wathen_matrix_test

wathen_matrix_test, an Octave code which calls wathen_matrix(), which compares storage schemes (full, banded, sparse triplet, sparse) and solution strategies (A\x, Linpack, conjugate gradient (CG)) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Related Data and Programs:

wathen_matrix, an Octave code which compares storage schemes (full, banded, sparse triplet, sparse) and solution strategies (A\x, linpack, conjugate gradient (CG)) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).

Source Code:

• wathen_matrix_test.m, calls all the tests;
• wathen_matrix_test.sh, runs all the tests;
• wathen_matrix_test.txt, the output file.

• wathen_test01.m, sets up and solves a system with wathen_ge();
• wathen_test02.m, sets up and solves a system with wathen_gb();
• wathen_test03.m, sets up and solves a system with wathen_sparse;
• wathen_test04.m, sets up and solves a system with wathen_davis;
• wathen_test05.m, reports the storage needed for the various formats;
• wathen_test06.m, times wathen_ge() for various problem sizes;
• wathen_test07.m, times wathen_banded for various problem sizes.
• wathen_test08.m, compares timings for GB, GE, sparse and davis on small problems;
• wathen_test09.m, compares timings for sparse and davis on larger problems;
• wathen_test10.m, uses wathen_ge() + cg_ge() for an iterative solution;
• wathen_test11.m, uses WATHEN_ST + CG_ST for an iterative solution;
• wathen_test115.m, uses WATHEN_BANDED + CG_BANDED for an iterative solution;
• wathen_test12.m, uses WATHEN_DAVIS + CG_SPARSE for an iterative solution;
• wathen_test13.m, uses spy() to display the sparsity of Wathen matrices of various sizes;
• wathen_spy.png, spy plots for wathen(1,1) through wathen(6,6).
• wathen_xy_test.m, get (X,Y) coordinates of nodes and plot the grid.
• wathen_xy_test.png