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Test_Code1_For_Pdf.m
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Test_Code1_For_Pdf.m
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function runFEMSimulation()
clc;
clear;
close all;
x = [0, 0.001, 0.002, 0.003, 0.004, 0.005, 0.006, 0.007, 0.008, ...
0.009, 0.01, 0.011, 0.012, 0.013, 0.014, 0.015, 0.016, 0.017, ...
0.018, 0.019, 0.020, 0.021, 0.022, 0.023, 0.024, 0.025, ...
0.027, 0.030, 0.035, 0.040, 0.050, 0.060, 0.070, 0.080, 0.090, 0.1];
y = [0, 0.001, 0.002, 0.003, 0.004, 0.005, 0.007, 0.01, 0.012, 0.015, ...
0.016, 0.017, 0.018, 0.019, 0.02, 0.022, 0.025, 0.027, 0.030, 0.032, ...
0.035, 0.037, 0.040, 0.045, 0.050, 0.060, 0.070, 0.080, 0.090, 0.1, 0.12];
[X, Y, NL, NDP, VAL] = generateMeshgridAndBoundaryConditions(x, y);
[V, result] = calculateVoltage(NL, X, Y, NDP, VAL);
visualizeResults(result, x, y);
end
function [X, Y, NL, NDP, VAL] = generateMeshgridAndBoundaryConditions(x, y)
Nodes = zeros(length(y), length(x));
XX = zeros(1, length(y) * length(x));
YY = zeros(1, length(y) * length(x));
NDP = zeros(1, length(y) * length(x));
VAL = zeros(1, length(y) * length(x));
n = 0;
m = 0;
for j = 1:length(y)
for i = 1:length(x)
if (x(i) < 0.01) && ((y(j) < 0.015) && (y(j) > 0.005))
continue;
end
n = n + 1;
Nodes(j, i) = n;
XX(n) = x(i);
YY(n) = y(j);
if (y(j) == 0) || (x(i) == 0.1) || (y(j) == 0.12)
m = m + 1;
NDP(m) = n;
VAL(m) = 0;
elseif ((y(j) == 0.005) && (x(i) <= 0.01)) || ((y(j) == 0.015) && (x(i) <= 0.01))
m = m + 1;
NDP(m) = n;
VAL(m) = 220;
elseif (x(i) == 0.01) && ((y(j) < 0.015) && (y(j) > 0.005))
m = m + 1;
NDP(m) = n;
VAL(m) = 220;
end
end
end
X = XX(1:n);
Y = YY(1:n);
NDP = NDP(1:m);
VAL = VAL(1:m);
[r, c] = size(Nodes);
I = 0;
NN = zeros((r-1)*(c-1)*2, 3);
for i = 1:r-1
for j = 1:c-1
I = I + 2;
NN(I, :) = [Nodes(i, j), Nodes(i, j + 1), Nodes(i + 1, j)];
NN(I + 1, :) = [Nodes(i, j + 1), Nodes(i + 1, j + 1), Nodes(i + 1, j)];
end
end
NL = NN(~any(NN == 0, 2), :);
end
function [V, result] = calculateVoltage(NL, X, Y, NDP, VAL)
NE = size(NL, 1);
ND = length(X);
NP = length(NDP);
B = zeros(ND, 1);
C = zeros(ND, ND);
for I = 1:NE
K = NL(I, :);
XL = X(K);
YL = Y(K);
P = [YL(2) - YL(3); YL(3) - YL(1); YL(1) - YL(2)];
Q = [XL(3) - XL(2); XL(1) - XL(3); XL(2) - XL(1)];
AREA = 0.5 * abs(P(2) * Q(3) - Q(2) * P(3));
CE = (P * P' + Q * Q') / (4.0 * (AREA + eps));
for J = 1:3
IR = K(J);
IFLAG1 = false;
if any(IR == NDP)
C(IR, IR) = 1.0;
B(IR) = VAL(NDP == IR);
IFLAG1 = true;
end
if ~IFLAG1
for L = 1:3
IC = K(L);
if any(IC == NDP)
B(IR) = B(IR) - CE(J, L) * VAL(NDP == IC);
else
C(IR, IC) = C(IR, IC) + CE(J, L);
end
end
end
end
end
if rank(C) < ND
error('The global stiffness matrix is singular. Check boundary conditions and mesh.');
end
V = C \ B;
N = (1:ND)';
result = [N, X', Y', V];
end
function visualizeResults(result, x, y)
X220 = result(result(:, 4) == 220, 2);
Y220 = result(result(:, 4) == 220, 3);
X0 = result(result(:, 4) == 0, 2);
Y0 = result(result(:, 4) == 0, 3);
[X220, Y220] = removeZeroCoordinates(X220, Y220);
[X0, Y0] = removeZeroCoordinates(X0, Y0);
[xx, yy] = meshgrid(x, y);
v = griddata(result(:, 2), result(:, 3), result(:, 4), xx, yy);
figure;
plot(X220, Y220, 'r', 'linewidth', 5);
hold on;
plot(X0, Y0, 'b', 'linewidth', 5);
contour(xx, yy, v, 30);
xlabel('x', 'fontsize', 20);
ylabel('y', 'fontsize', 20);
set(gca, 'fontsize', 20);
axis equal;
end
function [coord1Out, coord2Out] = removeZeroCoordinates(coord1, coord2)
if length(coord1) ~= length(coord2)
error('The input coordinate vectors must have the same length.');
end
mask = ~(coord1 == 0 & coord2 == 0);
coord1Out = coord1(mask);
coord2Out = coord2(mask);
end