addScalarBC first part almost done

Gral is changed by Scalar, Per by Periodic and added License Identifier. However, there are divGral, gradGral and lapGral operator that still need to be resolved

Author: mdumett

examples/matlab/elliptic1DGralNonPerBC.m

@@ -22,7 +22,7 @@
 v = [0;0];
 A = - lapGral1D(k,m,dx,dc,nc);
 b = ones(size(A,2),1);
-[A0,b0] = addGralBC1D(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/elliptic1DGralPerBC.m

@@ -23,7 +23,7 @@
 v = [0;0];
 A = - lapGral1D(k,m,dx,dc,nc);
 b = 4*pi^2 * sin(2*pi*xc);
-[A0,b0] = addGralBC1D(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/elliptic2DXPerYDirichlet.m

@@ -3,7 +3,7 @@
 % -(u_xx + u_yy) = 2 sin(2 pi x) (1+2 pi^2 y(1-y)), 0 < x,y < 1, u(x,0) = 0 = u(x,1)
 % exact solution: u(x) = y(1-y)sin(2 pi x)
 % ===================================================
-% example that uses addGralBC2D
+% example that uses addScalarBC2D
 %
 close all; clc;
 
@@ -31,7 +31,7 @@
 A = - lapGral2D(k,m,dx,n,dy,dc,nc);
 b = 2*sin(2*pi*X).*(1+2*pi^2*Y.*(1-Y));
 b = reshape(b,[],1);
-[A0, b0] = addGralBC2D(A, b, k, m, dx, n, dy, dc, nc, v);
+[A0, b0] = addScalarBC2D(A, b, k, m, dx, n, dy, dc, nc, v);
 ua = A0\b0; % approximate solution (there are infinity solutions) 
 ua = reshape(ua,m,n+2);
 

examples/matlab/elliptic3DXDirichletYPerZNeumann.m

@@ -39,7 +39,7 @@
 A = - lapGral3D(k,m,dx,n,dy,o,dz,dc,nc);
 b = 2*sin(2*pi*Y).*Z.*(1+2*pi^2*X.*(1-X));
 b = reshape(b,[],1);
-[A0,b0] = addGralBC3D(A,b,k,m,dx,n,dy,o,dz,dc,nc,v);
+[A0,b0] = addScalarBC3D(A,b,k,m,dx,n,dy,o,dz,dc,nc,v);
 ua = A0\b0; % approximate solution
 ua = reshape(ua,m+2,n,o+2);
 

examples/matlab/elliptic3DXDirichletYPerZPer.m

@@ -38,7 +38,7 @@
 A = - lapGral3D(k,m,dx,n,dy,o,dz,dc,nc);
 b = 16*(1-X.^2).*cos(4*X) - 16*X.*sin(4*X) + 2*(cos(4*X)+sin(2*Y)+sin(4*Z)) + (1-X.^2).*(4*sin(2*Y) + 16*sin(4*Z));
 b = reshape(b,[],1);
-[A0,b0] = addGralBC3D(A,b,k,m,dx,n,dy,o,dz,dc,nc,v);
+[A0,b0] = addScalarBC3D(A,b,k,m,dx,n,dy,o,dz,dc,nc,v);
 ua = A0\b0; % approximate solution
 ua = reshape(ua,m+2,n,o);
 

src/matlab/addGralBC1D.m src/matlab/addScalarBC1D.msrc/matlab/addGralBC1D.m renamed to src/matlab/addScalarBC1D.m

@@ -1,4 +1,4 @@
-function [A, b] = addGralBC1D(A, b, k, m, dx, dc, nc, v)
+function [A, b] = addScalarBC1D(A, b, k, m, dx, dc, nc, v)
 % Separates cases non-periodic and periodic for dealing with boundary data
 %
 % Parameters:
@@ -15,6 +15,13 @@
 %        dc : a0 (2x1 vector for left and right vertices, resp.)
 %        nc : b0 (2x1 vector for left and right vertices, resp.)
 %         v : g (2x1 vector for left and right vertices, resp.)
+%
+% ----------------------------------------------------------------------------
+% SPDX-License-Identifier: GPL-3.0-or-later
+% © 2008-2024 San Diego State University Research Foundation (SDSURF).
+% See LICENSE file or https://www.gnu.org/licenses/gpl-3.0.html for details.
+% ----------------------------------------------------------------------------
+%
 
