Wed Oct 8 09:15:49 2025 wathen_matrix_test(): python version: 3.10.12 numpy version: 1.26.4 Test wathen_matrix(). wathen_test01(): Assemble, factor and solve a Wathen system defined by wathen_ge(). Elements in X direction NX = 4 Elements in Y direction NY = 4 Number of elements = 16 Number of nodes N = 65 Norm of solution error is 2.70094e-15 wathen_test02(): Assemble, factor and solve a Wathen system defined by wathen_csc(). Elements in X direction NX = 4 Elements in Y direction NY = 4 Number of elements = 16 Number of nodes N = 65 Norm of solution error is 7.155411012286914e-14 wathen_test03(): For various problem sizes, time the assembly and factorization of a Wathen system using wathen_ge(). NX Elements Nodes Storage Assembly Factor Error 1 1 8 64 1.30e-04 1.17e-04 6.38e-16 2 4 21 441 4.53e-04 1.15e-04 1.32e-15 4 16 65 4225 1.74e-03 1.95e-04 3.29e-15 8 64 225 50625 7.27e-03 1.69e-03 4.76e-15 16 256 833 693889 3.33e-02 1.54e-01 9.77e-15 32 1024 3201 10246401 1.29e-01 4.68e-01 1.91e-14 wathen_test04(): For various problem sizes, time the assembly and factorization of a Wathen system using the wathen_csc() function. NX Elements Nodes Assembly Factor Error 1 1 8 4.11e-04 9.30e-05 7.60e-16 2 4 21 5.51e-04 9.64e-05 3.81e-15 4 16 65 1.50e-03 2.01e-04 9.02e-15 8 64 225 5.25e-03 7.60e-04 1.14e-14 16 256 833 2.02e-02 3.48e-03 2.42e-14 32 1024 3201 5.06e-02 1.90e-02 3.58e-14 64 4096 12545 1.76e-01 9.15e-02 1.36e-13 wathen_test05(): For various problem sizes, time the assembly and factorization of a Wathen system wathen_ge() and wathen_csc(). NX Elements Nodes Assembly Factor Error wathen_ge() 1 1 8 1.56e-04 1.74e-04 9.24e-16 wathen_csc() 1 1 8 4.00e-04 9.04e-05 2.79e+00 wathen_ge() 2 4 21 5.06e-04 1.19e-04 1.24e-15 wathen_csc() 2 4 21 6.01e-04 1.04e-04 8.98e-01 wathen_ge() 4 16 65 1.94e-03 2.18e-04 2.73e-15 wathen_csc() 4 16 65 1.66e-03 2.27e-04 9.20e+00 wathen_ge() 8 64 225 7.64e-03 1.22e-03 4.89e-15 wathen_csc() 8 64 225 5.87e-03 8.06e-04 1.46e+03 wathen_ge() 16 256 833 3.15e-02 1.58e-01 9.61e-15 wathen_csc() 16 256 833 2.05e-02 3.35e-03 4.86e+01 wathen_ge() 32 1024 3201 1.25e-01 4.76e-01 1.93e-14 wathen_csc() 32 1024 3201 7.10e-02 1.72e-02 1.05e+02 wathen_test06(): Assemble, factor and solve a Wathen system defined by wathen_ge() and cg_ge(). Elements in X direction NX = 2 Elements in Y direction NY = 2 Number of elements = 4 Number of nodes N = 21 Maximum solution error is 6.01506e-05 wathen_test07(): Assemble, factor and solve a Wathen system defined by wathen_csc() and cg_csc(). Elements in X direction NX = 2 Elements in Y direction NY = 2 Number of elements = 4 Number of nodes N = 21 Maximum solution error is 1.32268e-05 Normal end of execution. wathen_test08(): Assemble, factor and solve a Wathen system defined by wathen_st() and cg_st(). Elements in X direction NX = 1 Elements in Y direction NY = 1 Number of elements = 1 Number of nodes N = 8 Number of nonzeros = 64 Maximum solution error is 1.35848e-15 wathen_test09(): Display the sparsity of the Wathen matrix. Graphics saved as "wathen_spy.png" wathen_order_test(): wathen_order() returns N, the order of a Wathen finite element matrix given NX and NY, the number of rows and columns of nodes in the underlying grid. NX / NY: 1 2 3 4 5 6 1 8 13 18 23 28 33 2 13 21 29 37 45 53 3 18 29 40 51 62 73 4 23 37 51 65 79 93 5 28 45 62 79 96 113 6 33 53 73 93 113 133 7 38 61 84 107 130 153 8 43 69 95 121 147 173 9 48 77 106 135 164 193 10 53 85 117 149 181 213 wathen_st_size_test(): wathen_st_size() returns NZ_NUM, the number of nonzeros in a sparse triplet format for a Wathen finite element matrix, given NX and NY, the number of rows and columns of nodes in the underlying grid. NX / NY: 1 2 3 4 5 6 1 64 128 192 256 320 384 2 128 256 384 512 640 768 3 192 384 576 768 960 1152 4 256 512 768 1024 1280 1536 5 320 640 960 1280 1600 1920 6 384 768 1152 1536 1920 2304 7 448 896 1344 1792 2240 2688 8 512 1024 1536 2048 2560 3072 9 576 1152 1728 2304 2880 3456 10 640 1280 1920 2560 3200 3840 wathen_xy_test(): wathen_xy() returns the (X,Y) coordinates of nodes. Graphics saved as " wathen_xy.png " wathen_matrix_test(): Normal end of execution. Wed Oct 8 09:15:52 2025