28-Jul-2021 03:14:32 fem2d_heat_sparse_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) Test fem2d_heat_sparse(). 28-Jul-2021 03:14:32 FEM2D_HEAT_SPARSE: MATLAB/Octave version 9.9.0.1467703 (R2020b) A version of FEM2D_HEAT using MATLAB's sparse matrix storage, factor and solve facilities. Finite element solution of the time dependent heat equation on an arbitrary triangulated region D in 2 dimensions.n Ut - Uxx - Uyy + K(x,y,t) * U = F(x,y,t) in D; U = G(x,y,t) on boundary; U = H(x,y,t) at initial time. The finite element method is used, with 6 node quadratic triangular elements ("T6"). The time derivative is approximated using the backward Euler formula. Current status: * Time step information currently set internally! * Would be easy to do linear triangles as well. * Do you want ability to compare to an exact solution? Node file is "square_nodes.txt". Element file is "square_elements.txt". Number of nodes = 81 First 10 nodes Row: 1 2 Col 1 0.000000 0.000000 2 0.125000 0.000000 3 0.250000 0.000000 4 0.375000 0.000000 5 0.500000 0.000000 6 0.625000 0.000000 7 0.750000 0.000000 8 0.875000 0.000000 9 1.000000 0.000000 10 0.000000 0.125000 Element order = 6 Number of elements = 32 First 10 elements Row: 1 2 3 4 5 6 Col 1 1 19 3 10 11 2 2 21 3 19 12 11 20 3 3 21 5 12 13 4 4 23 5 21 14 13 22 5 5 23 7 14 15 6 6 25 7 23 16 15 24 7 7 25 9 16 17 8 8 27 9 25 18 17 26 9 19 37 21 28 29 20 10 39 21 37 30 29 38 Quadrature order = 3 Initial time = 0.000000 Final time = 0.500000 Step size = 0.050000 Number of steps = 10 TRIANGULATION_ORDER6_ADJ_COUNT returns NZ_NUM = 801 FEM2D_HEAT_SPARSE: Normal end of execution. 28-Jul-2021 03:14:33 fem2d_heat_sparse_test(): Normal end of execution. 28-Jul-2021 03:14:33