along the upper boundary would then become +\begin{equation} +u_{i+1,j} + u_{i-1,j} + 2 u_{i,j-1} - 4 u_{i,j} = 0 \;. +\end{equation}

+

Now let's try solving the above example, but with $\frac{\partial u}{\partial y} = 0$ at the top boundary and $u = 0$ at the bottom boundary:

+ +
+
+
+
+ +
+ +
+
+ +
+
+
clear; clc; close all
+
+h = 0.1;
+x = [0 : h : 1]; n = length(x);
+y = [0 : h : 1]; m = length(y);
+
+% The coefficient matrix A is now m*n by m*n, since that is the total number of points.
+% The right-hand side vector b is m*n by 1.
+A = zeros(m*n, m*n);
+b = zeros(m*n, 1);
+
+u_left = 100;
+u_right = 100;
+u_bottom = 0;
+
+for j = 1 : m
+    for i = 1 : n
+        % for convenience we calculate all the indices once
+        kij = (j-1)*n + i;
+        kim1j = (j-1)*n + i - 1;
+        kip1j = (j-1)*n + i + 1;
+        kijm1 = (j-2)*n + i;
+        kijp1 = j*n + i;
+        
+        if i == 1 
+            % this is the left boundary
+            A(kij, kij) = 1;
+            b(kij) = u_left;
+        elseif i == n 
+            % right boundary
+            A(kij, kij) = 1;
+            b(kij) = u_right;
+        elseif j == 1 
+            % bottom boundary
+            A(kij, kij) = 1;
+            b(kij) = u_bottom;
+        elseif j == m 
+            % top boundary, using the ghost node + recursion formula
+            A(kij, kim1j) = 1;
+            A(kij, kip1j) = 1;
+            A(kij, kijm1) = 2;
+            A(kij, kij) = -4;
+        else
+            % these are the coefficients for the interior points,
+            % based on the recursion formula
+            A(kij, kim1j) = 1;
+            A(kij, kip1j) = 1;
+            A(kij, kijm1) = 1;
+            A(kij, kijp1) = 1;
+            A(kij, kij) = -4;
+        end
+    end
+end
+u = A \ b;
+
+u_square = reshape(u, [n, m]);
+% the "20" indicates the number of levels for the contour plot
+contourf(x, y, u_square', 20);
+c = colorbar;
+c.Label.String = 'Temperature';
+
+ +
+
+
+ +
+
+ +
+
+ + + +
+ +
+ +
+
+
+
+ +
+
+ +
+
-

This gives us the values for temperature at each of the four points. As a quick check, they all fall between 0 and 100, with the colder points on the second row, near the top boundary where the temperature was fixed at 0.

+

Iterative solutions for (very) large problems

+
+
+
+
+ +
+ +
+
+ +
+
+
clear all; clc;
+
+h = 0.01;
+x = [0 : h : 1]; n = length(x);
+y = [0 : h : 1]; m = length(y);
+
+% The coefficient matrix A is now m*n by m*n, since that is the total number of points.
+% The right-hand side vector b is m*n by 1.
+A = zeros(m*n, m*n);
+b = zeros(m*n, 1);
+
+tic
+
+u_left = 100;
+u_right = 100;
+u_bottom = 100;
+u_top = 0;
+
+for j = 1 : m
+    for i = 1 : n
+        % for convenience we calculate all the indices once
+        kij = (j-1)*n + i;
+        kim1j = (j-1)*n + i - 1;
+        kip1j = (j-1)*n + i + 1;
+        kijm1 = (j-2)*n + i;
+        kijp1 = j*n + i;
+        
+        if i == 1 
+            % this is the left boundary
+            A(kij, kij) = 1;
+            b(kij) = u_left;
+        elseif i == n 
+            % right boundary
+            A(kij, kij) = 1;
+            b(kij) = u_right;
+        elseif j == 1 
+            % bottom boundary
+            A(kij, kij) = 1;
+            b(kij) = u_bottom;
+        elseif j == m 
+            % top boundary
+            A(kij, kij) = 1;
+            b(kij) = u_top;
+        else
+            % these are the coefficients for the interior points,
+            % based on the recursion formula
+            A(kij, kim1j) = 1;
+            A(kij, kip1j) = 1;
+            A(kij, kijm1) = 1;
+            A(kij, kijp1) = 1;
+            A(kij, kij) = -4;
+        end
+    end
+end
+u = A \ b;
+
+u_square = reshape(u, [n, m]);
+% the "20" indicates the number of levels for the contour plot
+contourf(x, y, u_square', 20);
+c = colorbar;
+c.Label.String = 'Temperature';
+
+toc
+
+ +
+
+
+ +
+
+ +
+
+ +
+
Elapsed time is 8.798152 seconds.
+
+
+
+
+
+
+ + + +
+ +
+ +
+
+
+
+ +
+
+
+ +
+
+ +
+
+
clear all; clc;
+
+h = 0.01;
+x = [0 : h : 1]; n = length(x);
+y = [0 : h : 1]; m = length(y);
+
+% The coefficient matrix A is now m*n by m*n, since that is the total number of points.
+% The right-hand side vector b is m*n by 1.
+A = zeros(m*n, m*n);
+b = zeros(m*n, 1);
+
+tic
+
+u_left = 100;
+u_right = 100;
+u_bottom = 100;
+u_top = 0;
+
+% initial guess
+u = 100*ones(m*n, 1);
+
+% dummy value for residual variable
+epsilon = 1.0; 
+
+num = 0;
+while epsilon > 1e-6
+    u_old = u;
+    
+    epsilon = 0;
+    for j = 1 : m
+        for i = 1 : n
+            kij = (j-1)*n + i;
+            kim1j = (j-1)*n + i - 1;
+            kip1j = (j-1)*n + i + 1;
+            kijm1 = (j-2)*n + i;
+            kijp1 = j*n + i;
+
+            if i == 1 
+                % this is the left boundary
+                u(kij) = u_left;
+            elseif i == n 
+                % right boundary
+                u(kij) = u_right;
+            elseif j == 1 
+                % bottom boundary
+                u(kij) = u_bottom;
+            elseif j == m 
+                % top boundary
+                u(kij) = u_top;
+            else
+                % interior points
+                u(kij) = (u(kip1j) + u(kim1j) + u(kijm1) + u(kijp1))/4.0;
+            end
+        end
+    end
+    
+    epsilon = max(abs(u - u_old));
+    num = num + 1;
+end
+
+u_square = reshape(u, [n, m]);
+% the "20" indicates the number of levels for the contour plot
+contourf(x, y, u_square', 20);
+c = colorbar;
+c.Label.String = 'Temperature';
+
+toc
+fprintf('Number of iterations: %d\n', num)
+
+ +
+
+
+ +
+
+ +
+
+ +
+
Elapsed time is 2.197245 seconds.
+Number of iterations: 10762
+
+
+
+
+
+ + + +
+
+ +
+
+
+
+
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zWPzi7+t{PacHSqE0tysaV%M9t_1YtJtE(?%t=w;uN-Bp?QGUG$kgrW=i5|UPtNZjZ zUTu?8#lX4+8O`O@r1c|YnI)1_Kt$EK7El~Hx~EPMCB zn~&-MMgQ_&haI3IP2t9r^dD|FP!&?dl&g>%Rm1AF21>yZW0KjQw{l{a%NEH}HS)F7aQm`4dS||KjTJ fBVqBXc4xN&x})hv^s4?Y_@i`9^=j@F!)N~klM_IB literal 0 HcmV?d00001 diff --git a/content/pdes/elliptic.ipynb b/content/pdes/elliptic.ipynb index b9969bc..b1d78fd 100644 --- a/content/pdes/elliptic.ipynb +++ b/content/pdes/elliptic.ipynb @@ -68,7 +68,7 @@ "\\end{equation}\n", "\n", "Consider a case where the square has sides of length $L$, and the boundary conditions are that the temperature is fixed at 100 on the left, right, and bottom sides, and fixed at 0 on the top.\n", - "For now, we'll use three segments to discretize the domain in both directions.\n", + "For now, we'll use two segments to discretize the domain in each directions, giving us nine total points in the grid.\n", "The following figures show the example problem, and the grid of points we'll use.\n", "\n", "\n", @@ -80,39 +80,45 @@ "\n", "\n", "
\n", "
\n", - " \"4x4 \n", - "
Figure: Simple 4x4 grid of points
\n", + " \"3x3 \n", + "
Figure: Simple 3x3 grid of points
\n", "
\n", "
\n", "\n", - "Using the above recursion formula, we can write an equation for each of the four unknown points (in the interior, not the boundary points):\n", + "Using the above recursion formula, we can write an equation for each of the nine unknown points (in the interior, not the boundary points):\n", "\\begin{align}\n", - "\\text{for } u_{1,1}: \\quad u_{2,1} + u_{1,2} + u_{0,1} + u_{1,0} - 4u_{1,1} &= 0 \\\\\n", - "\\text{for } u_{2,1}: \\quad u_{3,1} + u_{2,2} + u_{1,1} + u_{2,0} - 4u_{2,1} &= 0 \\\\\n", - "\\text{for } u_{1,2}: \\quad u_{2,2} + u_{1,3} + u_{0,2} + u_{1,1} - 4u_{1,2} &= 0 \\\\\n", - "\\text{for } u_{2,2}: \\quad u_{3,2} + u_{2,3} + u_{1,2} + u_{2,1} - 4u_{2,2} &= 0\n", + "u_{1,1} &= 100 \\\\\n", + "u_{2,1} &= 100 \\\\\n", + "u_{3,1} &= 100 \\\\\n", + "u_{1,2} &= 100 \\\\\n", + "\\text{for } u_{2,2}: \\quad u_{3,2} + u_{2,3} + u_{1,2} + u_{2,1} - 4u_{2,2} &= 0 \\\\\n", + "u_{3,2} &= 100 \\\\\n", + "u_{1,3} &= 100 \\\\\n", + "u_{2,3} &= 0 \\\\\n", + "u_{3,3} &= 100\n", "\\end{align}\n", - "where $u_{1,1}$, $u_{2,1}$, $u_{1,2}$, and $u_{2,2}$ are the unknowns, and $u_{0,j}$, $u_{3,j}$, $u_{i,0}$, and $u_{i,3}$ are known boundary values.\n", + "where $u_{i,j}$ are the unknowns. Note that in this we used the side boundary condition values for the corner points $u_{1,3}$ and $u_{3,3}$, rather than the top value. (In reality this would represent a discontinuity in temperature, so these aren't very realistic boundary conditions.)\n", "\n", - "Let's rearrange this system of equations slightly, to move all the constant terms to the right-hand side. These constants come from our boundary conditions, where $u_{1,0} = u_{2,0} = 100$, $u_{0,1} = u_{0,2} = 100$, $u_{3,1} = u_{3,2} = 100$, and $u_{1,3} = u_{2,3} = 0$. (The points in the corners do not play a role here.)\n", - "\\begin{align}\n", - "-4u_{1,1} + u_{2,1} + u_{1,2} &= -200 \\\\\n", - "u_{1,1} - 4u_{2,1} + u_{2,2} &= -200 \\\\\n", - "u_{1,1} - 4u_{1,2} + u_{2,2} &= -100 \\\\\n", - "u_{2,1} + u_{1,2} - 4u_{2,2} &= -100\n", - "\\end{align}\n", "This is a system of linear equations, that we can represent as a matrix-vector product:\n", "\\begin{align}\n", - "\\begin{bmatrix} -4 & 1 & 1 & 0 \\\\\n", - "1 & -4 & 0 & 1 \\\\\n", - "1 & 0 & -4 & 1 \\\\\n", - "0 & 1 & 1 & -4 \\end{bmatrix}\n", - "\\begin{bmatrix} u_{1,1} \\\\ u_{2,1} \\\\ u_{1,2} \\\\ u_{2,2} \\end{bmatrix} &= \n", - "\\begin{bmatrix} -200 \\\\ -200 \\\\ -100 \\\\ -100 \\end{bmatrix} \\\\\n", + "\\begin{bmatrix} \n", + "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", + "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", + "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", + "0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", + "0 & 1 & 0 & 1 & -4 & 1 & 0 & 1 & 0 \\\\\n", + "0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\\\\n", + "0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\\\\n", + "0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n", + "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\\end{bmatrix}\n", + "\\begin{bmatrix} u_{1,1} \\\\ u_{2,1} \\\\ u_{3,1} \\\\ u_{1,2} \\\\ u_{2,2} \\\\ u_{3,2} \\\\ u_{1,3} \\\\ u_{2,3} \\\\ u_{3,3} \\end{bmatrix} &= \n", + "\\begin{bmatrix} 100 \\\\ 100 \\\\ 100 \\\\ \n", + "100 \\\\ 0 \\\\ 100 \\\\\n", + "100 \\\\ 0 \\\\ 100 \\end{bmatrix} \\\\\n", "\\text{or} \\quad A \\mathbf{u} &= \\mathbf{b}\n", "\\end{align}\n", - "where $A$ is a $4\\times 4$ coefficient matrix, $\\mathbf{u}$ is a four-element vector of unknown variables, and $\\mathbf{b}$ is a four-element right-hand side vector.\n", + "where $A$ is a $9\\times 9$ coefficient matrix, $\\mathbf{u}$ is a nine-element vector of unknown variables, and $\\mathbf{b}$ is a nine-element right-hand side vector.\n", "For $\\mathbf{u}$, we had to take variables that physically represent points in a two-dimensional space and combine them in some order to form a one-dimensional column vector. Here, we used a **row-major** mapping, where we started with the point in the first row and first column, then added the remaining points in that row, before moving to the next row and repeating. We'll discuss this a bit more later.\n", "\n", "If we set this up in Matlab, we can solve with `u = A \\ b`:" @@ -120,17 +126,22 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - " 87.5000\n", - " 87.5000\n", - " 62.5000\n", - " 62.5000\n", + " 100\n", + " 100\n", + " 100\n", + " 100\n", + " 75\n", + " 100\n", + " 100\n", + " 0\n", + " 100\n", "\n" ] } @@ -138,12 +149,19 @@ "source": [ "clear all; clc\n", "\n", - "A = [-4 1 1 0; \n", - " 1 -4 0 1;\n", - " 1 0 -4 1;\n", - " 0 1 1 -4];\n", - "b = [-200; -200; -100; -100];\n", + "A = [\n", + "1 0 0 0 0 0 0 0 0;\n", + "0 1 0 0 0 0 0 0 0;\n", + "0 0 1 0 0 0 0 0 0;\n", + "0 0 0 1 0 0 0 0 0;\n", + "0 1 0 1 -4 1 0 1 0;\n", + "0 0 0 0 0 1 0 0 0;\n", + "0 0 0 0 0 0 1 0 0;\n", + "0 0 0 0 0 0 0 1 0;\n", + "0 0 0 0 0 0 0 0 1];\n", + "b = [100; 100; 100; 100; 0; 100; 100; 0; 100];\n", "\n", + "% solve system of linear equations\n", "u = A \\ b;\n", "\n", "disp(u)" @@ -153,7 +171,576 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This gives us the values for temperature at each of the four points. As a quick check, they all fall between 0 and 100, with the colder points on the second row, near the top boundary where the temperature was fixed at 0." + "This gives us the values for temperature at each of the nine points. In this example, we really only have one unknown temperature: $u_{2,2}$, located in the middle. Does the value given make sense? We can check by rearranging the recursion formula for Laplace's equation:\n", + "\\begin{equation}\n", + "u_{i,j} = \\frac{u_{i+1,j} + u_{i,j+1} + u_{i-1,j} + u_{i,j-1}}{4} \\;,\n", + "\\end{equation}\n", + "which shows that in such problems the value of the middle point should be the average of the four surrounding points. This matches the value of 75 found above.\n", + "\n", + "We can use a contour plot to visualize the results, though we'll need to convert the one-dimensional solution array into a two-dimensional matrix to plot. The Matlab `reshape()` function can help us here: it reshapes an array into a matrix, by specifying the target number of desired columns and rows:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "b array:\n", + " 1\n", + " 2\n", + " 3\n", + " 4\n", + " 5\n", + " 6\n", + " 7\n", + " 8\n", + " 9\n", + " 10\n", + "\n", + "A matrix:\n", + " 1 6\n", + " 2 7\n", + " 3 8\n", + " 4 9\n", + " 5 10\n", + "\n" + ] + } + ], + "source": [ + "% Example of using the reshape function, with a simple array going from 1 to 10\n", + "\n", + "% We want to convert it into a matrix with 5 columns and 2 rows.\n", + "% The expected output is:\n", + "% [1 2 3 4 5; \n", + "% 6 7 8 9 10]\n", + "\n", + "b = (1 : 10)';\n", + "A = reshape(b, [5, 2]);\n", + "disp('b array:')\n", + "disp(b)\n", + "disp('A matrix:')\n", + "disp(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This behavior may be a bit unexpected, because `reshape()` uses a column-major mapping. We can fix this by taking the transpose of the resulting matrix:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "transpose of output matrix:\n", + " 1 2 3 4 5\n", + " 6 7 8 9 10\n", + "\n" + ] + } + ], + "source": [ + "disp('transpose of output matrix:')\n", + "disp(A')" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "% We can use the reshape function to convert the calculated temperatures\n", + "% into a 3x3 matrix:\n", + "\n", + "n = 3; m = 3;\n", + "u_square = reshape(u, [n, m]);\n", + "\n", + "contourf(u_square')\n", + "colorbar" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Overall that looks correct: the boundary conditions are right, and we see that the center is the average of the boundaries.\n", + "\n", + "But, clearly only using nine points (with eight of those being boundary conditions) doesn't give us a very good solution. To make this more accurate, we'll need to use more points, which also means we need to automate the construction of the system of equations." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Row-major mapping\n", + "\n", + "For a two-dimensional elliptic PDE like Laplace's equation, we can generate a general recursion formula, but we need a way to take a grid of points where location is defined by row and column index and map these into a one-dimensional column vector, which has its own index.\n", + "\n", + "The following figure shows a general 2D grid of points, with $n$ number of columns in the $x$ direction (using index $i$) and $m$ number of rows in the $y$ direction (using index $j$):\n", + "
\n", + "
\n", + " \"2D\n", + "
Figure: 2D grid of points with n columns and m columns.