     % verify bc sizes and square linear system
     assert(all(size(dc) == [2 1]), 'dc is a 2x1 vector');
@@ -39,8 +46,8 @@
         % remove first and last coefficients of right-hand-side vector b
         b(vec) = 0;
 
-        [Abcl,Abcr] = addGralBC1Dlhs(k, m, dx, dc, nc);
+        [Abcl,Abcr] = addScalarBC1Dlhs(k, m, dx, dc, nc);
         A = A + Abcl + Abcr;
-        b = addGralBC1Drhs(b, v, vec);
+        b = addScalarBC1Drhs(b, v, vec);
     end
 end

src/matlab/addGralBC1Dlhs.m src/matlab/addScalarBC1Dlhs.msrc/matlab/addGralBC1Dlhs.m renamed to src/matlab/addScalarBC1Dlhs.m

@@ -1,4 +1,4 @@
-function [Al, Ar] = addGralBC1Dlhs(k, m, dx, dc, nc)
+function [Al, Ar] = addScalarBC1Dlhs(k, m, dx, dc, nc)
 % This functions uses geometry and boundary type conditions to create
 % modifications of matrix A associated to each of the boundary faces.
 %
@@ -13,6 +13,13 @@
 %        dx : Step size
 %        dc : Dirichlet coefficient (2x1 vector for left and right vertices, resp.)
 %        nc : Neumann coefficient (2x1 vector for left and right vertices, resp.)
+%
+% ----------------------------------------------------------------------------
+% SPDX-License-Identifier: GPL-3.0-or-later
+% © 2008-2024 San Diego State University Research Foundation (SDSURF).
+% See LICENSE file or https://www.gnu.org/licenses/gpl-3.0.html for details.
+% ----------------------------------------------------------------------------
+%
 
     % Dirichlet coefficient
     Al = sparse(m+2, m+2);

src/matlab/addGralBC1Drhs.m src/matlab/addScalarBC1Drhs.msrc/matlab/addGralBC1Drhs.m renamed to src/matlab/addScalarBC1Drhs.m

@@ -1,4 +1,4 @@
-function b = addGralBC1Drhs(b, v, vec)
+function b = addScalarBC1Drhs(b, v, vec)
 % This function uses the non-periodic boundary condition type of each vertex 
 % and the rhs b values associated to left, and right vertices to modify the rhs vector b.
 %
@@ -10,6 +10,13 @@
 %         b : Right hand side without boundary conditions added
 %         v : value (2x1 vector for left and right vertices, resp.)
 %       vec : vector with indices of rhs associated to bc
+%
+% ----------------------------------------------------------------------------
+% SPDX-License-Identifier: GPL-3.0-or-later
+% © 2008-2024 San Diego State University Research Foundation (SDSURF).
+% See LICENSE file or https://www.gnu.org/licenses/gpl-3.0.html for details.
+% ----------------------------------------------------------------------------
+%
 
     % rhs for non-periodic boundary conditions
     b(vec) = v; 

src/matlab/addGralBC2D.m src/matlab/addScalarBC2D.msrc/matlab/addGralBC2D.m renamed to src/matlab/addScalarBC2D.m

