38 lines
899 B
Matlab
Executable file
38 lines
899 B
Matlab
Executable file
function [A,xyz] = grid3dt(k)
|
|
% GRID3DT : Generate 3-dimensional tetrahedral finite element mesh.
|
|
%
|
|
% [A,xyz] = GRID3DT(k) returns a k^3-by-k^3 symmetric positive definite
|
|
% matrix A of the k-by-k-by-k grid, with cells divided into tetrahedra,
|
|
% and an array xyz of coordinates for the grid points.
|
|
|
|
% 1-d mesh
|
|
a = blockdiags ([-1 14 -1], -1:1, k, k);
|
|
|
|
% glue to laminate 1-d meshes into 2-d meshes
|
|
b = blockdiags ([-1 -1], [0 1], k, k);
|
|
|
|
% 2-d mesh
|
|
aa = blockdiags ([b a b'], -1:1, k, k);
|
|
|
|
% glue to laminate 2-d meshes into 3-d meshes
|
|
bb = blockdiags ([b b'], [0 1], k, k);
|
|
|
|
% 3-d mesh
|
|
A = blockdiags ([bb aa bb'], -1:1, k, k);
|
|
A = diag(diag(A)) - A;
|
|
|
|
|
|
% xyz coordinates of nodes
|
|
xyz = zeros(k^3,3);
|
|
x = ones(k,1) * (1:k);
|
|
y = x';
|
|
j = 1;
|
|
for i = 1:k
|
|
slab = j:j+k^2-1;
|
|
xyz(slab,1) = x(:);
|
|
xyz(slab,2) = y(:);
|
|
xyz(slab,3) = i * ones(k^2,1);
|
|
j = j + k^2;
|
|
end
|
|
|
|
end
|