\n", + "
\n", + "
\n", + "\n", + "We want to convert the rows and columns of $u_{i,j}$ points defined by column and row index into a single column array using a different index, $k$ (this choice is arbitrary):\n", + "\\begin{equation}\n", + "\\begin{bmatrix} u_{1,1} \\\\ u_{2,1} \\\\ u_{3,1} \\\\ \\vdots \\\\ u_{n,1} \\\\\n", + "u_{1,2} \\\\ u_{2,2} \\\\ u_{3,2} \\\\ \\vdots \\\\ u_{n, 2} \\\\ u_{1,3} \\\\ \\vdots \\\\\n", + "u_{1,m} \\\\ u_{2,m} \\\\ \\vdots \\\\ u_{n,m}\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "where $k$ refers to the index used in that array.\n", + "\n", + "To do this mapping, we can use this formula:\n", + "\\begin{equation}\n", + "k_{i,j} = (j-1)n + i\n", + "\\end{equation}\n", + "where $k_{i,j}$ refers to the 1D index $k$ mapped from the 2D indices $i$ and $j$.\n", + "\n", + "
\n", + " \"3x3 \n", + "
Figure: Simple 3x3 grid of points
\n", + "
\n", + "\n", + "For example, in this $3\\times 3$ grid, where $n=3$ and $m=3$, consider the point where $i=2$ and $j=2$ (the point right in the center). Using our formula, \n", + "\\begin{equation}\n", + "k_{2,2} = (2-1)3 + 2 = 5\n", + "\\end{equation}\n", + "which matches what we can visually confirm.\n", + "\n", + "Using that mapping, we can also identify the 1D indices associated with the points surrounding location $(i,j)$:\n", + "\\begin{align}\n", + "k_{i-1,j} &= (j-1)n + i - 1 \\\\\n", + "k_{i+1,j} &= (j-1)n + i + 1 \\\\\n", + "k_{i,j-1} &= (j-2)n + i \\\\\n", + "k_{i,j+1} &= j n + i\n", + "\\end{align}\n", + "which we can use to determine the appropriate locations to place values in the coefficient and right-hand side matrices." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example: heat transfer in a square plate (redux)\n", + "\n", + "Let's return to the example of steady-state heat transfer in a square plate—but this time we'll set the solution up more generally so we can vary the step size $h = \\Delta x = \\Delta y$." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": 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SesHjcoU0DDVHxxpGA23qAiSBAZLGACmsAQAu1x8AUDLNAQIDPCajjQNFb9ShKJCTWxBPMN3JLTBo1J5nhdPRPhSrt9ui+N6u3l8mum58FB61f3BQNC8U9QpCUPJ1krqOR7ESAABU1XfhRUjmwaYEKVDEQS1WiXB76hjXi6cbiR1Q1q4mLU/U1ywkeOXMupUniR2QBVx27bxz5ELHUc81nk0kW8CFTy13cgtCXwDT0YqHjrbyAadP6vSrWGQI9YI+oQJS1AXaNYzIGaLd1DWM2E6+3MCSNEIhyHSSNlJqM8QhnSThIX4Rj0IZ90C0xd0pnLx94GqMbvRRIAoUq7fvopPQtxKWsHoDaqVKCo/U83XFeS1rZzxK0FUy16OhF+yy045NCRIABIociLWxoFZGAoAFcUFJn+USgoTarcpSUoneVsgCjoamuC+Krz7dawF3nxyDLOCUK9qkPunGIPWCPk0C7RqGtpP2r9Z4OIFGiXK071/GdE+06lTTEnV1QbKhYwfQ9C+D9KP3NdcfOGyiNgOPhzW2KjD9QkOByOiwert/tJ/YrTMjkxIe1ablTpr7WPO94ryWqW8/+n1ViTsjGFyEBChlZ9zhtoutCRIAVNZ3Te17TXRZJbJ2gwVO8toK8v6jd7ycvfIkIUhsX7596NPSIxt4aw44Ry6UXTuHLOAeE2LFxWuQBVzH1Z9AfeoX0vM+M5+26hJFkTRQUzWNR1FA8kCGLCS9W7j+j+/whOqH8RipQGSktdfr7qWMXtkKmqze5PBIlpL69M755GObc8vCD0cS32ani4HUUxV6C0hM5+tsWlSMwdYEaXqYC6WM5O/rSBEkStaOmElBdLhyXr5UowXcbXIMsoDrfz9Yn0yBphAEC4O1w6ACUdDH6g19kyYITxP05esoZ6M4Ghhsq4rpF1sTJFDL+cZEeW46/VhehZK1A4DgN2bm7kwlBEmbBdwleBphAad3b1ifME8OplMgMqW5u/SxeoOm8Ehjvu7Vx3uqVtZ3zYqwqpQdYzdihdiaIEWEuV7NbiBvUS8jDRY4NefeIhYkwePtVtEWbRZw0aufVHyxqjR3N08wnSecTluZEP3qEzLjYn3CDAjkHVXN0v/JO6pMqkAA0NFWXnsvpaOtou5eigMvYMjq/4AeVm/ypAkEJV8HmpbEMo/KOFHBgjSwoERIAXwOV6mkZO3Co33rcsvIf53Bb8zM3XmQaHWlzQLO8QwYsvo/Xc2VD0t+qC3JKkpa4eQWJHhqGU8Qqbu2pA+69Un668tcJ38ifrJhhxVmQCDvqJLLq5pb/tfR96JXgTyZVyAE0qGW2uvSuusuweEuwdNQ3Qihw+oNAJ3fZj69eiZ5i8Z8HWVJLADk5LclvDuYybehAuPWIdmyItmaIGlcv0b5CwOA8GjfxIS8YSsf/YFyhTxqkKTFAg4AHM8AjmcsLyzWZ/aWhyU/SEuyq3NO2PWweYLpgqeWG69MCHV9AgBp3fVefaq7TjSpxCEUxtQgSwglBcd1DfQQTufACL5glSkUCIF0qO7eSYW9khcW6zFxoyj4EmUf3Vbv7lsF9g1VnuMXkw8pScqK3x5I3mLanqoYPbA1QUJj+igbp451u5BcvvnIOGLLYIGTvE5KztpR2q0iKBZwNCqJfGZCmaBvDthvd/+uuF7NSEKPAmrVJXALIk6rLYQCACxRGCOh5N8AwHQpOHWQCAFAWe5uB14ALyxWsPQwehzUSMPlve6L4tFr8tAjhDwldfjKmZRD5HXSEaFjyVvUC0hgilWxxnZqYO5OrA9bEyQACBRycvLbiCEUgLqsXpGS99GYtfMcP8Q+KYscJGmzgGu8LmoyBLAFJfQqfjlemrsbPUIyktBTR1sIJa29XtPytby9gtWtAOySwOgBkX8DtQBokGdUkGCPKf6A1dGQlPuwtd+jkNUbDT1qPZtoH/o0JTyitFIFgMJd59TzdeoFpMr6LkZH8wEAsABYRoiKbRvGbVGQRNSsnbqvATRm7QS84JUziXarCGQBVzRWo1FJDYmbtQkSARE2IWWSlmSXpe1GT5cMJvTU0TOEwlk+DGgJgARPLQMAMwRAFChJOedhi0Vh1KScDshW77aziUQlGNGZkUmeNIFozi177fF8HWgpIKl/nhgLriFpxwYFKUjIIa+NBU1dVgFgRKhHoKCcnLWDvnarlCCJu+JVYlQSsoDzwpboyB4QEMrkt/ioqRN6GqGEUADQ0VYurbsubytvavtVev+flBAKGyVsFR0BkG/gG08LUtHTjDkh/hT1TMppBDnryFZv7vKlxNAjRGdGpui998lbmnNL1fN12gpIzK+KxWjHBgUpUOSgsYxEESQAGBHqcTMtjyxIve1WHw+SHMaOeZCS2rtOds2B1rOJtdd3K8/UuQRP01OZwBIJPY04uQUJSB891BDqcaMEAOAoasCB3Aco+gGS/ACApQIgMuSkHNKhp/5WiFr+6A96vGu4vNfO2885ciFvUTz0Wb15y3eR90StVCmH12ry1xXntVDbcvQWkBiPkFgso3rZ2XLSzhYFSci58r2cspHSZRURHu2bseY3ykZKu1UAYPvynZcvlR7eiJY4uC+Kh0Xxisbqh9fO01MmjQk9przjBqEthAKAptrrvUWpX1+mDMjhDrRpBTYJCnqI6SFS6Y+9s6/cggAAPeuApeWHgJKUc/Cagoa6GgRFh9CSDOKn6lZvUGulimjOLXv7yHDKxuK8lldj+ZSNlfVds4ZzDb3PflABXhirDUsKkkKhuHDhwt27dz09PefPn+/vT/10k8vlX331VWlpqUAgePnllz08PDSeh0KgiFMlbqFs1FhGoozsQ/QGSR8cJC/zdpwT1fltJrKAoy3Id8eIMvnM3tItrXhYkt1g3oSeRogQinwDhF0CAKS112UKSYf4a3l7RUdbOSFO0GftAwuNDbVJiMbqKNvWQRIhJDxo3Q8ABI3aAwBmfqDRDYq/pXXXjEnKAcDDkh8elmRr0yGEutUbAGQpqZRWqgBQk5bnAnJye2+EpK6D7IRCVIk7ARgWJBYAy4gaki3HR5YVpHXr1t24cSMqKurnn39OSkr66quvhg59JAwymeyll17q7OycPHnymTNnUlJS0tPT3d3d+z0tZUwfQr3LKkI9aweagiQgWcAp27Upk0tweL/2BwTHM4DjGeASPE09oScYvpwnmG7+/D4Fwi4BmoQKJf1QXYosVABAeNABZ/90op5nAwDCa8B1DXRyC3JyC0QrfrhugRb/k9ABI0k50E+HCNSt3oDCo6RllI3S3NIFcUGUjdnp4qljXNUXLFbWd01nttW3aThz5kxqauqDBw+ee+65bdu2oWf3rKysjz/+uKGh4Zlnntm2bZufn9Z/PevBYoJ0586dq1evHj16dMaMGV1dXfPmzfvss8/27NlD7HDu3DmxWHzlypXBgwe3tbXNmTMnJSXlrbfeon1FjWUkjVk79Xar8LgFXOP5ycrUeecnybUTDZf3GqRMoJbQqy3JKjq9Ajn0eMLpTq5BVvUIjD4WUdKP8iOiOgU4+0dCzzybb+AbTq5B1pBq0xNi2RBKyrkET+M8QycpB2o6JPqytN9D1K3e0NdKlRIeAUBzbtmI16n5OgDw93VU32iS0XxM15D++9//Hjx48MMPP+Tz+R988MHf/va3I0eOVFRUxMfHb926dcKECYcOHYqPjz9//rxRt20WLCZI+fn5XC43MjISADgczowZM7Kzs8k7lJSUDB8+fPDgwQDg5ub27LPPFhQU6HNmtDaWPKYPobGMpDFrB2rtVhFkC7iOG7Dz9nOO9HOOXMiIMqGEXldzZW1J1sP8H+x62Oa3QtCAqE6BIdk/Yjdi7gMx7sFJbYaF+j4mVTXKVCd4fLATsVvH4xOeKPtYf55NT4h0HBEJoSifXlIOFYfQf/XXIYRGqzdoaqUKADVpeYEClXq+TuOSWFNhrO2buuGHH36YOXPm9OnTAeCtt95asmRJT0/P1atXQ0JCYmJiAGDDhg2zZs2qra0VCoX0r2sWLCZIzc3NPj4+bDYbfevr69vc3Ezegc/nf/vttzKZzNnZWaFQ/P777xyOhkeVmga4WdhbIgwb3Xu2iDAX8pg+hMYyEgCER/t+9WkWRZBQu1X1IIm74tXGnUucIxe6RC7ULUvApDIFuAQD0Q8CWSEa7l59mJZttcGTNrRl/6BPqxDytt6ZVSjGAgB5WzkAdLRVyBSS3h+Jv+79UXsF+XB9hA3to7+QEHfeezbXQPIWpC6IQW7/DwD4rqSd3QIphw9QiDCInI4zdM0QhYbLex/ToY366hAAoCS57Np5103vqlu91VupAoA0t/QPav460NJTNSe/jTyar6ZBVdugAoCaBvA3Yogxi1aERFy9tgH8H2+t5+LiUl5ejl5LJBKVSlVfXy+RSEQiEdooFApZLJZEIsGCpBWl8jGjCZvNVigU5C0LFiw4duzYn/70p+jo6O+++66+vp749yVz844S/Z7CRrMIQdKIjjKSS3qF+v4agyTHOVEOY8d0ZGQ2f/K244hwoluJbjQq05DV/6GRWKc0KwIAlNlruXYKWfXQnHVDT2sNkG+b9NpglVUXNkLVoE/Ymtp+hSdGSIyEbJBzCZ7G8QzQ2E3OULqaK2u+WNXRWm6oDiFazyY+/OGM45woly1/oSTrQFMrVURNWt6I1ydRNhbntagviQW10XxHvlD0ClKjyn+UofdrLLUNqiNf9ABATYPKf+RjP3r++edXrFjxySefBAcHf/jhhwAgl8t7enrs7Xs/3u3s7FgsVk9Pj7lv2nAsJkiOjo4ymYz4tr293cnpsThaKBSePXv2+PHjWVlZEydODAkJKS4uVj/PgufZa16lvovpYS45Be3qnhmNZSSUtSvcdY6ynFt9JgUCucCVc+plKamtZxP11CQEoUytZxPLjs5FGTn9D6eA9Iyc2ZPe/LwubSZyQ1jKp2dxNAnbAIgdrQ3Cm9DeUcYLi/Wau0n/sL5fHpb8UHY0mrfmgIeaS0gfJDtjlA5y9TQdojMj082+TT08up+UFR7tq56v07YklrIIac9bvZ8zSBjoowKW4bbviSPZE3dxAOCw2tWnTJmyY8eOU6dOAcCyZcsSEhJ4PJ69vX1nZyfaobu7W6lUOjgwvaDKBOgKKUyKv79/Y2OjRNKbfrl79y7F9n3//v3c3Nz333//5MmT69aty8/PDwkJ0fPkEWGuOflt6tunjnFFI4opLIgLas4tU98e/MZMeUqqxksgWepxbhKvjVA0Uqdl94v7oniv91Kbfv13w+W9hh6rEZTB91t8NOCtNOeIxRVVx3NOBxddW1F3T/P/tBiMNqS110tzd+WcDq4uPeHwzJThWwt9Zm9hUI0aLu+tPPfm4J2fq3tW+0XRWC1eG8EOC3H/x35t+3R+mymcN159e8mnWer+OgAozmuJifJU326KRna9qFj0v9Tvs7Ly6aefTktLS0tLCw4OdnV15fF4fD6/rKz3Mw0l9Ph86iorK8RigjRlyhRnZ+fdu3fX1NSkpaVduXIlKioKALZu3Yqk3tPT84MPPkhKSmpqakpNTS0oKFiwYIGeJ9fo/AaAqWPdUNaOsp2Ya07ZzhXy3Ozbum9pNlMgTXLZ8pfGnUtazybqeW8Edt5+3js/lw+S/bZnNEq+MQLHM4AXFjtk9X8C3kpjPzuJUCZp7XWmLoGxSTrayktzd2Ul2d3O+dNDr+7RH7YiKWLwEl3NlWVH5z6ovup7+HvU7McgZNfONyQsctnyF+flS7XtgyZNqHdnQNOPNNoZNK5AAoCc/LYB4fmWyWTLly///fffOzo6kpKSZsyYwWazJ0+eXFZWdunSJblcfuzYsaFDh/r4+Fj6TvvHYik7Dw+P/fv3b9u2Df3zRUdHx8bGAsDFixdlMllsbKynp+emTZuOHz/+j3/8w83NbceOHWPGUDPFOlDvHoSYOtYtO11MydoBQNz2EdvXZFH+jjXOpKDgMG6Me+KeB+9sBNTEwRB6neIAZUfnohHpBh2uG7KDnGijZ5F+EBhrhtJDgd6aIX1AaTq3RfGDDfzfBCE9sqGjOHvQR/sp/gUKGidNgKbpRwgdM5BM4vlGpgZjFsaqBUkjRoyIiYlZsmSJXC4fOXLkgQMHACAkJGT9+vWbN29WqVSenp6JiQY/ZNUesAAAIABJREFUMVsESy6MjYqKmjVrlkQicXNzIwpIt2/fJnaIiYmJiYlpamry9PRksQz4FQaKOBFhLpQhFIjFs72Ob7yvfggRJFE0SX0mhTpsX/6gj/Z3ZGSK10Z47/y8X/cdBfdF8S6RC8X/t9mtZDqzD6QIchu9ll9OlaXNGOj2B4zxUHQo4K00E+kQouHy3qZf/z145+c0AiNFY7X08Abwd9dWNCLQOGkCAGrS8saHOqo/hgJAcV7L/+3XMLM8J7/NZPk6ozo1aGwdtHnz5s2bN1M2rl69evXq1fQvZAkslrJDsFgsb29vip2BgpeXl0FqpBvCa6f+owVxQSVJWZSNaCaFtkoSAUrfceZG0k7fDfrLPvkgWdnRuYYeqz9ImZ76W6Fg6WEpqyQ3bWbepRm4yPREgfJyeZdm/Pzt8w+9ur3mbkJ5OdOpkZFpus6iG+K1EY5xC8mtvLTurGnSBACUJGWpd1MFgOx0sUZ/HZi0R4PK6C/bxQabqyK0Ge1Ae9ZO40AKAPAcP0Rx7AfdQRLCeflSpzlRtNN3LpELHwL8tmc0PUe4nhCdishtiizbQA9jBqS118lt5YbPNta3rQ9IjZxmvUgvTYe83e4f7e/3fz0AUIrr1SdNQN9iWG3hkc583QCwpdkYFo6QTIc2ox0ALJ7tpTFCAoAFcUGFu6gNNrgC3sg3p3VmZOpzXZS+o+e+QyUlr/dSq86vZMp9pwNsf3gSMINVQRvSm6dKPv1/g+L3GfpwBgCKxmrJzpiu1iLe5yn6qBEAyFJSg9/QUD2qTcvVaK4DgOK8lo2vCTT+yLQWO6URX3j8xEBEm9EOtK+QBZ1BUvexk0pxve6CKgKl7wCgcecS90XxhnpbUfpOengDXAbzfHBotD+ghp4DqAcEBkEMvjO+vakxVJ9ZLZfdRxNbDKWz6IZk5xLu8qU63HQajsrIFKlNmqhJy/NRSUeEarYzaMvXAUBOflvCu4M1/shIWJqMCQYdbsPYrCCBdqMdaM/agZZOQr0zKVJS9UlkI1D67uHe/+tprKaRvuOtPfDw2nlTp+8oUKYIPizJbq063tVcadfDBoCB1aPoCQG1paB09EEpWedhi72DD5tZh6CvBQM7dPzgRQk0DjcoTUeABvGpt1KtTct9SVP1CHTm68BkFjuAvgjJmMNtF5sVJB1GO9DutQOAEaEePunFGtqtappJoRu2L99ly186MjIlO2N4aw8Y5L5D6TvHUc+VJRrb0IEG5AZFANDVXEk0eO2uqqD00LPyaQg2BtHVtKOtQlp3vaOt3IEXwGBHH2NAEXbTr//mrd1P202nowWDDrQM4itl19aFR2u+E23+OjCpxQ6jE5sVJERlfddUTdt1ZO0GC5x0BUmPD+7rF5S+k0Fq484lNBzhjiMneb2X2no2UbpntEHT/5hFvcEr9PXQ666qeFiSTczswSEU46in4ACAFxYLXkLBTDqttU0BMcvVceRzNP7OgZSmczUkTYfQOIgPAEo+zXpJS/VId77OtGOQVMZFOdhlN0CZHuZCL2s3ItSDnXyLkSAJgdJ3zXsN6MdKYOftx1tzgDz9jxcW6zEh1vypGAJyDz20BaX4AABJlOJ6NeAUHy2IAAjUUnAWD4DUQTokvXlKaa80aGYEBXppOgJ5SqrG8Kg5tyz8cKTGQ3Tn63IK2kOGmcxip2KB0gg3GU7ZDVAiwlx3/qMBtLhodGTtBgucFsQF/Vdtkiwa3CdLSTWo1opA6TtZSqqOEX86IE//az2bKD06l+MZ4DEhlsEOY8aAUnwAj0IojSk+AMASRYEyWAgAkA0BAKxQgQikN089LMluq7juHLnQ671UGiERge5Oqf3SmZGppXqUF7d9hLajdOTrEKZM2RnplMOCNDDRYbQDnVk7ABgR6nEq+Tf1ICnskze+f+GADICeJjkvX0q7oQOCCJjIA5YslcrThrYUH3JJPOEpPvWpQoQHwcNzo1X9HtUhUnO9Y8U30jHRESgaqxt3LuHMjaSRpkPIUlLhcvpotfBIXietScsL3xap8Sjd+TowpcUOoxtbFiTQabQDnVm7wQKnOdGDbqoFSQAQdiyu5lJe2ZLl/bbVUgdpksPYMQaNU1KHPGDp4bXzlefeZPewze990BONKT5yCIVSfOSpd05ugQDARa9dg8DqpxMhtxt5/JK8byxTR1tF70/bK6zKg6A/lNSc7+HvjQmJELJr5x989aHrlnfppemU4vr2Dw76+NurqxEAlCRpbuyN0J2vA5Na7ID5ibG2hC0Lkm6jHejM2gFAeLRvxprf5HVSSjaAK+ANWzkTAMre2eg4J4pGqOQwbozdFj69hg4UUCrPJXJh552f2otuWNb7oD8aQ6huaQXx+qG0squ5UtpeAgDdVRWkfSqhT5aoY1vdArnE6z4NoydgxIg/QmDI6kLsgAQGbUdeAyS9DrxAAOB49Rb5HIZN8vB8BQA8AKz896IO2a3gGvMWjYERGtGzU6o2um8VtL6zcfSOl9W7eiNq0vLe/lqrzU93vs7kFjstUyQMONx2sWVBQmgz2kF/WbvBAqfxoY4lSVkau2MNWzlTND/05pvJtNN3xvRjpUAJmKzE+6A/fSFUAAC4BPe/v7qAAcBDaaW0OYvYDr1x2CMBA01BGDl8gT6lQeoCZIFh9b0eNgkAkMB4I+EZCP/ChsKUW0Ed/TulagOl6cI+iVPPXiAKd53TOGkCkZ0u5iqVOvJ1prXYIWxaVIzBxgVJt9EOdGbtAGBBXND2Nb9pO5Yr4BmfvgOAxp1LnCMXGhkqIazc+8AU9AQMAFCeEL1+KK2Ex8MXB16gTaqLQTDoVlAHebtpu+lQms7Nvi1MU5qOoN/wSFu7IIRpLXYYndi4IOk22kF/WTsUJKlPNycwPn1nTD9WHQwI74PZIGQG5Qkx6jDrVtCIkd5ulKYLfmPmsJXU6RJktM0pJyjOa5m6WJe/DkxrscOdGnRh44Kk22gH/WXtoL8gCWFV6TsyA8v7gDE/pnArqGOGNB1BbVre6iPDtf00O1083NteR74OzGCxwwtjtWPjggT9Ge2gv6ydtsF9FBhM39Hox9ovA9T7gDEd5JDIPYb5PzkCep1SCfRM0yHQID7d4ZFufx2Y2mKH5vMZIUgqYG46nPVh44LUr9EO+svagZbp5uqQ03fOy5c6zoky9G6N6ceqDwPd+4AxHtO5FTRinjQdgbY55QT95utwFzvLYuOChNBhtAM9snZ6BkkIlL7L3XFJJq6n3dDBFOk7MureB5fgaS7B4TbmfcCQIbsVBsXvo9H81CCM6ZSK0D9Nh9AxiA+hT77ODBY7lQpURqTdVCpbbtVgswP6CPo12kFf1k7HDhqnm2uDK+CN3zVfyKlrfXujUlyv7432QZ6G3ll0w9DDDQJ5H7zeS2VNHCe5feK3PaMbLu9FXekwtkFXc2XD5b2Ff3UXX92jGDLY9/D37oviTa1GaO44OyzE/R/7aRyuFNe3vr2RW5gTcXGDnmoE/S2GBf3ydTkF7aYeFKsCUKrof9l0CekJiJD6NdqBHlk7bYP7tNGXvssqe2ej60Y6a9FR+q5170HHO/QbOugJJZXXdO5Ndg8bxUyoq41Jr45hHNTrtltaaWq3gkbMnKZD9BsegX7+OjC1xQ5ABSqlEbJi25Jk+4LUr9EO9MjaAcCCuKDEXecj9KisEvSl7453508wph+reG2EKZwO6hDeh57GakVDjbToiuyL80SrG5fgcCxO1glqxfSwJBs1DLTz9rP3FnFGTTJDao5M69lE2bXzbKGn2dJ0BLVpuSt1hkf65OsAd7GzNLYvSIEiTr8pO+jPaweGB0kIlL4rScpqeHsjjfQF25fvuundzozM9m//3Xo20TlyoUvkQlM/6tp5+9l5+8FIcI5cSCxmai+68eD61c6jPyF9wsGTxUH2BOjrWovWD7FDx4v20pmQYgwosG47m8j25TvOpbMaDwx001FAg/g0zikn0CdfB6a32EFvhKQ05nAGb8basH1BAoB+jXagR9YOtEw37xeugBe8cqYTXUc4ADjOiXKcE6UU1yOzg+PI55wjXzZDwIQgEnoAoGisJoKnzqs/sXvYHM8AB14gdpCbAfUwyHHUc3beftzX1niMNLcIIWTXzncW3egoznacE8X7PIVeYzoAUIrrH7yzccj80Qal6Qh0DOIj0Cdfl5PfFmHqpkFYkHRiSUFSKBQXLly4e/eup6fn/Pnz/f39KTt0dXVduHChuLjYy8tr3rx5gYG6noB0o9toB/pl7bRNN+8XVFISzQ/N3bFXOYZO+g76zA5Oc6K68wvMGTCRIQdPAICCp86iG7XXd+PgyRQQYZD05qluaSUKgzhz/ugRaRkFQjwWEs2J4v2dZoIOgdJ043cuNPR/K4TuQXwIPfN1lfVdQab3fGNB0oElBWndunU3btyIior6+eefk5KSvvrqq6FDH/uLjIuLu3v3blRU1H/+859jx46dP38+JCSExoX0MdqBHlk7NN381K7zYcfi1AeC9QuRvmumNeIPwfblO/paMmAiQwmeAKDzzk/SoiuK29XKM3UoeMJucoPQFgaZuRqkDaZCIoLWtzfSS9Mh5HXSkk+zNh8Zp3s3PfN1A7eL3X//+9+jR49KJJJRo0Zt27YNPbtnZWV9/PHHDQ0NzzzzzLZt2/z8zPfkShuLCdKdO3euXr169OjRGTNmdHV1zZs377PPPtuzZw+xQ1VV1U8//fTJJ588//zzcrl82rRp//nPf+Lj6fjN9DHagd5ZO0ldR8abycJ5oWgZrEEYn74jsIaAiQy6LlmfOu/81NNYLbl9ouaL1Th40gERBqG+CciPYMFEnDrMhkQII9N0ANCcW3pzVfLmI+N0m+sAIDtd/H+LR+tzTjOsimU8QqqsrHz33Xf37NkzcuTIjz76aNOmTWfOnKmoqIiPj9+6deuECRMOHToUHx9//vx5427cHFhMkPLz87lcbmRkJABwOJwZM2ZkZ2eTdxg0aJCdnV1HRwcAdHd3d3d3Dx5M0/2ij9EO9MvaAcCCuKDw6I59a3LuA9DTpGErZ3qOH1J0gH76joASMDXuXOI46jnHkZMsEjCRQcETAMCieOjTJyJ4AoAnWZ8IWzbZjwAAg3d+bg1hEBm0dJrBkAjRmZGpOHmcdpoOAO4nZT1Iy9FTjRbP9uo3XwfmstipQKUAhTGHU7Y8fPhQqVTOmTPH2dl5woQJ33zzDQBcvXo1JCQkJiYGADZs2DBr1qza2lqhUGjMnZsBiwlSc3Ozj48Pm927MtfX17e5uZm8g7u7+6ZNm/76179+/fXXt2/fHjVq1IIFC9TPc+E75YXvugBA5M36V4LmcFtPox0ALJ7tdTi5vN8MwGCB0+Yj47LTS75fVRr2yRv6nJmC5/ih43fxCnedk6XQ6ceqjsaAydQLmPRH3RnReecnye0TnUWPVZ5scgAEMb0JzWey2jCIQmfRDenhjSq7bqZCIoL2Dw66SO7TTtMBwM1Vn470lW/XPmOCTHFey6tjXPXZU7fFbuuhnpt3lABQ26Bat07PO9UAvQjp198Ve/7dBQDiZurVR4wYMXXq1BUrVjzzzDMXL17csmULAEgkEpFIhHYQCoUsFksikWBB0opS+divhM1mKxSPPTW0traePXuWx+OJRCK5XF5YWPjjjz9GRVEbxIWNYq951Q4ARD66GmroY7QDgKlj3Xad0qu3wmCB04K4IEguv6l9OIVuuALe6B0vM6hJ8HjA1P7BQdna86brP0Qb5IxwHDmJHDxJrp0AgJ7GGkVjtfr0VZfgcPIWqxItit5AXx0ISBMC0a8AiZA516jSA3X96W4upz1fXAedGZkukvv0HuMQSI3ito/Qc38983WnLzct+6OuwvCaV+0A7ADgm+/oxze08fVkH4p3AoD//tRD+VFbW1tbW1t1dbWDg8PDhw/r6uoAoKenx96+9+Pdzs6OxWL19FAPtEIsJkiOjo4ymYz4tr293cnpsR69165dq6yszMzM5PP5APCXv/zl008/VRckkU8/UoSYHuaSU9DeryChrN2F5HLdPUgIwqN9IV18OymLRu4OTKNJCLSAqSMjs/mTtx1HmLzXgzGQgycE8kcgfzl6Ia2/AgCK29VIsYA0Mtyhb2yrAy/AFIqlQ28elmQDSWzsfPx6lWbQYM7EcXY+IjdvPyvXHgqoVvTwhzOOc6J4y3cxfv7uWwWKk8eNiY3uJ2X5qKRx2/vJYRDon6/rN4miz+eMPqhApWQZHCHx+1KJ6im7zMxMsVj87bffuru7f/fdd6tXr46JibG3t+/s7EQ7dHd3K5VKB4cB4NewmCD5+/s3NjZKJBJUGbp79y7F9o0En8frfWYZOXJkbm4u7cvp6WsAgI2vCV7/qEpPQUK+u+KE3PtJdOpJ0KdJuTsudd8aw+zTKEriKef0mvGsKoOnG/Qhjvzl2qCIVnvRDai/p7iNNj4WZpEVi9iCFEtdbAAAtfJTD24IvbEfNo7rEw0Abt7vDyy90U3r2cS2s4nc5Utp91nQTfetgu4Dew3qdUKhJi3PITe334w6mQvJ5Z+9Q11PopGc/LY/v9JPOYoRGG8ddP/+/cDAQHd3dwAIDw9XqVTl5eV8Pj8rq7f9Znl5OQCgJ3srx2KCNGXKFGdn5927d2/atOnXX3+9cuXK5s2bAWDr1q0jR46MjY2dMGFCYmLiwYMHly9fLpFITp8+PXnyZNqX09PXAABTx7rpY20gGCxwits+IjGhqCaNp087cHWQHTx3x3GAFYxnSIjaEsrg8dbut7ayOT0ooqVu4qAolryxul0tzEJnsPcWAQChN5w5fxyIwY0xoHIRavnDlG2BAlKj0Tvoe22ac0vFSWkf6lc3QmSni7lKZb95EUROQfuJAyK6d2cASpZKYXiERD6csmXEiBEpKSk//fTTxIkTU1NTnZycgoODXVxc9uzZc+nSpVmzZh07dmzo0KE+Pj7G3bg5sJggeXh47N+/f9u2bTNmzGCz2dHR0bGxsQBw8eJFmUwWGxs7ceLELVu2HDp06MSJEwAwffr0rVu30r5coIgzJMBBnzIS6G1tIBgscIrfHpiYkMMVeNBzDSFNyl550EgvuDbYvnz3f+zvzMhs/uRtpxHh7ovibf7TVp8wC0OY6ExRLiJQiutb39lIo0MdAeHwNuio4ryWjXokRQAgJ78NAEzdNMhEzJ8//5dffvnzn/9sZ2fn7Oy8b98+Nzc3Nze39evXb968WaVSeXp6JiYmWvo29cKSC2OjoqJmzZolkUjc3NyIAtLt27eJHf70pz8tW7ZMIpG4uro6Ozsbf0V9ykhgiLWBAGnS9jU018wCAFfAG/nmtKJ3NppIkwDAcU6Uw9gxyB0+gDJ4GBPxKEfHqImOAvLXGKNG8jqpnuuNKOi//Kiyvku3o4FBVADGpeyosNnshISEhIQEyvbVq1evXr2a9oUsgoXnIbFYLG9vb4qdgQybzfbx8WFEjZb9kYeeg/qFsDYYdP7BAqfYOP7NN5Pp3BwAAIjmhY58c9qDdzbSPkO/oAyee+KeHucm8dqI1rMD47kJwyyya+drXhna49zkdfVbZt006rR/cHDc6om01QgACnedo6dGetoZACCnoN0MXewQKlApjPiy7dZBtj+gj2B6mIueZSQA2PiaQPfIPo2ER/vOiR70/QsHDD2QQDQvdMj80a1vm1CTgCRLHfe+E6+NMPUYQIz1oGisluyMefDVh+4f7Te1FAFA69sbAyZ6G6NGN1d9+tJcR0PVCAAuJJfHRHnquXNOfpupB8USKAEULBXtL/rVp4HAEyRIaHmsodYGQ6+yIC5oTvSgwl3nDL/BXoatnBkw0bv9g