Adding KP-I example to the example folder for MOLE

examples/matlab/KP-I.m

@@ -0,0 +1,99 @@
+clear;
+clc;
+
+% path to mimetic operators
+addpath('C:\Users\littl\sdsu\comp670\calderonTE-master\calderonTE\src\matlab');
+
+% Parameters
+k = 2;          % Order of accuracy
+m = 99;          % Number of cells along x-axis
+n = m;          % Number of cells along y-axis
+
+a = 1;          % Used for solution
+b = 0.5;        % Used for solution
+
+% Spatial Discretization
+x_1 = -10;      
+x_2 = 10;
+y_1 = -10;
+y_2 = 10;
+dx = (x_2 - x_1) / m;
+dy = (y_2 - y_1) / n;
+dt = dx;
+
+% Staggered grid
+xgrid = [x_1, x_1+dx/2:dx:x_2-dx/2, x_2];
+ygrid = [y_1, y_1+dy/2:dy:y_2-dy/2, y_2];
+
+num_steps = 1;
+tgrid = 0:dt:(num_steps * dt);
+
+% Mesh-grid implementation
+[Y, X, T] = meshgrid(ygrid, xgrid, tgrid);
+
+% Interpolation operators
+I = interpolCentersToFacesD2D(k,m,n);
+Ix = I(1:(n+2)*(m+2), 1:n*(m+1));
+Iy = I((n+2)*(m+2)+1:end, n*(m+1)+1:end);
+
+
+% Mimetic operators
+G = grad2D(k, m, dx, n, dy);
+Gx = G(1:end/2, :); % Gradient in x-direction (size: (m+1) x (m+2))
+Gy = G(end/2+1:end,:); % Gradient in y-direction
+
+D = div2D(k, m, dx, n, dy);
+Dx = D(:, 1:end/2); % Divergence in x-direction
+Dy = D(:,end/2+1:end); % Divergence in y-direction
+
+
+Lyy = Dy*Gy;
+Lxx = Dx*Gx;
+Lxxxx = Lxx*Lxx;
+Lx = Ix*Gx;
+
+% Initial condition
+num = - (X + a*Y + 3*T*(a^2 - b^2)).^2 + b^2*(Y + 6*a*T).^2 + (1/b^2);
+den = ( (X + a*Y + 3*T*(a^2 - b^2)).^2 + b^2*(Y + 6*a*T).^2 + (1/b^2) ).^2;
+u0 = 4 * num ./ den; %exact solution
+
+u = u0(:,:,1);            
+u = reshape(u,[],1);     % Vectorize [49x1]
+
+% Boundary conditions (Dirichlet: u=0 at all boundaries)
+dc = [1; 1; 1; 1];     % Dirichlet flags
+nc = [0; 0; 0; 0];     % Neumann flags
+
+v = cell(4,1);
+v{1} = zeros(n,1);     % Left BC
+v{2} = zeros(n,1);     % Right BC
+v{3} = zeros(m+2,1);   % Bottom BC
+v{4} = zeros(m+2,1);   % Top BC
+
+% Time-stepping
+for t = 1:num_steps
+
+    u_at_faces = Ix.' * u;
+    M1 = Ix * diag(u_at_faces) * Gx;
+
+    % Build system matrix
+    A = Lx - dt*(6*M1 + Lxxxx - 3*Lyy);
+    b = u + dt*(6*M1 + Lxxxx - 3*Lyy)*u;
+
+    % Apply boundary conditions
+    [A0, b0] = addBC2D(A, b, k, m, dx, n, dy, dc, nc, v);
+
+    % Solve
+    u = A0 \ b0;
+
+    u_2d = reshape(u, m+2, n+2);
+
+
+    if t <= size(X,3)
+        surf(X(:,:,t), Y(:,:,t), u_2d);
+        title(['KP-I Solution at t = ', num2str(t)]);
+        xlabel('x'); ylabel('y'); zlabel('u');
+        colorbar;
+        drawnow;
+    end
+end