Merge pull request #117 from csrc-sdsu/addBCs3_fixed

Add Periodic Boundary Conditions, operators, and examples ( Add BCs3 fixed )

Author: mdumett

examples/matlab/elliptic1DHomogeneousDirichlet.m

@@ -3,7 +3,7 @@
 % - u'' = 1, 0 < x < 1, u(0) = 0, u(1) = 0
 % exact solution: u(x) = x(1-x)/2
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -22,7 +22,7 @@
 v = [0;0];
 A = - lap(k,m,dx);
 b = ones(size(A,2),1);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DLeftDirichletRightNeumann.m

@@ -3,7 +3,7 @@
 % - u'' = 1, 0 < x < 1, u'(0) = 0, u(1) = 0
 % exact solution: u(x) = (1 - x^2)/2
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -22,7 +22,7 @@
 v = [0;0];
 A = - lap(k,m,dx);
 b = ones(size(A,2),1);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DLeftDirichletRightRobin.m

@@ -9,7 +9,7 @@
 % b = 400, c = 10, d = 15
 % So, E = (pi - 3985)/401, F = 10
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -28,7 +28,7 @@
 v = [10;15];
 A = - lap(k,m,dx);
 b = pi^2 * sin(pi*xc);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DLeftNeumannRightNeumann.m

@@ -5,7 +5,7 @@
 % Compatibility condition: 
 % integ(f) = integ(-u'') = - u'(1) + u'(0) 
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -24,7 +24,7 @@
 v = [0;0];
 A = - lap(k,m,dx);
 b = xc - 0.5*ones(size(A,2),1);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution (there are infinity solutions)
 ua = ua - ua(1) + ue(1); % shifting ua to match ue(1) with ua(1)
 

examples/matlab/elliptic1DLeftNeumannRightRobin.m

@@ -9,7 +9,7 @@
 % b = 400, c = 10, d = 15
 % So, E = - (10 + pi), F = (402 pi + 4025)/400
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -28,7 +28,7 @@
 v = [10;15];
 A = - lap(k,m,dx);
 b = pi^2 * sin(pi*xc);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DLeftRobinRightRobin.m

@@ -11,7 +11,7 @@
 % a = -200, b = 400, c = 10, d = 15
 % So, E = (35 - pi)/403, F = (402 pi - 3995)/80600
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -30,7 +30,7 @@
 v = [10;15];
 A = - lap(k,m,dx);
 b = pi^2 * sin(pi*xc);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DNonHomogeneousDirichlet.m

@@ -3,7 +3,7 @@
 % - u'' = 1, 0 < x < 1, u(0) = 1/2, u(1) = 1/2
 % exact solution: u(x) = (-x^2 + x + 1)/2
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -22,7 +22,7 @@
 v = [1/2;1/2];
 A = - lap(k,m,dx);
 b = ones(size(A,2),1);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DNonPeriodicBC.m

@@ -0,0 +1,34 @@
+% ====================== Test 1 =====================
+% 1D Poisson BVP: Dirichlet, Dirichlet Homogeneous BC
+% - u'' = 1, 0 < x < 1, u(0) = 0, u(1) = 0
+% exact solution: u(x) = x(1-x)/2
+% ===================================================
+% example that uses addScalarBC1D with non-periodic boundary conditions
+%
+close all; clc;
+
+addpath('../../src/matlab');
+
+k = 2;
+bvp = 1;
+m = 2*k+1; 
+dx = 1/m;
+% centers and vertices
+xc = [0 dx/2:dx:1-dx/2 1]';
+t = '- u" = 1, 0 < x < 1, u(0) = 0, u(1) = 0, with exact solution u(x) = x(1-x)/2';
+ue = 0.5*xc.*(1-xc); % exact solution
+dc = [1;1];
+nc = [0;0];
+v = [0;0];
+A = - lap(k,m,dx,dc,nc);
+b = ones(size(A,2),1);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
+ua = A0\b0; % approximate solution
+
+% plot
+figure(bvp)
+plot(xc,ue,'b*',xc,ua,'ro');
+title(t); %,'interpreter','latex');
+xlabel('x');
+ylabel('u');
+legend({'exact','approx'});

examples/matlab/elliptic1DPeriodicBC.m

@@ -3,7 +3,7 @@
 % - u'' = 4 pi^2 sin(2 pi x), 0 < x < 1, u(0) = u(1), u'(0) = u'(1)
 % exact solution: u(x) = sin(2 pi x) + constant
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D with periodic boundary conditions
 % testing 1D bc
 %
 close all; clc;
@@ -15,15 +15,15 @@
 m = 20; 
 dx = 1/m;
 % centers and vertices
-xc = [0 dx/2:dx:1-dx/2 1]';
+xc = (dx/2:dx:1-dx/2)';
 t = '- u" = 4 pi^2 sin(2 pi x), 0 < x < 1, u(0) = u(1), u''(0) = u''(1), with exact solution u(x) = sin(2 pi x) + constant';
 ue = sin(2*pi*xc); % exact solution
 dc = [0;0];
 nc = [0;0];
 v = [0;0];
-A = - lap(k,m,dx);
+A = - lap(k,m,dx,dc,nc);
 b = 4*pi^2 * sin(2*pi*xc);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution (there are infinity solutions) 
 ua = ua - ua(1) + ue(1); % shifting ua to match ue(1) with ua(1)
 

examples/matlab/elliptic1DaddBC.m examples/matlab/elliptic1DaddScalarBC.mexamples/matlab/elliptic1DaddBC.m renamed to examples/matlab/elliptic1DaddScalarBC.m

@@ -1,4 +1,6 @@
 % Solves the 1D Poisson's equation with Robin boundary conditions
+% same example as elliptic1D that uses addScalarBC1D
+%
 
 clc
 close all
@@ -20,7 +22,7 @@
 
 L = lap(k, m, dx);  % 1D Mimetic laplacian operator
 U = exp(grid)'; % RHS
-[L0,U0] = addBC1D(L,U,k,m,dx,dc,nc,v); % add BC to system
+[L0,U0] = addScalarBC1D(L,U,k,m,dx,dc,nc,v); % add BC to system
 U0 = L0\U0;  % Solve a linear system of equations
 
 % Plot result