4O0z6AnqLDEXfFq8ydvt55NJOr8GJsElYsaEhaxw0J4n6eYrmJE0Pr2Rh9/e3ruUwRachQe7Wvogaibqp52BjDL1AmMPjxBggQAEWEuVeJOPXdePNvL0KwdIjzad4iq9r7eI8/VEc0P9QtQylJSaZ9BfxznRA36aH+Pc1PjziU4g2ertJ5NFK+N6HFu4n2eYobACADQcCN6a8YRfUuO9F0AS0bPbqqIfpfEMgwLlEZ8ATOroayUJ0uQ0PJYPXeeOtZNUtchqesw9CqoiYNDbi5tTeIKeKL5odzCHPNoEpHB62otEq+NkF0bAE0YMXrSWXRDvDai4953ZpMiYKIdQ3NuqaFLjshkp4tj9BaknIL2QJH5Fo0qjashGWOIsH6eLEGKCHPV09cAAAF8zqxnXGhUkqBvcVJXblFzbimNw6FvwazZNAn6mju4J+558NWHyO+Aa0sDF5SgE6+NaP7kbZctf3H/h6msm+r0tmMwTo3KdqUao0b6h0cAkJPfZoYm3wRKAAWL/heuIdkO+i+PRcREedITJOgzgouT0o3UJHbBL50ZmfTOQAO2L3/QR/u5K17tai2S7FwiXhshPbIBK9NAobPoRuvZxJpXhjYkLOpxbuLMjTRPuYjA+HYMaMkRvUwdwiA7AwBU1XeZzdGA0c0TMcKcwKDlsWB41wYKjCxOGr9r/s03k6Upqa4bTbh0kQzRodV107toqsWDr/cpDzfbe4ucI1+28xHZRq8HmwE1oOu6c6Oz6Cc0r8j9o/3mFCEEWm9k31AVdiyO9kloLzkiMNTOcPpyU6CQY05HgwqMGD6haR2SLfFkCRLo3WWVwNCuDRTQ4qRTbybTfmbkCnhhx+JqLuWJ/328O3+C05wos+VeoK+8BMtBKa7vzi+Q3brceSQTjTF1jlyIlcmCdBbd6Lzzk+zaeTQhgh0W4vUx8+1Q9QE9tcDl9IB5obSn7SHoLTkik50uXmtIvg4AzBweqZA3wYjDbZgnTpD077KKQF0baAdJQAyZfeGAMZo0bOVM0XxpzaW8snc2Os6JMlt1mkBb2ITmAeKwyTyoB0MuW/5i/mCIjCwlVZ6SGvzGzGFGpOkQtJcckSnOa4nZZ8Cyp5yC9lkRZhUkJbAULPqqYts1pCdOkAwtIyFrgzGCBAAL4oIA6E9OQvTJUmjNpbyyJcstIksIHDaZGaRDKBhyGDvGgsEQGSRFonmhwRc30MtIk+lbchRozEkuJJcbZGcAc02JxejJEydIaHms/mUkANj4mmD2xvt6DqTQRni0ryS5/D7dyUkEhCwV7jonXZJptsKSRoiwCUkjJWxyHPWczbdwNR1WGAwRKMX1D97Z6MjqMqZDHRlDpxxpIztdrOewCQLzL4lVASiMWExk262DnjhBAgBDm1ah1nZGBklocVKyEZOTyHAFvLBP3qhJyys5sLdzzATn5UvNWVhSB12dEjZJj2zAYZOhWGcwREA4F0a+OZPesBV1jFxyRGConQHMvyQWAACULONSdkYca/08iYJkqK8BjLY2IIjJSc25Qxh5rhTNC/UcP4QoLJnZ76ANctikENd35xfgsEk3SIQUjdWya+etLRgiYNC5QAYtOTJoypE2aNgZzF9AAgAVsBQs+uttcIRka0SEua7YXK3noBSE8dYGBGEEH71jISOa9FhhyUJ+B22wfflsX77DuDHqYZNz5EKkT5a+R0tCDobs+Hz7cWO8rn5r6ZvSDIPOBTKEyZuRsxlqZwCAnPy212MGMXJ1DCM8iYIUJDS4TQjRtcFIQQKAwQKnhCPDjVmcpI71+B20oR42dZDCJvV5r7YKEiEAaDubaLXBEJnOjExZSqqHyDmMCecCGXmd9PsXDhhp8iZITig21M4AFloSqwToMaKGhF12toahy2MRyNrAyA0YvzhJI1bld9CGjrDJ3ltk5+MHAChysvMREa8HFuTp6T2N1WiLoqEaALqby608GCIgykXjdzITzVMwfskRmeK8lv/bP8ygQ05fbjLbDCQySpZRKTtcQ7JBaJSRGLE2EKDFSd+v+tSYll8asTa/gw4oJr3u/AIAUIjrZSWXAUCZU6+or1eK66FvHrlGxbL39jNzUUqH3vQ01igaq9E/uB2fj9QXACCQ6/jCQgBwtb5HBHWU4npZSiq74JfhK2eK5jFWLiJzc9WnEc+qmFIjZGfQcxYfQVV9V5AZW9gRqIClMKJnm8qm230/oYJk6PJYBCPWBoIFcUGQbOziJG1Q/A7WlsGjgD61HX2jNP4UaZJCXA8Ayvp6UyuWDr3pLPqJuFuy3tg9F2TPfw4AnAkFGpgQzgW/eaHD3mMyfCeDlhwtiKPfrY4CDTsDAFTWd5nf0YDRzRMqSIYuj0VMHev21ocVTAVJwNziJI1Yf2FJT9BHvO4PekK0lPX1ACC71atYAIBEi6JYdt5+9t5+ZL1BwQ30ozdrBrTe6MZEzgUKTC05IkPDzgCWWxKrNM5lp8QRku0RKOKw7cDQMlIAn7N4thcj1gYEs4uTNELIUklSVt1AliXdUETLcQ412KIoVtetgq7WIrLeOAJYYcnNPHTfKmjff9AUzgUKTC05IkPPzlBZ32WpKbEq42pIKlxDskkCRQ6V9V1TDTxq42uC1w9WZqeLaYxV1gjji5M0giZZBNdJrdnvYFL6VawnE1M7F8gwuOSIoDivpeKX5gv/Hm3ogTn5beZfEotQAqvHiBqSbUdIT9Y8JDLTw1zOXG4y9KgAPuezdwNyL9UW57UwdSdocVLhrvO0JyfpCfI7jHxzWveBve0fHERBA+bJBElRx7vrAyZ6R1zcYGo1QkuOjJlypE5xXsu+Nbc+/iud9nc5Be0WsdhhdGPJCEmhUFy4cOHu3buenp7z58/393+sCVVxcfH//vc/8pZBgwa99NJLTF09Isz1xHk6ooI0afbG4s1Hxg0WODFyM6ZYnKSNgeV3wDAOci70lotM5lwgw+ySI4SkriM5ofibAyEGZd0JLNhTFdeQdGBJQVq3bt2NGzeioqJ+/vnnpKSkr776aujQR49pVVVVGRkZxLclJSW+vr4MClKQ0KHKcF8DIoDP2RHL37XmFoP5BxMtTtKIzfgdMIbyyLlhxgBIAAAgAElEQVRw832zXZTZJUeI5ITiz97xp6dGYImeqgSMp+y+/vrr1NRU8pbExEQ/P7+srKyPP/64oaHhmWee2bZtm5/fAGjZZTFBunPnztWrV48ePTpjxoyurq558+Z99tlne/bsIXaIioqKiooidl6+fPnu3bsZvIFAEScizMVQXwNBzGyvqvqu5IRiBrMQplucpBGK38F5+VJcWbFhzOZcoMDskiPEvjW3XhjFpa1GFumpSqBisRUsO2MOp2x57rnnvL290euMjIyff/7Zw8OjoqIiPj5+69atEyZMOHToUHx8/Pnz5+nftLmwWA0pPz+fy+VGRkYCAIfDmTFjRn5+vsY95XL5unXrVq1a9eyzzzJ7D2h5LO3DF8/28uvuvpBcztwdwYK4oIhnVYW7zjF4Tt0gv0N40jLFyePSJcu7bxWY7dIY86AU17e+vbH7wN7xO+eHffKGmdVopK/cyNEtFC4kl3v19BjUi5IC7dSIdSIUCsPDw8PDw93c3K5evfqvf/3L1dX16tWrISEhMTExISEhGzZsKCwsrK2ttfSd9o/FBKm5udnHx4fN7r0BX1/f5uZmjXsmJSUBwLJlyzT+9Gahauuhnq2Heo580WPoPUSEuebktxl6FEEAn7PxNUHjz5LsdDHtk6gTHu3rVlt6PymLwXP2CxqUPmT+6O4De2Upqf0fgBkIKMX1nRmZZnMuUOhbcsSwkSH3Uu03Hz5lzEly8ttoOBoufKdAHzUXvjOqn5wSWApgG/pVerf7wqetFz5tvfWDXNuZ9+3bt3jxYqFQCAASiUQkEqHtQqGQxWJJJBJjbts8WCxlp1Q+9ktls9kKhUJ9t5aWls8++2zr1q0cjtaEb9hoFgCIvA2u9dFbHksmgM85tCFo9sb7I0I9GDQ4xG0fsW9NTo2Qx9TIGX0gF5bE767v8fF3nBP1pLnDbYbHnAumr0qq05xb+iAth1mTt6SuY9+aW98cCDHyPDkF7ScOiGgciD5qjHyOVwKrx/CUnasPx+9pFWhvHZSTk3P37t1jx46hb3t6euztez/e7ezsWCxWT4/Bj+zmx2KC5OjoKJPJiG/b29udnDR8oKenp6tUqj/84Q/azhM2mrXgeZoJWXpdVimYyOCw+ci47WuyPMcPMWeCBR7JkrTmUp701FHpfpnjnCiHsWOwMg0IkA51ZmQ6srqE80JF5i0XETA7V4LAGFsdASog0XA0EJ8ztQ0W+GQfNNj+mWn2APCgUfPVL126NG3aNHd3d/Stvb19Z2cnet3d3a1UKh0cDJ5yYH4sJkj+/v6NjY0SiWTw4MEAcPfuXYrtG5Genh4eHk78KzPO9DCX/f+u+8a4P/GY2V45Be0XkssZzJWb03SnDpIlgJnyOmnNpbySd1LRrARsxrNOkA713Cqwb6gSzgv13DnfzNk5Cqaw1aHSkZFqBBYaykdGBWwFGGFq0BSfKRSKK1eu/P3vfye28Pn8rKzetH95eTnaQvuiZsNiNaQpU6Y4Ozvv3r27pqYmLS3typUryFO3devWU6dOoX1UKtXdu3fHjDHhs/myP/KMzNohNr4mqPilmcHVsgAQHu07J3qQOQ0O6iBliri4YeSb0zybiqRLlrd/cLAzI9OCt4Qh032roP2Dg9Ily7mFOcMXPBVxccOwlTMtq0amsNUxUjpC5OS3mX8GEhkli9XDYtP+0jh+oqqqqq2tbezYscSWyZMnl5WVXbp0SS6XHzt2bOjQoT4+PmZ8lzSxWITk4eGxf//+bdu2zZgxg81mR0dHx8bGAsDFixdlMhl6XVdXJ5PJhg0zbMyJQTCStQPSallmk+bh0b7FCcUm6r6qP1wBTzSPJ5oXGlwnbc4tq037SpqS6jB2DC4yWQqiRMQV8PzmhZpzUZFuatLyfFTSBXHMJ+s+o9WRgcLpy00WXIGEUALLmAhJ48LY0tJSBwcH8kqjkJCQ9evXb968WaVSeXp6JiYm0r6iObHkwtioqKhZs2ZJJBI3NzeigHT79m1iB6FQ+Ntvv5n6NmjMRtJIAJ+zYhaP2ZVJhMGhsE4avHKmReoBZAhlQqk8XGQyM1ZSItKIvE5auOscu7aO2WcyANi35taKWTzj/w8FgJyCdguuQDIdM2bMKCwspGxcvXr16tWrLXI/tLFwc1UWi0Us6bIUEWGuKzZXG7OsgWDxbK+cA+WMF5M2HxmXnS7OeDNZOC/UsqESAS4ymROqDiUtsx4dQjTnlt5clbwgLmjBYYbVKDtdbOSqIzI5+W3H91m4YYES2DRcduTDGbwZa+PJ7fZNgHoIGZ+1A5ILPDzalykXOPRNqQiP7ti3Juc+mGpQBT0Is3hzbpk0t6huyXIULeGmD4zQmZHZfaugMyNTNC+U9+Y0cy4D0J/7SVkP0nIYdzFAX8O6PMObeWujqr7LsgUk6G0dxHDKzmbAgtTXQ4iJrB2YxgWO6AuVSjJeyBu9w+TDAgwCF5mYxWpLRBSac0sLd52fEz1oAdN/7Qjk8zZ0Nrk2LNsxiACPMNcBFiQAgO1r+DQmmmsDucCZLSYhSKFSavO8qVYVKiFwkckYrLlEpA4KjOK3j2A8MEIw5fMmOHO56c+vmORWMUyBBQmAiZYNFDa+JvjjX+8xOOycjDWHSgS4yKQ/1l8ioiCvk958M3l8qON20wRG0Ofz/pW5ZB0A5BS0f/f5EAZPSA8ly7gakhGjK6wfLEgAzJm/CQL4nG8+fIrZmUlkUKg0IrTlVFJ68/iRVhgqEeAikw4GRImIgqkDIwRTPm8CK8nXgWls3zYDFqRelv2RZ3zLBjLIBX4huZzxxB3BiFCP+O1OKFQyw2Q/Y8BFJjIDpUREARm7fVRSxuujFBj0eRNYvEEDAR5hrgMsSL1MD3PZdaiB2XOawgVOAYVKAOVWZQrXwZNcZBpYJSIKKDBauX3EiFAmAxd1mPV5E1hwRCxGf7Ag9cJ41g4e7wVu0vwGcjoMiFCJgFJkqj2Q3lonZfvyAcCOz2f78tm+fDtfPpvPB4CBolVKcT0AKMT1yvp6hbgeAHpuFQBAd34BAHAFvAFRIqJgtsAITODzRpy+3MS2A8s2aCBQAts42zeuIT0ZMNWygUyvCzyB4ZZC6gy4UIkAKRO6YXmdFACac8sAQJpbBE1F8itSeW0LRaugT6LYfL6db+8Ws0GoDpIZpbheKa5X1Nej7VwBjyv04Ap4TgIeAHiunggAnuMXm/MOGaQmLa9w17kFcUGMdwPSCLM+b4KcgnaLLz8iUBlXQ8K27ycFBls2kDHFsHNtoFApOSH35qrS0TteHlhP4gCAblg0D/33sQo/0ip5rVRe1yKvlXbc+Y6sXmxfPrNapRTXkwMdsuqgm+QKPdyQ6gSA54tIdazR7kgbcmBkCmOOOheSy8cNtmP2iRBhDQ0aCHCnBh1gQXrE9DAXplo2UFg82+u0yVzgFFD7O2trNWQ8vTKgSWLJWgUA0tzvAACFVnLtaUA7Xz7oTK8BAFfowQsdCgDcSTyuIJAr5A04jafHo1ZAZgmMwDQ+bwJraNCA0QcsSI+x7I88xrN2YHoXOAVyq6HCOunoHS+b+oqWhaJV6qEVSaseSwNS0mvcBU9xBR5c4ZwnRHU0QvRINUUrIB0wMgpWI9Zj+EZgl50OsCA9xmsLeAy2bCBD9AJnfIymNh51ZX3hgC2FSobCFfC0aRWGgul6pOpm35pbG18TmCJZB9bXoAGvQ9KBLacjacB4ywYyi2d7efX0XEguN9H51UGhUsKR4Q/Scu4nZZntupiByP2krLJdqZuPjDPdKgWNmMjnTZBT0L5sgVVFSOwesKP9Zds1JFt+bzQgzN+mODlygTM+WLZfUKj0jKrk+xcONOeWmvPSmAFBc27p9y8ceEZV8uHXk8yZpgOA4ryW5ITiQxuCTHR+a8vXYXSDBYkKatlgopMTiTsTnV8bRKgkTkrHoRKGDAqM4rcHmjkwQlxILjeFz5sgp6A9wsrsDMj2TfvLtm3fWJCoTA9zMV3WDgBiZntZRJMAYLDAKX57IAqVkDMN8yQjr5PeXPWpoPaO+QMjRHJCsYl83gRnLjdZm79OCWxjBAmn7J4sTJq1Qyye7aWqajdz4g6BQqX47YFlO1NxqPQkcz8pq+jNQytfH2SG5XEaKc5rqfil+WNGO6hSOH25KSLMxUoaNBCgeUi0v3CE9MQxPczldGaz6c6PiknJCcWSug7TXUUHI0I9cKj0xIICI4fcXEsFRgAgqevYt+aWSdUIrKxBA0YfsCBpYNkfeSaNkKCvpZBFEncIFCrNiR50881kHCo9OaDAKOJZldmWH2gkOaHYdD5vgpz8Nit0NCiB1aOyo/2Fbd9PHGbI2gFAjNld4Oogp4NDbi4OlWwecmBkEf8CARoFazqfN6Kyvquqvsva8nWAa0g6seX3ZgxBQk5OQbupr2IRFzgFZArHoZJtU5OW9/0LByweGAFAcV7LheTybz58ytQXss7wCHANSSeWFCSFQnH+/Pn33nvvyJEjVVVVGvfJy8s7dOhQcnKyth1MxGsLTJ61A4AAPmenRRN3BESodHPVpzhUsiVQYCROSrN4YIRAPm8zXOjM5SZrM3xj+sWSgrRu3br33nuvtbX122+/nT9/fmkpdc3m6dOnly1bVlhYeOXKlaioqLKyMrPdW5DQwQwREgBMHetmKRc4BdSVNeJZFQ6VbAN5nfR+UhYKjMzWsVs3+9bcMrXPm8DaGjQQKI1bh6SxhlReXr5u3brIyMj169cXF/d+mGRlZb344otTp05dtWpVdXW1ed8lTSwmSHfu3Ll69erBgwf3799/7tw5Hx+fzz77jLxDW1vb+++/v3379mPHjp05c2bChAlnz5412+0FijgRYS6nLzeZ4VrIBZ6dLjbDtXRDrJ9FVaXCXedq0vIsfVMYw0A6VLjr3PcvHHiQlmP+VkDaKM5reVgjM7WzDmHNDRoYT9nJ5fLXXnstJCTk6NGjHh4e27dvB4CKior4+PhXXnnlxIkTHA4nPj7eEu/VYCzWXDU/P5/L5UZGRgIAh8OZMWNGdnY2eYdr1645OjouXLiwsrKyp6fn5MmTbLZZ5XPZH3n/+rIpZraXqS9EHixrDY+xqKokqesozmvJvnTl+6Qsz/FDeOOH4s6k1gwavNtRJ61JyxsscAqP9t1zI9LSN/UI5PM2T7IOAHIK2mdFWGm+TqliK1RGNFdVUT8Gr1y5wuPx4uPjFQrFtm3bKisrlUrl1atXQ0JCYmJiAGDDhg2zZs2qra0VCoVG3brpsZggNTc3+/j4EBrj6+vb3PzY0p+qqipPT89XX321qKhIqVQGBwd/8sknAQEBlPPUNMDNQiV6HTaaScWaHuay61ADgyfUAXKBHzZjL/B+QR9q4dG+ZGXiCj2E88ZjZbIekA5J80qbc8usUIcIzOPzJjhzuSnh3eHMnrOmQVXboAKAmgbw92b23P3T3djeI2kHgB5JOzwuK/fv3xeJREuXLs3LyxMKhQkJCUOHDpVIJCKRCO0gFApZLJZEIqEnSO3t7bdv3x4+fLiTk5Ozs7PRb0UXFkvZKZXKx+6DzVYoFOQtDx48qKioCA0NLSgoyMrK6unp2bt3r/p5bt5RHvlCceQLxc07SvWfGoN5zN8E1uAC1wj6mNt8ZFzCkeEvzXX0+CUbZfNwn1bLQpSIHqTlRDyrOnEj0kpsC+qYx+dNgPJ1jBu+0eeM8R819FJ2nRKZ5HyB5HyB7G495YQtLS1Xr16dPHnyxYsXJ06c+M4778jl8p6eHnv73njDzs6OxWL19PTQuNuTJ0+Gh4f/6U9/+vXXX2fNmpWenm7Me+8Xi0VIjo6OMpmM+La9vd3J6bFslYuLC5vNfvfddx0cHPz8/GJiYg4fPqx+ngXPs9e8aqp3gRqtfmOux7pDG4JeP1hZHOphqfXzuiFipgV1Hdnp4uxdqYXADV45EwdMZuZ+UlZtWp4LyMOjfbdbZTxExqSjYDVionzdnrd6P2eOfEHnk52A3jwkztMi/jYRALScp5Z1ORxOYGDg2rVrAWDbtm1ff/11cXGxvb19Z2cn2qG7u1upVDo4OBh60ZKSko8++ig5OfngwYOOjo7vv//+1q1b586dy2KZynpusQjJ39+/sbFRIpGgb+/evevv70/eYejQoQBAhE1kwTcbpm60SsF6XOC6Qd6HzUfGxcbxey5dwQGTeUAhUUbY3x6k5cTG8a02HqKQnFBsHiMDgRU2VCWjApZCxab9pW5qEIlERCbN0dGRzWZ3d3fz+XzCllxeXg4AfD7f0FstKCiYMmXKhAkTkAJFRkayWCx0NhNhMUGaMmWKs7Pz7t27a2pq0tLSkLEbALZu3Xrq1CkAmD59uqura0JCglQqLSwsPHny5MyZ5p55auasHViTC7xfyKm8MN/msl2p379wALvyTAFKzRW9eQiNLPrw60nh0b6Wvim92Lfm1opZPLOVjsBk+TprJiIi4t69e99//z0AnDhxwsnJaeTIkZMnTy4rK7t06ZJcLj927NjQoUN9fHwMPXNAQMDdu3fb2no/AIuLi6VSqa+vCf/2LJay8/Dw2L9//7Zt22bMmMFms6Ojo2NjYwHg4sWLMpksNjbWzc3t6NGjW7dunTRpkp2d3fPPP79p0ybz36eZs3YAsHi2V86B8gvJ5QPi+Rf6AqbwaF+yK084L9Rz/FBL39rABhkWSj7NGixwio0LGigiRGDqUbAasWZ/HUIFLGPa/6hHSEOHDt2+ffvGjRvlcrmLi8v+/ftdXV1DQkLWr1+/efNmlUrl6emZmJhI41rjx48PDQ39wx/+IJfL//nPf96/f3/t2rVcLpf2zfcLS6VSme7s/aJSqSQSiZubG6WARKalpYXL5To6Oqr/6NChQ8rGo6arIQFARU3XjGVl5syAA0Blfdfsjffjto+wzmKSbiSowpQufogrTHS5n5QlzStl19ahop01LAYwFEldx19fvJH379GmG76nkcGz837PGG7SCOnIFz1s79VvvfUWjWMPHTr0r9qfXF8Ko3319q9u/ln4HL2rG3yt9vb29vbi4uL8/Hw7O7tp06aNHTvWpFe0WISEYLFY3t79OCg9PCz5oYyydqcvm2NBEgFyge9KKP7w60lmuyhTqAdMwnmhnuOH4ICpX8ghUUS074LDA++3T5CcUGzSUbAaGRD5OpWKpb6WyKDDGbwZ3fzyyy9bt27NyclBC0bNgIUFaUCwfQ1/5z8azClIABAz26uqvis5odhS89OMhLyMKTu95MKqLK6AhwMmbZBDotXW0ebHGMzZIojMmctNf35l4CUVrJaJEyf6+PgcO3YsLi7Ozo7+Yl79wYLUP0FCB3N67QhQMSk7XTzgigdkNAZMovmhXIGVdnYxJ7YUEhEU57V49fR8/FcLBMT/v707D2vqzh4Gfm4CYaeAmrCIVCzaVjuOCm1BR5GCVhGF6ftaKJUZq/OrUCx2lBELvP2NWy0WR0drawvq6FC1tRYVrRt0k9oW1IJgcGOrAYUIsphASHLfP65NIztZ7pbzefL0ScJN7rlFcnK+a2Fp+9efjqb/vENi8j4k87l27VpLS8uWLVu2b9/u6upKjbU7ceKEk5O5vmpgQhoYI612wL4lhYzRvWCaTw18sNxFH2R5l5ovVnZevMqPkkiH5iWC9LF5/bpHEaQRTXZAY0IaM2bM+vXruz1p1sUaMCENCiOtdqDrTEr4JWXnH/nxmWXhBZN+STQt3D2Sg32E/ZDXd1BdR/Q31gF32utIILRDnxir/3ITBtM/BweHSZMmdXvSrG13mJAGhdqNorCkjf6/tJhZw0ZJRP/7z6s+/m5cGQg+oF4LJjsPV9cpvgBg5+Fi5+nKgxSlrG9W1jUr6+8r65oBgE+9RD2dP3Hn9MeVO1b5MJKNgCPtddxy4cKFJUuWdHuyqKjI2dnZTGfEhDQo1G4UhaXtjPyxTZ3olO1us3xz9aZL99mz+qpJ6AomeX2HvF5RUXweAOT1HUWX7gOAnYernacLlZlcp/jaebgAANtG61H7GeoST0d9s7K+WVl3X1nfTGWdJye7PEHdWeLy5GRa1yygB1UYDVOraZ4doY877XVAkkY12dE5yi4gIOCbb76h7iuVyoMHD8pkMvNlI8CENHjpCZLXUm7TPMtPh+pPOnjm3qqoHzk6P6kfwz1sqc9u/eEb8voO6r/yeoW8vkNeXCev75DXdxTVd1Apym3KaACgraiiEk/TxSpduUM91MU/3MP2CQ9bcIcn57oM95DwrwbqVcWl+5sSfvnHIg+m/jQoGfvrd28ayWAAg8ehQQ02NjYeHr//Wt9+++3AwMDGxsYB5+oYDBPSYD3uaf3rXRUjrXaUURLRPxZ5RM8atiSzsoJHzXd9oT7Qe/1YpzKTvF4BABXF5+X1HW0ARZfuUwmJKqpsPVztPF0NSFQ929n0y53hHrbPTHYBgOFzbYd72D75QbAJLpWzcrOqLx6vY6rTSN+vd1VsXr/uUZwZ1NDNjRs3WlpalEql+U6BCWmwfLxEcQtcmWq10xklEWWvHEWVSrwZ6TBUuooK+i6qKi7VQR3I6zuq6jvk9R29tv7BbyUO1c7WS7kD8OQSF4DHnpxs3gnqnMOGZjodDrXXccvPP/+cmJioe9jS0hIUFNRtFWzTwoQ0BIsiXRlstdOhSiUA2JTwy7Rwd96XSoOnX1T1lajgt6KK+pEHlX4m2Q6f+9jwNB6ONTAHljTT6XCovQ441Yc0fvz4jz76SPfQ2dl5zJgx5tt7AjAhDcmMAAdq8W/GGygAgGq+W7DqOgBgTupft9Y/Tk80Zhx7mukohSVtnGqv41IfUkNDQ3l5+aJFi3TPbN68OTEx0Xzrq2JCGpoZAQ4Hzjax5E9xlER09P2xFt58h2hDNdP9cbiQDc10OgfONnGtvY4DfUhKpfL777+XSqWnTp3SbaTU2dmZnZ2dkJBgvvNiQhqauAWuIXFVtXdVNK8a2Req+c5bIvonNt8hc2J8mlGvau+qDp65d+P0OKYD4ZuWlpZt27a1t7ffv39ft3UFQRALFixwcDBjMYoJaWh8vETvLBdn7K+neRPM/sXMGjZ1otPyzdVZ9R0cXYwVsZZu/MLR98ey5HuYzvLN1ekJYpYv790NCYTWiCqHniY7d3f3EydOXLx4cc+ePTt27NA9n5eX19HR0c9uQUbChDRkMwIc1u1sYElPkg6/JyohplBr070W6sqS8Qv6CkvabstV6QkcW52BQ4MaJk2a9P3337/66qsajQYAtFptaWnpqVOnfHzM9XWcsS3MucvHS5SeIE58v4bpQLqjmu/OZDxx+uPK3KxqpsNBnJebVb1t2aXsv3uzMBsBQMb++qwNnBlcp0MNajD4Rueghh9++GH//v1Tp04tKyubO3euk5PTnDlzzJeNABOSYeIiXan1v5kOpBfURKWxnZ2ron7UDW5GaEiowqjxZ/nl/RNY1RKgc+DMPaENyaHBdVwkk8mmTp0aHx/v7+8/ZcqU7du3f//99wqFwnxnxIRkoOz1IzP21zMdRe+oUum1UNdNCb9gqYSGquLS/VVRP84fb3f0/bFMx9Kn5e/XpCdImI7CECQQWlJg8I3OCmnYsGHXr19/8ODB2LFjS0pK7Ozs7OzsZDKZ+c6ICclAPl6imc87sLDhTodqvrt4vA5zEhq83KzqnH9ePbrZj53NdJTE92viFrhytDziUJPdtGnTCIJYsmRJcHDw5s2bo6Oj29raPD09zXdGTEiGS08QF5a0FZa0MR1In6iJSth8hwaDaqazrW1jbTMdhRrqzcXeIwpJgpYkDL6RJH2hqtXqEydOpKenBwYGbtq0yd/ff+/evTjsm6V0Q8CPsvivF9cZQoNx/sQdBvfWG5Llm6uz1nM1G3FLcXFxampqYWEhAMyaNWvWrFnmPiNWSEaZEeAgtCHZXCRRsPkO9WNTwi+nP668xO7CiFJY0ia0IeMiubU0wyNIIDQgMPhGZ5Pds88+KxaLd+3aRQ37pgEmJKP4eInSEyRs7knSweY71JO8voMav3B5/wS2TXrtVSJnxzLoaIHQkAKDb8ZMqh2qa9eutbS0bNmyZeLEiX/605+mT58+ffr0tjYzfv9msslOo9Hk5uZKpVI3N7eIiIieq5pfunSppKRE9zAkJMSsQ+ANMyPAYebzDhn769ncCUz5fUclfm2IjgxDLZOazbLVgPqRsb9+5vMOHB3LoENVSAa/XEhjQhozZsz69eu7PWlvb2++MzKZkBITE3/88cewsLCff/75448/PnLkiK/vI7tTf/rpp6WlpaNHP5yJPWHCBBYmJABITxCHxFVFzxrGie+YuKMSYtVuRoNUe1eVsb8el63r1bvvvltcXEzd9/f3X7NmDQDk5+fv2LGjoaHhmWeeSUtLGzlyyB1vzs7OQUFB7e3tV65cGTdunK2trVmzETCYkMrLywsKCj788MOQkBCVSjVv3rzs7OwNGzboH1NRUfH666+/9NJLTAU5SOxc4K4fONLBkrFtN6NB4uKydb3SkoTGiOV/tL29tqCgYNmyZdQXemdnZwCoqalJSkpKTU319/ffvn17UlLSF198YcDp9u3bt2XLFqVSuXPnzvT09NTU1PDwcIODHxBjfUjUNKvg4GAAEIlEISEh+q1zANDV1VVZWeni4nLy5MkLFy50dXUxE+jgzAhwuFDG6iHgPeFIBwvEiWlGPf22bB23e48opHF9SD0HNSgUCplMNmPGDBcXl2eeeWbMmDEAUFBQ4OfnFxMT4+fnl5ycXFZWVldXN9RQb926tWXLlqysrMmTJ9vY2GzcuHHjxo2kOQeeM1YhNTU1icVigeBhRnR3d29qatI/4NatWxqNZsWKFV5eXrdv3/b29t6/f//w4cO7vc/OQ5qdhzQAEDBesGedNT3B96Rb4I5DbSCAOypZEnbuZjRIbFi2bnF6V1G5lrqvt683TWwu/OTwn4MdpbAAACAASURBVBzo7fTXr18HgLCwMKVS6ebmtm3btoCAALlc7uXlRR3g6elJEIRcLh/qnNbS0tKgoCB/f39ql9jg4GCCIKqrq3XdKCbHWIWk1WofiUMg6DayUK1WL1iw4OTJk6dOnTpx4kRzc7P+Kug6CS8Ly47YlB2xYTAbUeIiXanRDcyGMVS4zpAloFYDeiPkMa60KuvL2F/PhmXr9qyzpj5qEl4WGvM+WiDUIBjq7UFgYMNHOxo+2vFg3txub9jc3Ozv7//FF18UFxdPmTKF6kBSq9VWVg/rDaFQSBCEWq0eaqijRo2SSqW6YXUVFRXNzc3u7mbccJmxCsnGxkZ/kb729vZue2xMmDAhIyODuu/j4zNv3rxLly7RGuLQpSeIX1sjKyxx5MqwJZ2Ho+8ya3NxQ3TeYdum40NSWNJ2KP/ejTP8GcugJQmNEdtP9OxDmjlz5syZM6n7q1atmjVrVmNjo5WVVWdnJ/VkV1eXVqu1th7yV/YpU6ZMnjx5zpw5SqVy69atN2/efOONN8y3fzkwmJC8vb0bGxvlcjnVCieVSrsN+/7ss89qamqSk5Oph+3t7Qb8D6WZj5fo/y0Xv5bCsYY7im703aaEX5amP4nNdzzAxdF03bChsc60tABqI4Zua3s8k5eXZ21tPXv2bACgOkG6urokEkl+fj51QHV1NQDodiIfkszMzG+++aakpEQoFKanp0+cONHgyAeDsSa7oKAge3v7tWvXymSyvLy8c+fOhYWFAUBqampOTg4AODs77969+8iRIw8ePCgoKDhx4gQNC1cYb0aAw19fcuHEVNmeqOa7+ePtNiX8krWuouLSfaYjQgaS13fkZlWzf9Hu/iW+XzNmtDXjjXUsJ5fLN27cWFdXp9FoPv74Yx8fHw8Pj8DAwKqqquPHjyuVyl27dvn6+orFYgPevKGhobCw8MKFCz/99NN3333X3t5u8vj1MVYhubi4ZGRkpKWlhYSECASC8PDw2NhYADh27JhCoYiNjX3xxRevXr36zjvvrFmzxsbGJjY29q9//StT0Q5J3ALX0MVVbNtSdvCo5ruDZ+7l/POqUiCIXPr4tHAzthojE5LXd5w/cef8iTt2Wm3MrGGXOLL+Qq8KS9oulLXxqbGOQo2yM+bl3Z555ZVXLl26FBoaKhKJPD09//WvfxEE4efnt2LFipSUFJIkqZEOBpzrwYMHsbGxjz322IsvvqhSqb788svLly/v3r3b4OAHxOTE2LCwsNDQULlc7uTkpOtAunLliu6Av//972+++WZTU9OwYcOEQqM6Eunk4yU6t2d0SFwVd9tJdGs6FJa0HTx6Ozer+snJLtPC3XFndNaiUlFuVrW3RPTOIo+YWcOYjshYie/X7N7Eq8Y6CkkSWpNuYS4Sif7973/3PDI+Pj4+Pt7gEwHATz/9JBQKDxw4QHWXxMTETJ8+vbGxccSIEca8bT8YXu2bIIj+r83KysqwSpNZPl4iquGOi4OadEZJRKNmDYuZNYxa8J8qmHAiLat0K4nkZyYzHZFpLFh1/a8vufCysY4Ewpj16OhcXFWhUHh7e+s6711dXR0cHNra2syXkHBxVXOJW+Ba19zBzm3Oh4oqmI6+P/adWIltbduqqB+xh4lxul6ii8fr3omVXN4/gVtzXftBLenNj2mwnPb888/fvHnz5MmTWq22o6Nj+/btHh4e5puEBIxXSDzm4yXKXj8yJK5q6kQn7rbj68OCiQ34WhLp1N5VLUi+cXaP78CHchMJBGnSPiTzuXHjxp07d956663k5GStVqvVaoVC4R//+EcAWL169SuvvGLyM2JCMiNqjbvlm6u5O8ypV/o9TIWlbauifsQeJhrwr5eoV9SadbxsrPsNQRrVNEVfQpo4ceLhw4d7/ZGHh1nKcUxI5jUjwGHf0eYDZ+7x7+MDCyZ68L4k0nfgzD3+N9aRAEYsrgo0bmFub29fWVlZXFysv4xOamqq+ebGYkIyL/413PWEBZOZWEhJpFN7V7X