5th semester files

5th-Semester-Fall-2023/EEMAGS/Labs/Lab-06/cemLaplace03.m

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+% cemLaplace01.m
+
+% Solution of Laplace's equation
+clear
+clf
+tic
+
+% INPUTS  ================================================================
+
+% Number of XY grid points (integer)
+     Nx = 5;
+% Range for X and Y values  [minX maxX minY maxY minZ maxZ]
+     XY = [0 5];
+% Boundary potential
+     V0 = 100;
+% tolerance for ending iterations
+    tol = 0.1;
+
+% SETUP ==================================================================
+
+    V = zeros(Nx,1);
+    minX = XY(1);  maxX = XY(2);
+    x = linspace(minX, maxX,Nx);
+    hx = x(2) - x(1);
+    V(1) = V0;  V(Nx) = 0;
+
+% CALCULATIONS ===========================================================
+
+% dSum difference in sum of squares  /  n  number of iterations
+dSum = 10; n = 0;
+while dSum > tol
+    sum1 =  sum(sum(V.^2));
+
+    for nx = 2: Nx-1
+           V(nx) = 0.5*(V(nx+1) + V(nx-1));
+    end
+    sum2 =  sum(sum(V.^2));
+    dSum = abs(sum2 - sum1);
+    n = n+1;
+end
+
+% exact solution
+VT = -(V0/maxX)*x + V0;
+
+% electric field
+E = -gradient(V,hx);
+
+% GRAPHICS ===============================================================
+
+figure(1)
+    set(gcf,'units','normalized','position',[0.05 0.2 0.3 0.4]);
+    subplot(2,1,1)
+    plot(x,V,'b','lineWidth',2);
+    hold on
+    plot(x,VT,'r','lineWidth',2);
+    %set(gca,'xLim',[minX, maxX]);
+    %set(gca,'yLim',[minY, maxY]);
+    xlabel('x  [ m ]'); ylabel('V  [ V ]');
+    set(gca,'fontsize',14)
+
+    subplot(2,1,2)
+    plot(x,E,'b','lineWidth',2)
+    set(gca,'yLim',[0, 25]);
+    xlabel('x  [ m ]'); ylabel('E  [ V / m ]');
+    set(gca,'fontsize',14)
+
+ % =======================================================================
+    toc