copied the templates

mgrid_2/tet_elem.m

@@ -0,0 +1,29 @@
+%% 3D: P1 element matrix tetrahedral element
+
+x = sym('x', [4 1]);
+y = sym('y', [4 1]);
+z = sym('z', [4 1]);
+
+A = [ones(4,1), x , y, z ];
+
+detA = det(A);
+Ainv = inv(A);
+T = Ainv*detA;      %  T/detA == Ainv
+
+grad_phi1=T(2:4,1)  %  /detA
+grad_phi2=T(2:4,2)  %  /detA
+grad_phi3=T(2:4,3)  %  /detA
+grad_phi4=T(2:4,4)  %  /detA
+
+%% Laplace 3D
+%   - laplace u = rhs
+clear
+syms x y z
+% u(x,y,z) = x^2*sin(pi*y)*cos(pi*z)
+u(x,y,z) = (x^2*(2*x - 3))*cos(pi*y)*cos(pi*z)
+
+gu(x,y,z) = simplify(gradient(u));
+% rhs = -diff(u,2)
+% rhs = -divergence(gradient(u))
+rhs = -laplacian(u,[x,y,z]);
+rhs(x,y,z) = simplify(rhs)