8/RrcYII9Ll26tHr16oiICFfX37fopda1MxNMSGbH14a7brBgMhWLKon0Ld9cnbV+JA82mBgIAUb0IdHZZFdVVfWnP/3pvffeo+2MOMqODnGRrkIbknPrrhoGh+QZTDdwrvFnOc8Gzg2IWkE1LtJ14EO5jiQII25GNfcN0TPPPFNaWtra2krbGbFCosnDhrs/cG/dVcNgwTR4FlsS6VjUbrAEEIQRlQBBY4X0xBNPjB49etq0aU8//bSupS4rK8vBwVxDTjAh0YRquOPchknGowqmfyzyKCxpO3C2CXuY9Ol6iaJnDXsnVsL7XqK+LN9cfXaPrwU01nHMDz/8IJVK33jjDTc3N92TZl3kGhMSfeIiXb8repCxv95y2mH0TZ3oNHWiExZMgCXRo1iy3RFtCCAERvQh0Vkh3b9/PzAw8PXXX6ftjNiHRKv0BPGFco7tdG5aVMF0ef+E7L97W2APk66XyLa2zdJ6iXpFbXd0jr/TYHsiSBCQhME3gsZh388///ytW7ekUiltZ8QKiVac3jDJtHoWTMM9bHvemA7TcPL6Dt0NACou3bfTauX1HVgS6ePfdkcD4lCFVFNTI5fLIyMjnZ2ddX1I586dc3Z2NtMZMSHRTbdhEqfXXTUVXQ9T7V0VVTgWlra117ZJ73TW3lX9eldF5SSqw4n6L6tyVc+so/uvt0Q0SiLydrcZKxEBwOKYEQBgIUNaBgm3O2K5sWPHfvLJJ92eNN+IBsCExAiub5hkDtSoPADo1rFfe1f1653O2rsqACj8qREA9HOVLjOZNVfpkg11h0o/uqwDAFMnOlFZ54WQx0ZJRFM3WVADlMH4ut3RgAiSEBoxdJugcdi3k5PT5MmT29vbr1y5Mm7cOFtbW3t7e7OeERMSA3iwYRJtRklEoySiqQDwaK6iUpR+rvr1TicAFJa2w6OZaZC5SpdsqEyjX/pQWWeURER9gXjhKZtRwU7eb43k69Ib9ODrdkcDEgAhNKLzXkBjkx0A7Nu3b8uWLUqlcufOnenp6ampqeHh4eY7HSYkZvBjwyQGjdIlCQDoO1f9eldVq5erqISkn5l6Zh1vd5tREtHDrONug1nHHHi83dGACACBMRWSCUMZyK1bt7Zs2ZKVlZWZmWljY7Nx48bU1NS5c+eab/UgTEiMiVvguiTtNi/XXWVWt1ylr1uuAoCpwdi1Qzfc7ogrSktLg4KC/P39qQwUHBxMEER1dbX5tkTChMQYS1h3lW36yVWINvze7mhABEkYVSHR2Ic0atQoqVTa1vZwmkpFRUVzc7O7u7v5zogJiUlUwx3v111FSGfBqut83+5oABwa9j1lypTJkyfPmTNHqVRu3br15s2bb7zxhvn2ngBMSIyLW+D6bdEDbLhDlsAitjsaCCcqJK1WSxAEQRCZmZnffPNNSUmJUChMT0+fOHGiWc+LCYlh2HCHLAS13ZElN9ZxyOrVq8eNG7d06VIACA4ODg4Opue8uHQQ83QbJjEdCEJmRG13ZMmNdTpGbT/Ba0xWSBqNJjc3VyqVurm5RUREeHt793Xkl19+2dnZGR0dTWd4dIqLdN13tNli111FvGdB2x0NhCCN60OiKyfdu3evsrKy5/OPP/64QGCuSobJhJSYmPjjjz+GhYX9/PPPH3/88ZEjR3x9eynny8vL09LSQkNDeZyQwPI2TEKWw6K2OxoQYVxS6eeVFRUVf/nLX7766itqt4j8/PwdO3Y0NDQ888wzaWlpI0cObRry7t27d+/e3fP5oqIiHq5lV15eXlBQ8OGHH4aEhKhUqnnz5mVnZ2/YsKHbYR0dHcnJyRIJ/3tBLXbDJMR7uN0RDVQq1dtvv33//n2NRgMANTU1SUlJqamp/v7+27dvT0pK+uKLL4b0hq+//nqvNYCjo6NpIu4NYwmppKTEzs6O6isTiUQhISHnz5/vedjmzZvHjRsnFovv3LlDd4i0s/ANkxAvWdp2RwMzsiuoj9du27YtODi4vLycelhQUODn5xcTEwMAycnJoaGhdXV1np6egz+Ps7PzkI43CcYSUlNTk1gs1rVFuru7NzU1dTvm/Pnzp0+fzsvL+/DDD/t6n9yvtUVlXQDgKSY2LOf8oMH0BPFra2SFJdhwh/iA2u6IHyuo7jykLiojAUDWSP55oeHvY1iTnaCq1LpgPwAImu/C0/+3208vXrz43XffHTly5IMPPqCekcvlXl5e1H1PT0+CIORy+eATjEgkMl9HUT8Y+wTXarX6DwUCAVVp6ty/fz8lJWXdunUuLv3tdR0wXhA5UwAAnmI+jD/RbZh09P2xOAoccR2fVlANGC8IGA8AkPu1dqBj+2VYheTirp65CACsLp/t9hOFQrFmzZrNmzfrby6uVqutrB5+vAuFQoIg1Gr14M/Ws/eEHowN+7axsVEoFLqH7e3ttraPrMScmZnp6OjY0tKSm5t78+bNurq6kydP9nwfLzEETBAETBB48SIhwW8bJuEocMR1PFtBlfqcCZgg8BIzcHbSRaIdPVE7eqLWpXuH+pYtW7y9vUmSvHz5MgBcuXJFoVBYWVl1dnZSB3R1dWm1Wv10xVqMJSRvb+/Gxka5XE49lEql3YZ9Ozs7Ozk55eTk5OTkVFRU1NTUHDx4kIlIGZCeIBkz2jpjfz3TgSBkIKrryMIXZegTSRh+66GhoeHq1avx8fEJCQkAsGbNmmvXrkkkkqqqKuqA6upqAODE0DDGmuyCgoLs7e3Xrl27evXqy5cvnzt3LiUlBQBSU1Offvrp2NjY5ORk3cHvvvvunTt3tm3bxlS09EtPEIcurvKWiHBJIcQ5fOo6MjmCBII06uXd/Pvf/9bdHzduXF5e3ogRIxwdHTds2HD8+PHQ0NBdu3b5+vqKxUxUdkPEWEJycXHJyMhIS0sLCQkRCATh4eGxsbEAcOzYMYVCQd3Xx0gPG4N0m/jhkkKIW2rvqix8Pe+BGLngwqBe6+fnt2LFipSUFJIk3dzcuPJtnslhaWFhYaGhoXK53MnJSdeBdOXKlZ5Hrlmzht7QWIGambRg1XWcmYQ4hJp1xJuuI265du2a7n58fHx8fDyDwRiA4bKDIIgRI0Z0G86AdOIiXf/6ksuCVdepneUQYrPau6oFq66HTLPHbNQPgjRqLTtjmvvYz7LawbgoPUESMs1+warrOMYBsVlhSdvkRWUh0+xxIMMASCC0ht+A1wmJ8zNJLUF6giRugWvo4qrau6odq3yYDgehR9TeVS3fXH1brsKWusEgjOtDonODPvphhcQN1BgHvyeEkxaVYamE2ENXGN04Mw6zETISVkic4eMl0pVKAIDr3SHGZeyvP5R/DwujoTFu2De/m+ywQuIYqlSycdJMWlRWWNLGdDjIQhWWtE1aVGbjpMHCyBAmnRjLJ1ghcY9+qfTyC8OwVEI0owqj3Ztw+1dDEKRRVQ6OskNshKUSol/tXdWkRWV3WjuwMELmgBUSh1Gl0vQAx7Xb6wtL27FUQmaFhZGJGNnyxudWO6yQOG9GgMPud72oUgnnzyJzoGa8/ljRioWRCZBAaAmDb/we1IAVEh9QpZKPpyjpX9WB452wVEImRBVGWRuwMDIRI8cm8HpcA1ZI/BEX6YqlEjIhLIwQzbBC4hWqVAKABauux8zCAXjIcFRhFBfpgksBmRYBPJ9LZAxMSDxEDQpfknZ70qJ7uBU6GipqKSChDYkbGpkFaVyzG6+TGTbZ8ZOPl+jcHl9qpXBcaggN3oEz96ilgM7hhkbmYsxS3wSOskNclZ4gKdg3+seKVtzAAg2I6jF6/9P6G6fHYTMdYgQmJJ7z8RJlrx+JG1ig/umvkerjhW285kQat3QQr5vssA+J//SXGqq9q/rHIg/sVUI6uHkEzQiSILQ47Lt3WCFZCt0GFlgqIR3cPIIRxvUh8RlWSBYEN7BAOrV3VQfP3MPNIxCrYIVkcXBVVlRY0rZg1XXcPIIRxpRHvC+SsEKyRLiBhSXDNVIZRoJxfUimi4R9sEKyXFgqWRpq8wgsjJhFGDcPieD1PCQmKySNRpObmyuVSt3c3CIiIry9vbsdoFQqDx8+XFVVJZFIoqKixGIxI3HyGG5gYTmwMELsx2SFlJiYuH79+tbW1lOnTkVERFRWVur/VKPRvPLKK1lZWe3t7QcOHJg/f35jYyNTofIbbmDBb9SMV9xVjy3MMA/ps88+mzdv3rRp09588025XE49mZ+fHxUVNXXq1GXLlt2+fZvWazQUYwmpvLy8oKAgMzMzIyPj8OHDYrE4Oztb/4Bvv/32xo0bBw8ezMjIyMnJaWlp+frrr5mKlveoUumd5eKkf1XjoHA+ydhfH7X6+v++Jc7aMJLpWBDFxEsHXbx48b333lu5cuXOnTtlMtmGDRsAoKamJikpaeHChXv37hWJRElJSUxc6ZAx1mRXUlJiZ2cXHBwMACKRKCQk5Pz58/oHODg4/O1vf/Pw8AAAOzs7gUDg5OTESKiWIy7SdUaAw76jzVEp1wPHO039g+PUifj/nJOoUd0HztwbPcoa10hlFxLApIMaqquro6OjZ86cCQDBwcE///wzABQUFPj5+cXExABAcnJyaGhoXV2dp6en4eelBWMJqampSSwWCwQPSzR3d/empib9A5577rnnnnuuqanpgw8++Prrr4OCgkJCQnq+j6wBcr/WUPcjZwrNHTbv/TYAT7XvaHPmZ3WJ73dNnegUE+aGmYkTqDyUsb/ex1MUF+lSsG80rgNkKkVlWlkjCQBFZeRzM+k+O9lWp62/CABk3UWAQP0fvfTSSwBQWVl59uzZ//73v2vXrgUAuVzu5eVFHeDp6UkQhFwux4TUJ61Wq/9QIBBoNJpeDxOJRB4eHlKptLS0NCAgoNsBReVaquExYAKfB5/QjEpL6QA1MsxMHNAtD904jevRmV5RuVbWYIo3MmjHWLKtnqy72M8BN27cKCwsVKlUbW1tAKBWq62sHn68C4VCgiDUarVh8dKJsYRkY2OjUCh0D9vb221tbfUPUCqVADB8+PDVq1cDwGuvvZadnd0zIUXOFCS8jLOpzAUzE5thHqKT7nNm5yGjP9mHnpAE7gEC9wAAUF/6qNcDZs+ePXv27JMnT65Zs2b+/PlWVladnZ3Uj7q6urRarbW1tTEh04OxQQ3e3t6NjY26ASFSqbTbsO8NGzZER0frHo4ZM0Ymk9EaItJDZaZze3wL9o32e0KY+VndpEVlie/X4AQm+tXeVWXsrx8+61LU6us2Tpobp8fdODMuPUGC2cgyvf322xs3bqTuP/vssx0dHXV1dRKJpKqqinqyuroaACQSDmwpwlhCCgoKsre3X7t2rUwmy8vLO3fuXFhYGACkpqbm5OQAwLPPPltRUZGVlSWXywsLC3NzcwMDAwd6V2R2vWamjP31mJnMDfMQT5AEaI249aiuRo8enZeXV1JSotVq9+zZ4+zs7O3tHRgYWFVVdfz4caVSuWvXLl9fX07M42SsscvFxSUjIyMtLS0kJEQgEISHh8fGxgLAsWPHFApFbGzs/Pnzr127tnXr1s2bN1MHvPXWW0xFi3rq1pr35r9qtBqImTUMx+aZlm68nEAI2C7HAwQJxqxHR/QYZbdo0aJffvnl5ZdfFolEbm5uW7duFQqFfn5+K1asSElJIUnSzc1t27ZtRgVNF4IkmVwaiSRJuVzu5OTUrQNJR6PRyOVyV1dXkaiXP8Lt27drGz/EPiSWoDLTvtz7mJmM1y0PTQ9wxDmtLLHzkFowIn758uUGvHb79u0fnddY/THe4LOrf/lw2TShYWdnP4Y/ygmCGDFiRD8HCIVCTjR9ItDVTAkSrJkM1i0P4Uo/yKJgbYFMTz8zrdvZsCC53lsiwszUD8xDFoQE0A58VH8v5y9MSMiMfLxEWRtGpieIq+u69uc2Y2bqBvOQJSKN24YcExJCxvDxEvl4iWYEOPTMTNGzho2SWFwXPZWHCkvabstVmIcsj5Gb7PF5BQBMSIg++pnp26IH3xU9mLyozHJqpm55aPFCl7hIV6aDQohFMCEhBvh4ieK8RHGRrrrMtCC5HgC8JSIAGCURebvbjJKIuj1kOOhBqL2r+vVOZ+1d1a93VbqHAFBY2g4A1HoKmIcsHfYh9Q0TEmKSLjNlbRhZI1MBQHVdF3Wnpk5VdKO1uk4FADWyrpo6lX5+AoCpf3CkHgIAPdUVtVlUz5Sje+jjKQIAHy/rxz1FPl7Wfk7CJTFiAHjc0wsnDyGKyech8QkmJMQW1Ee2j5cI+uhQ6ZaxvitqBYDPv1X1mq6oAotKV4MvsHqmHGoFCv2Uo8s3ABA6zs7H6zEAwE4gNFgkQRi1/QT2ISHEAt0yVreGrx7p6sGd1o7Pv314Hx5tD4TfSquerWqgV+IAwOKFLj5eosc9rbHEQcjcMCEhnug/XQFAjUxVXddF3ampU9XIOrBVDdGPMK7Zjc/1ESYkZDmoMX4A0FeTIEJ0IMG4JjvTRcI+mJAQQog+BAkCYyokXickxrafQAghhPRhhYQQQvQhjBtlZ9wqD2yHCQkhhOhDgHFNdqaLhIUwISGEEI1wUEPfsA8JIYQQK2CFhBBC9MFRdv3AhIQQQvQhSCCMWFwVExJCCCHTwEEN/cA+JIQQQqyAFRJCCNHIuCY7fo+yw4SEEEL0IUggSMOzCvYhmYtGo8nNzZVKpW5ubhEREd7e3t0OUKlUubm5169fHz58eGRkpLu7OyNxIoSQyWCF1Dcm+5ASExPXr1/f2tp66tSpiIiIyspK/Z9qNJpXX31169atCoXi6NGjc+fOra6uZihShBBir+PHj0dFRU2bNi0xMbGuro56Mj8/PyoqaurUqcuWLbt9+zazEQ4SYwmpvLy8oKAgMzMzIyPj8OHDYrE4Oztb/4CCgoIrV67897//3bhx45EjR5ycnD7//HOmokUIIZMgHrbaGXrr8YZFRUVpaWmvv/76nj17tFrtypUrAaCmpiYpKWnhwoV79+4ViURJSUn0X6kBGEtIJSUldnZ2wcHBACASiUJCQkpKSvQPuHfvnr+/v6+vLwDY2dl5eHg0NzczEipCCJkMCYTW8FvPJruioqJp06a9+OKLfn5+MTExV69eBYCCggLqoZ+fX3JycllZma5yYjPG+pCamprEYrFA8DAjuru7NzU16R8QHR0dHR1N3S8uLi4tLY2Jien5PrIGkDU8/BV5ifk9Rh8hxBjd54yxSBKGPqhB3SH7/eWPlklLlizRaDTU/a+//vqJJ54AALlc7uXlRT3p6elJEIRcLvf09DQmcBowlpC02kf69QQCge7/qT6SJA8cOPDee+/NmTNn/vz5PQ8oKtcu/n9aAAgYL9iwHAcNIoTMYuchTVG5FgDqGsjERLrPrumQNUnfhoeZ6ZHT29jYAIBGo9m2bdtnn31G9X2o1Worq4efh0KhkCAItVpNd9BDx9gnuI2NjUKh0D1sb2+3tbXtdkxDQ8PKlSulUmlKSkp0dDRB9FIARc4UJLyMeQghZF6677s7Dxn1yW7Y0kG2zs96PncOAFqqd/T86Z07d1asWHHnzp29e/f6+/sDgJWVVWdnJ/XTrq4urVZrbW1tTNj0YOyj3Nvbu7GxUS6XDx8+HACkUmm3Yd9KpfLVV1+VSCRfffXViBEjGAoTIYRMzLRziR48eLBo0aKnnnoqKyvL0dGRelIikeTn51P3qfHJEonElGc1D8YGNQQFBdnb269du1Ymk+Xl5Z07dy4sLAwAUlNTc3JyAODQoUONjY1r1qxpb2+vqqqqqqq6d+8eU9EihJBpkABa0vBbj2R24MABW1vbd999VygUKpXKjo4OAAgMDKyqqjp+/LhSqdy1a5evr69YLGbgYoeIsQrJxcUlIyMjLS0tJCREIBCEh4fHxsYCwLFjxxQKRWxs7MWLFxUKRVRUlO4lcXFxqampTAWMEEIsVFxcfP369cmTJ1MPhw0b9sMPP/j5+a1YsSIlJYUkSTc3t23btjEb5CAx2fsSFhYWGhoql8udnJx0HUhXrlyh7mzfvp250BBCyCyo6UTGvLybjz76qNcj