@@ -1,4 +1,4 @@
-function [A, b] = addGralBC2D(A, b, k, m, dx, n, dy, dc, nc, v)
+function [A, b] = addScalarBC2D(A, b, k, m, dx, n, dy, dc, nc, v)
 % This function assumes that the unknown u, which represents the discrete
 % solution the continuous second-order 2D PDE operator 
 %                                   L U = f, 
@@ -61,6 +61,13 @@
 %        dc : a0 (4x1 vector for left, right, bottom, top boundaries, resp.)
 %        nc : b0 (4x1 vector for left, right, bottom, top boundaries, resp.)
 %         v : g (4x1 vector of arrays for left, right, bottom, top boundaries, resp.)
+%
+% ----------------------------------------------------------------------------
+% SPDX-License-Identifier: GPL-3.0-or-later
+% © 2008-2024 San Diego State University Research Foundation (SDSURF).
+% See LICENSE file or https://www.gnu.org/licenses/gpl-3.0.html for details.
+% ----------------------------------------------------------------------------
+%
 
     % verify bc sizes and square linear system
     cellsz = cellfun(@size,v,'uni',false);
@@ -93,7 +100,7 @@
     rl = 0; rr = 0; rb = 0; rt = 0; % periodic case
 
     % get modifications of A for left, right, bottom, top edges, resp.
-    [Abcl,Abcr,Abcb,Abct] = addGralBC2Dlhs(k, m, dx, n, dy, dc, nc);
+    [Abcl,Abcr,Abcb,Abct] = addScalarBC2Dlhs(k, m, dx, n, dy, dc, nc);
 
     % get rhs entries affected by bcs for left, right, bottom, top edges, resp.
     if ~isempty(qrl)    
@@ -126,6 +133,6 @@
 
     % update b with boundary information
     if ~(isempty(qrl) && isempty(qbt))  
-        b = addGralBC2Drhs(b, dc, nc, v, rl, rr, rb, rt);
+        b = addScalarBC2Drhs(b, dc, nc, v, rl, rr, rb, rt);
     end
 end

src/matlab/addGralBC2Dlhs.m src/matlab/addScalarBC2Dlhs.msrc/matlab/addGralBC2Dlhs.m renamed to src/matlab/addScalarBC2Dlhs.m

@@ -1,4 +1,4 @@
-function [Abcl,Abcr,Abcb,Abct] = addGralBC2Dlhs(k, m, dx, n, dy, dc, nc)
+function [Abcl,Abcr,Abcb,Abct] = addScalarBC2Dlhs(k, m, dx, n, dy, dc, nc)
 % This functions uses geometry and boundary type conditions to create
 % modifications of matrix A associated to each of the boundary edges.
 %
@@ -17,6 +17,13 @@
 %        dy : Horizontal cell size
 %        dc : a0 (4x1 vector for left, right, bottom, top boundaries, resp.)
 %        nc : b0 (4x1 vector for left, right, bottom, top boundaries resp.)
+%
+% ----------------------------------------------------------------------------
+% SPDX-License-Identifier: GPL-3.0-or-later
+% © 2008-2024 San Diego State University Research Foundation (SDSURF).
+% See LICENSE file or https://www.gnu.org/licenses/gpl-3.0.html for details.
+% ----------------------------------------------------------------------------
+%
 
     Abcl = 0; Abcr = 0; Abcb = 0; Abct = 0; % periodic case
 
@@ -26,7 +33,7 @@
 
     % 2D boundary operator
     if ~isempty(qrl)    
-        [Abcl0,Abcr0] = addGralBC1Dlhs(k, m, dx, dc(1:2,1), nc(1:2,1));
+        [Abcl0,Abcr0] = addScalarBC1Dlhs(k, m, dx, dc(1:2,1), nc(1:2,1));
         if isempty(qbt)
             In = speye(n);
         else
@@ -40,7 +47,7 @@
     end
 
     if ~isempty(qbt)    
-        [Abcb0,Abct0] = addGralBC1Dlhs(k, n, dy, dc(3:4,1), nc(3:4,1));
+        [Abcb0,Abct0] = addScalarBC1Dlhs(k, n, dy, dc(3:4,1), nc(3:4,1));
         if isempty(qrl) 
             Im = speye(m);
         else