4+Pj4+PjDT8TExgeDkAQBPYPIYQsiSHDvh95OX/3oMDxaQghRCMSANey6wPuh4QQQogVsEJCCCEaGbf9BL8rJExICCFEI2yy6xsmJIQQopPxgxp4C/uQEEIIsQJWSAghRCMSjKqQ+FwgYUJCCCE6kSRojUlIfM5ImJAQQohefM4pRsE+JIQQQqyAFRJCCNGHIIEwosnOtFtXsA0mJIQQopFBW5g/8nL+woSEEEL04nVSMQb2ISGEEGIFrJAQQohGOOy7b5iQEEKIRjgxtm+YkBBCiE64ll2fsA8JIYQQK2CFhBBCNCLBuD4k00XCPpiQEEKIRiQJpBEbIuGgBoQQQqaBo+z6hn1ICCGEWAErJIQQohevqxxjMJmQNBpNbm6uVCp1c3OLiIjw9vbu9bCrV6/m5+cvX76c5vAQQsjkSJIkjWiyI3mdzJhssktMTFy/fn1ra+upU6ciIiIqKyt7HiOXy9euXXv69Gn6w0MIIdOjBjUYfuszIS1ZsiQ/P1/3MD8/PyoqaurUqcuWLbt9+zYt12YsxhJSeXl5QUFBZmZmRkbG4cOHxWJxdnZ2t2P+/Oc/T58+/fLly4xEiBBC7KfRaHbt2vXaa6+dP3++s7OTerKmpiYpKWnhwoV79+4ViURJSUnMBjlIjDXZlZSU2NnZBQcHA4BIJAoJCTl//ny3Y9atW6dSqY4dO1ZcXMxAiAghZA4mbXYjCMLR0fGFF164ceOG7smCggI/P7+YmBgASE5ODg0Nraur8/T0NOF5zYGxhNTU1CQWiwWChyWau7t7U1NTt2PGjx8PABcvXuwnIeV+rS0q6wIATzGxYTmO0UAImcXOQ+qiMhIAZI3knxca8UYkCdohz0Pq6PyluXUvAKjVdwD+j/6PBAJBbGwsABw6cX/z/wAADQhJREFUdEj3pFwu9/Lyou57enoSBCGXyzEh9Un76K9EIBBoNBoD3kfZ1XbvXld6gthTTJgoNIQQ6i5gvCBgPKzb2VBxU0j/2a2E7q7OfwWAtgenBnO8Wq22snr48S4UCgmCUKvV5gvPVBhLSDY2NgqFQvewvb3d1tbWgPcJDAJHxwe7DtRlbRhpuugQQugRARMEoYsrwU61OsXdqDcyaMdYK6HESigBAGXHoPrUraysdP1JXV1dWq3W2tp6qCelH2ODGry9vRsbG+VyOfVQKpX2Ney7fz4+wvR0+1F/6PSbdc2kASKE0O9CF1f6PKU+e+4xY9+IarIz+Da4ZCaRSKqqqqj71dXV1DPGRm5+jCWkoKAge3v7tWvXymSyvLy8c+fOhYWFAUBqampOTs5Q3y093X7REiu/WddqZCozBIsQslw1MlXo4srpL5JZWU6meD/jhn0PbnXVwMDAqqqq48ePK5XKXbt2+fr6isViUwRvXow12bm4uGRkZKSlpYWEhAgEgvDwcKpf7tixYwqFgrqvQxAD9w+lp9sDKEIXV53bM9rHS2SuuBFClqRGpgpdXJX1H7vpM9je5KX/Oenn57dixYqUlBSSJN3c3LZt28ZgYIPH5LC0sLCw0NBQuVzu5OSk60C6cuVKt8OWLl26dOnSwbxherr9jOldoX/BnIQQMoFvix6ELa48e/YxU2Yj0rjVFvp+6dGjR/UfxsfHx8fHG34iJjA8TpogiBEjRpjwDafPsD77rWDJX2pm/NE5PYEDbaYIIXb6tujB0v+tNnE2AgOHfT/ycv7i4WrfPj7CrP/YfftL67qdd5mOBSHESVQ2yspyMkNLHR19SBzFz5mkVE4KC5UDANZJCKEh2ZfbvO6Tuus33JgOxOLwsEKi+PgIz557rLq9BeskhNDgLU29ve/MXTNmI5IEUmPEjc8VEm8TEvw2RYkc1r40lRsr3SKEmBW6uLK6ud0Ek436RoKWJI24gRH9T6zH54QEOG0WITRoJpv62j+zbT/BAzxPSBScNosQ6oepp74iA/FzUENPOG0WIdQruqe+kiRoDVlI+veX85dFVEiU9HT7rP/YhS6uwjoJIUT5tuiB3+xr9C7EQBrTh8TvYd8WlJDg4bRZhyX/rMGhdwghc0197R+pNW6UHQ5q4BGcNosQAvNOfUUGspQ+JH04bRYhC8fg1FcSSJI0vA+JxCY7/sFpswhZLLNPfe0fDvvum4UmJMBpswhZJBqmvg7EuD4knBjLVzhtFiGLQtPUV2Qoi05IFJw2ixDvsWjqK0mSpMbgG7+b7CxxUENPOG0WIR5j2a6vWjBiUAM22VkEnDaLEC8xMfW1PyRp1MRYo3abZT1MSL/DabMI8QwzU1+RoTAhPQKnzSLEG2yd+mrcfki8noeEfUjd4bRZhHiAvbu+klpjJsbye+kgTEi9oKbNLl3SDDsxJyHEPUtTb1c3t7MxGwE8rJCMeTl/YZNd73x8hFnZjjhtFiHOYcHUV2QgVldIGo0mNzdXKpW6ublFRER4e3vTeXYfH2FcnM2+fZ1+s67dODOOzlMjhAxDTX3NymJvNqJG2RnzchMGwzasrpASExPXr1/f2tp66tSpiIiIyspKmgOglnJgdtqsrIFM3a5m5NR0WpzexXQIZpe6XS1r4POnCQDsPKQuKmOmk4NFU18HYPqlg/Lz86OioqZOnbps2bLbtzncqMPehFReXl5QUJCZmZmRkXH48GGxWJydnc1IJFROYmqKUl0DWcf3TzFZAylr5Pk1AkBROZ+7oylFZcz8HmtkqiVpt+NeJ9LT7RkJYAhMvVJDTU1NUlLSwoUL9+7dKxKJkpKSGLksk2BvQiopKbGzswsODgYAkUgUEhJSUlLCVDA4bRYh1qqRqfxmX0vfaLUozpbpWBhQUFDg5+cXExPj5+eXnJxcVlZWV1fHdFAGYm8fUlNTk1gsFggepkx3d/empqaehxUXWe3caUdLRHZRLzu8vKp1RoCDjxd90xpkDSBrJHce4nOrnawBAIDf10jZeUjjJWY6CHOSNZK5X2tprgXX7ZRHRbmXlVuXldNxuuIiq+eeM/zlKrjVbkQfkgqqAJ7Sf0Yul3t5eVH3PT09CYKQy+Wenp6Gh8gc9iYkrfaR35lAINBouo+VXL58OY0Rge9o8P0bnScEAPAeAd7j6T4pzSzhGgHgzwuZjsD8GLnGd96h9XTPPWf4J48pPrLGd3sTtVptZfXwk1woFBIEoVZz9bsdexOSjY2NQqHQPWxvb7e17aUepzknIYSQMUz+kWVlZdXZ2Und7+rq0mq11tasWpliCNjbh+Tt7d3Y2CiXy6mHUqmU5mHfCCHEfhKJpKqqirpfXV1NPcNkQEZgb0IKCgqyt7dfu3atTCbLy8s7d+5cWFgY00EhhBC7BAYGVlVVHT9+XKlU7tq1y9fXVyzmakclweZpVmfPnk1LS7t//75AIAgPD9+0aZOuqRQhhBDlww8/3LFjB0mSbm5u27ZtmzJlCtMRGYjVCQkASJKUy+VOTk69diAhhBDiDbYnJIQQQhaCvX1ICCGELApXu2SYXXfVTAa8KJVKlZube/369eHDh0dGRrq7uzMSpzEG/4v78ssvOzs7o6Oj6QzPVAZzmZcuXSosLLSzs5s9ezYX/wEP8p9rRUXFsGHD5s2b5+Pjw0icJnf16tX8/HyccGIOXK2QGF931Rz6vyiNRvPqq69u3bpVoVAcPXp07ty51BBPbhnkL668vDwtLe3ChQs0h2cqA17mgQMH4uLiysrKqOGjumG7HDLgNS5dunTz5s0dHR0nT56MiIi4ceMGI3GallwuX7t27enTp5kOhKdIDiorKxs7dmx+fj5Jkp2dnWFhYW+//TbTQRlrwIs6c+bMk08+eevWLZIkFQrF9OnTMzIymInVUIP8xSmVyjlz5sycOfPNN9+kPUYTGPAyW1tbJ0yYcPDgQephbGzse++9x0CgRhjwGmtra8eOHVtQUECSpEKhmDJlytatW5mJ1XSioqKeeuqpsWPHhoeHMx0LP3Gyya7nuqvnz59nOihjDXhR9+7d8/f39/X1BQA7OzsPD4/m5mZGQjXYIH9xmzdvHjdunFgsvnPnDt0hmsKAl/nNN9/Y2Ni89NJLtbW1arV63759ujUbuWLAa3zssceEQmFHRwcAdHV1dXV1DR8+nJFQTWjdunUqlerYsWPFxcVMx8JPHPszoAxy3VVuGfCioqOj9+/fT90vLi4uLS19zpglHpkwmF/c+fPnT58+/Q7Ny5OZ1ICX+euvv7q5ub388suzZ8+eM2fOvHnzamtrmYjUcANeo7Oz8+rVq1etWvU///M/s2fPHj9+fGRkJBORmtL48eMnTZqkW8kUmRwnE9Jg1l3lnEFeFEmSn3766ZIlS+bMmTN//ny6ojONAa/x/v37KSkp69atc3FxoTc0UxrwMltaWmpqaiZPnlxaWpqfn69Wq9999116YzTWgNfY2tr6+eefu7q6enl5PfHEE1Kp9IcffqA3RsQ9nGyyG+S6q9wymItqaGhYuXKlVCpNSUmJjo4mCILeGI014DVmZmY6Ojq2tLTk5ubevHmztbX15MmTc+fOpT1Sowx4mQ4ODgKBYOXKldbW1iNHjoyJifnggw9oD9MoA17jN998U1tbe/bsWWpdtTfffPOTTz7B1b9Q/zhZIfFy3dUBL0qpVL766qsA8NVXX8XExHAuG8EgrtHZ2dnJySknJycnJ6eioqKmpubgwYNMRGqUAS+T6gjUlRT62wdwxYDXePv2bWtra1dXV+rh008/LZPJ6I4ScQ0nExIv113t66JSU1NzcnIA4NChQ42NjWvWrGlvb6+qqqqqqrp37x7TUQ/NgNeYnJz8+W/mzZsXGBi4b98+pqMesgEvc8aMGY6OjuvWrWtubi4rK9u3b98LL7zAdNRDM+A1+vv7t7e3Z2Zm1tXVlZaWHjhwIDAwkOmoEesxPczPQGfOnHn22WfHjh375JNPrly5squri+mITKDXi5owYcKKFStIkkxMTBz7qPXr1zMd8pD1f436Nm7c2PNJrhjwMouKimbNmjV27NinnnoqISGhpaWF0XgNMeA17tmzZ/LkydS/1b/97W9NTU2Mxmsyn3zySUREBNNR8BOH17Ij+bjuKi8vqhtLuEYY3GXev3/fzs7OxsaGzsBMaMBr1Gq1crnc0dHR3t6e5tgQF3E4ISGEEOITTvYhIYQQ4h9MSAghhFgBExJCCCFWwISEEEKIFTAhIYQQYgVMSAghhFgBExJCCCFWwISEEEKIFTAhIYQQYgVMSAghhFgBExJCCCFWwISEEEKIFTAhIYQQYgVMSAghhFgBExJCCCFWwISEEEKIFTAhIYQQYgVMSAghhFgBExJCCCFWwISEEEKIFTAhIYQQYgVMSAghhFgBExJCCCFWwISEEEKIFTAhIYQQYgVMSAghhFjh/wONQJHUlQqE8QAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "clear; clc; close all\n", + "\n", + "h = 0.1;\n", + "x = [0 : h : 1]; n = length(x);\n", + "y = [0 : h : 1]; m = length(y);\n", + "\n", + "% The coefficient matrix A is now m*n by m*n, since that is the total number of points.\n", + "% The right-hand side vector b is m*n by 1.\n", + "A = zeros(m*n, m*n);\n", + "b = zeros(m*n, 1);\n", + "\n", + "u_left = 100;\n", + "u_right = 100;\n", + "u_bottom = 100;\n", + "u_top = 0;\n", + "\n", + "for j = 1 : m\n", + " for i = 1 : n\n", + " % for convenience we calculate all the indices once\n", + " kij = (j-1)*n + i;\n", + " kim1j = (j-1)*n + i - 1;\n", + " kip1j = (j-1)*n + i + 1;\n", + " kijm1 = (j-2)*n + i;\n", + " kijp1 = j*n + i;\n", + " \n", + " if i == 1 \n", + " % this is the left boundary\n", + " A(kij, kij) = 1;\n", + " b(kij) = u_left;\n", + " elseif i == n \n", + " % right boundary\n", + " A(kij, kij) = 1;\n", + " b(kij) = u_right;\n", + " elseif j == 1 \n", + " % bottom boundary\n", + " A(kij, kij) = 1;\n", + " b(kij) = u_bottom;\n", + " elseif j == m \n", + " % top boundary\n", + " A(kij, kij) = 1;\n", + " b(kij) = u_top;\n", + " else\n", + " % these are the coefficients for the interior points,\n", + " % based on the recursion formula\n", + " A(kij, kim1j) = 1;\n", + " A(kij, kip1j) = 1;\n", + " A(kij, kijm1) = 1;\n", + " A(kij, kijp1) = 1;\n", + " A(kij, kij) = -4;\n", + " end\n", + " end\n", + "end\n", + "u = A \\ b;\n", + "\n", + "u_square = reshape(u, [n, m]);\n", + "contourf(x, y, u_square')\n", + "c = colorbar;\n", + "c.Label.String = 'Temperature';" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Neumann (derivative) boundary conditions\n", + "\n", + "So far, we have only discussed cases where we have Dirichlet boundary conditions; in other words, when we have all fixed values at the boundary. Frequently we also encounter Neumann-style boundary conditions, where we have the *derivative* specified at the boundary.\n", + "\n", + "We can handle this in the same way we do for one-dimensional boundary value problems: either with a forward or backward difference (both of which are first-order accurate), or with a central difference using an imaginary point/ghost node (which is second-order accurate). Let's focus on using the central difference, since it is more accurate.\n", + "\n", + "
\n", + "
\n", + " \"ghost\n", + "
Figure: Ghost/imaginary node beyond an upper boundary
\n", + "
\n", + "
\n", + "\n", + "For example, let's say that at the upper boundary, the derivative of temperature is zero:\n", + "\\begin{equation}\n", + "\\left. \\frac{\\partial u}{\\partial y} \\right|_{\\text{boundary}} = 0\n", + "\\end{equation}\n", + "\n", + "Let's consider this boundary condition applied at the point shown, $u_{2,3}$.\n", + "We can approximate this derivative using a central difference:\n", + "\\begin{align}\n", + "\\frac{u_{2,3}}{\\partial y} \\approx \\frac{u_{2,4} - u_{2,2}}{\\Delta x} &= 0 \\\\\n", + "u_{2,4} &= u_{2,2}\n", + "\\end{align}\n", + "This tells us the value of the point above the boundary, $u_{2,4}$; however, this point is a \"ghost\" or imaginary point located outside the boundary, so we don't really care about its value. Instead, we can use this relationship to give us a usable equation for the boundary point, by incorporating it into the normal recursion formula for Laplace's equation:\n", + "\\begin{align}\n", + "u_{1,3} + u_{3,3} + u_{2,4} + u_{2,2} - 4u_{2,3} &= 0 \\\\\n", + "u_{1,3} + u_{3,3} + u_{2,2} + u_{2,2} - 4u_{2,3} &= 0 \\\\\n", + "\\rightarrow u_{1,3} + u_{3,3} + 2 u_{2,2} - 4u_{2,3} &= 0\n", + "\\end{align}\n", + "\n", + "The recursion formula for points along the upper boundary would then become\n", + "\\begin{equation}\n", + "u_{i+1,j} + u_{i-1,j} + 2 u_{i,j-1} - 4 u_{i,j} = 0 \\;.\n", + "\\end{equation}\n", + "\n", + "Now let's try solving the above example, but with $\\frac{\\partial u}{\\partial y} = 0$ at the top boundary and $u = 0$ at the bottom boundary:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "clear; clc; close all\n", + "\n", + "h = 0.1;\n", + "x = [0 : h : 1]; n = length(x);\n", + "y = [0 : h : 1]; m = length(y);\n", + "\n", + "% The coefficient matrix A is now m*n by m*n, since that is the total number of points.\n", + "% The right-hand side vector b is m*n by 1.\n", + "A = zeros(m*n, m*n);\n", + "b = zeros(m*n, 1);\n", + "\n", + "u_left = 100;\n", + "u_right = 100;\n", + "u_bottom = 0;\n", + "\n", + "for j = 1 : m\n", + " for i = 1 : n\n", + " % for convenience we calculate all the indices once\n", + " kij = (j-1)*n + i;\n", + " kim1j = (j-1)*n + i - 1;\n", + " kip1j = (j-1)*n + i + 1;\n", + " kijm1 = (j-2)*n + i;\n", + " kijp1 = j*n + i;\n", + " \n", + " if i == 1 \n", + " % this is the left boundary\n", + " A(kij, kij) = 1;\n", + " b(kij) = u_left;\n", + " elseif i == n \n", + " % right boundary\n", + " A(kij, kij) = 1;\n", + " b(kij) = u_right;\n", + " elseif j == 1 \n", + " % bottom boundary\n", + " A(kij, kij) = 1;\n", + " b(kij) = u_bottom;\n", + " elseif j == m \n", + " % top boundary, using the ghost node + recursion formula\n", + " A(kij, kim1j) = 1;\n", + " A(kij, kip1j) = 1;\n", + " A(kij, kijm1) = 2;\n", + " A(kij, kij) = -4;\n", + " else\n", + " % these are the coefficients for the interior points,\n", + " % based on the recursion formula\n", + " A(kij, kim1j) = 1;\n", + " A(kij, kip1j) = 1;\n", + " A(kij, kijm1) = 1;\n", + " A(kij, kijp1) = 1;\n", + " A(kij, kij) = -4;\n", + " end\n", + " end\n", + "end\n", + "u = A \\ b;\n", + "\n", + "u_square = reshape(u, [n, m]);\n", + "% the \"20\" indicates the number of levels for the contour plot\n", + "contourf(x, y, u_square', 20);\n", + "c = colorbar;\n", + "c.Label.String = 'Temperature';" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Iterative solutions for (very) large problems\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Elapsed time is 8.798152 seconds.\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "clear all; clc;\n", + "\n", + "h = 0.01;\n", + "x = [0 : h : 1]; n = length(x);\n", + "y = [0 : h : 1]; m = length(y);\n", + "\n", + "% The coefficient matrix A is now m*n by m*n, since that is the total number of points.\n", + "% The right-hand side vector b is m*n by 1.\n", + "A = zeros(m*n, m*n);\n", + "b = zeros(m*n, 1);\n", + "\n", + "tic\n", + "\n", + "u_left = 100;\n", + "u_right = 100;\n", + "u_bottom = 100;\n", + "u_top = 0;\n", + "\n", + "for j = 1 : m\n", + " for i = 1 : n\n", + " % for convenience we calculate all the indices once\n", + " kij = (j-1)*n + i;\n", + " kim1j = (j-1)*n + i - 1;\n", + " kip1j = (j-1)*n + i + 1;\n", + " kijm1 = (j-2)*n + i;\n", + " kijp1 = j*n + i;\n", + " \n", + " if i == 1 \n", + " % this is the left boundary\n", + " A(kij, kij) = 1;\n", + " b(kij) = u_left;\n", + " elseif i == n \n", + " % right boundary\n", + " A(kij, kij) = 1;\n", + " b(kij) = u_right;\n", + " elseif j == 1 \n", + " % bottom boundary\n", + " A(kij, kij) = 1;\n", + " b(kij) = u_bottom;\n", + " elseif j == m \n", + " % top boundary\n", + " A(kij, kij) = 1;\n", + " b(kij) = u_top;\n", + " else\n", + " % these are the coefficients for the interior points,\n", + " % based on the recursion formula\n", + " A(kij, kim1j) = 1;\n", + " A(kij, kip1j) = 1;\n", + " A(kij, kijm1) = 1;\n", + " A(kij, kijp1) = 1;\n", + " A(kij, kij) = -4;\n", + " end\n", + " end\n", + "end\n", + "u = A \\ b;\n", + "\n", + "u_square = reshape(u, [n, m]);\n", + "% the \"20\" indicates the number of levels for the contour plot\n", + "contourf(x, y, u_square', 20);\n", + "c = colorbar;\n", + "c.Label.String = 'Temperature';\n", + "\n", + "toc\n" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Elapsed time is 2.197245 seconds.\n", + "Number of iterations: 10762\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "clear all; clc;\n", + "\n", + "h = 0.01;\n", + "x = [0 : h : 1]; n = length(x);\n", + "y = [0 : h : 1]; m = length(y);\n", + "\n", + "% The coefficient matrix A is now m*n by m*n, since that is the total number of points.\n", + "% The right-hand side vector b is m*n by 1.\n", + "A = zeros(m*n, m*n);\n", + "b = zeros(m*n, 1);\n", + "\n", + "tic\n", + "\n", + "u_left = 100;\n", + "u_right = 100;\n", + "u_bottom = 100;\n", + "u_top = 0;\n", + "\n", + "% initial guess\n", + "u = 100*ones(m*n, 1);\n", + "\n", + "% dummy value for residual variable\n", + "epsilon = 1.0; \n", + "\n", + "num = 0;\n", + "while epsilon > 1e-6\n", + " u_old = u;\n", + " \n", + " epsilon = 0;\n", + " for j = 1 : m\n", + " for i = 1 : n\n", + " kij = (j-1)*n + i;\n", + " kim1j = (j-1)*n + i - 1;\n", + " kip1j = (j-1)*n + i + 1;\n", + " kijm1 = (j-2)*n + i;\n", + " kijp1 = j*n + i;\n", + "\n", + " if i == 1 \n", + " % this is the left boundary\n", + " u(kij) = u_left;\n", + " elseif i == n \n", + " % right boundary\n", + " u(kij) = u_right;\n", + " elseif j == 1 \n", + " % bottom boundary\n", + " u(kij) = u_bottom;\n", + " elseif j == m \n", + " % top boundary\n", + " u(kij) = u_top;\n", + " else\n", + " % interior points\n", + " u(kij) = (u(kip1j) + u(kim1j) + u(kijm1) + u(kijp1))/4.0;\n", + " end\n", + " end\n", + " end\n", + " \n", + " epsilon = max(abs(u - u_old));\n", + " num = num + 1;\n", + "end\n", + "\n", + "u_square = reshape(u, [n, m]);\n", + "% the \"20\" indicates the number of levels for the contour plot\n", + "contourf(x, y, u_square', 20);\n", + "c = colorbar;\n", + "c.Label.String = 'Temperature';\n", + "\n", + "toc\n", + "fprintf('Number of iterations: %d\\n', num)" ] }, {

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src images png alt style width px figcaptionfigure figcaption gives using values fixed well b laplace shows physical problems t alpha left steady state any described domain approximate second derivatives both approx index used direction xi yj following known uniform h lets consider problem object recursion formula sides conditions top figurecenter unknown not system +search: u j equation partial x points y boundary begin end frac where grid point delta heat align using example figure center laplaces index n k us transfer value d square formula bmatrix row right temperature style conditions dimensional column nabla img src images png alt width px figcaptionfigure figcaption lets recursion well nine elliptic pde problems difference values matrix vector mathbf mapping into columns m ghost shows also equations finite differences central used direction five stencil consider td above major need array accurate vdots derivative node dimensions left steady state solve approximate directions approx following location general gives h fixed comment: "***PROGRAMMATICALLY GENERATED, DO NOT EDIT. SEE ORIGINAL FILES IN /content***" --- @@ -79,7 +79,7 @@