Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 13-May-2025 19:21:29 wathen_matrix_test(): MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7. 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 Maximum solution error is 1.19349e-15 wathen_test02(): Assemble, factor and solve a Wathen system using wathen_gb(). Elements in X direction NX = 4 Elements in Y direction NY = 4 Number of elements = 16 Number of nodes N = 65 Lower bandwidth ML = 16 Lower bandwidth MU = 16 B: 1: -14.353 2: 208.104 3: -59.2505 4: 183.561 5: -109.191 6: 346.997 7: -162.022 8: 394.787 9: -99.0463 10: 149.407 11: 255.758 12: 442.971 13: 772.95 14: 446.624 15: -242.719 16: 822.789 17: -206.488 18: 115.062 19: -185.18 20: 498.883 21: -341.719 22: 1464.52 23: -401.276 24: 534.639 25: 703.893 26: 239.649 27: 1805.25 28: 1294.47 29: -249.564 30: 1092.04 31: -357.872 32: 117.193 33: 104.54 34: 460.651 35: -241.503 36: 2149.8 37: -304.826 38: 446.266 39: 706.224 40: 135.007 41: 1481.58 42: 471.899 43: -191.104 44: 1189.84 45: -65.2016 46: 103.149 47: -62.2339 48: 313.986 49: -82.293 50: 1255.23 51: -204.121 52: 390.411 53: 486.895 54: 168.581 55: 484.24 56: 589.142 57: -94.4358 58: 407.807 59: -144.653 60: 122.795 61: 63.1933 62: 179.845 63: -80.9119 64: 441.314 65: -125.937 Maximum solution error is 8.88178e-16 wathen_test03(): Assemble, factor and solve a Wathen system defined by wathen_sparse(). Elements in X direction NX = 4 Elements in Y direction NY = 4 Number of elements = 16 Number of nodes N = 65 Maximum solution error is 8.88178e-16 wathen_test04() Assemble, factor and solve a Wathen system defined by wathen_davis(). Elements in X direction NX = 4 Elements in Y direction NY = 4 Number of elements = 16 Number of nodes N = 65 Maximum solution error is 1.44329e-15 wathen_test05() For various problem sizes and storage schemes, measure the storage used for the Wathen system. Predicted Observed GE Band Band Band Sparse NX Elements Nodes storage width width storage storage 1 1 8 64 15 15 176 64 2 4 21 441 21 21 651 221 4 16 65 4225 33 33 3185 817 8 64 225 50625 57 57 19125 3137 16 256 833 693889 105 105 130781 12289 32 1024 3201 10246401 201 201 963501 48641 wathen_test06(): For various problem sizes, time the assembly and factorization of a Wathen system using the wathen_ge() function. NX Elements Nodes Storage Assembly Factor Error 1 1 8 64 1.30e-04 5.60e-05 1.11e-15 2 4 21 441 4.80e-05 3.90e-05 5.55e-16 4 16 65 4225 4.40e-05 5.60e-05 1.33e-15 8 64 225 50625 9.90e-05 4.66e-04 1.22e-15 16 256 833 693889 2.35e-03 7.22e-03 2.04e-15 32 1024 3201 10246401 8.63e-03 1.53e-01 2.45e-15 wathen_test07(): For various problem sizes, time the assembly and factorization of a Wathen system using the wathen_gb() function. NX Elements Nodes Storage Assembly Factor Error 1 1 8 176 1.82e-03 4.17e-03 1.22e-15 2 4 21 651 3.89e-04 1.61e-03 1.44e-15 4 16 65 3185 1.40e-04 4.44e-03 1.78e-15 8 64 225 19125 1.17e-03 2.53e-02 2.16e-15 16 256 833 130781 6.06e-04 1.50e-01 4.00e-15 32 1024 3201 963501 6.11e-03 1.14e+00 6.64e-12 wathen_test08(): For various problem sizes, time the assembly and factorization of a Wathen system wathen_gb()/wathen_ge()/wathen_sparse()/wathen_davis(). NX Elements Nodes Storage Assembly Factor Error WATHEN_GE 1 1 8 64 5.70e-05 5.40e-05 8.36e-16 WATHEN_GB 1 1 8 176 4.10e-05 1.31e-03 6.66e-16 WATHEN_SPARSE 1 1 8 64 1.44e-03 5.80e-05 7.38e-01 WATHEN_DAVIS 1 1 8 64 1.56e-03 2.20e-05 7.59e-01 WATHEN_GE 2 4 21 441 4.80e-05 3.20e-05 1.44e-15 WATHEN_GB 2 4 21 651 3.90e-05 8.49e-04 9.99e-16 WATHEN_SPARSE 2 4 21 221 7.46e-04 2.20e-05 7.28e-01 WATHEN_DAVIS 2 4 21 221 6.02e-04 2.20e-05 1.26e+01 WATHEN_GE 4 16 65 4225 4.60e-05 5.70e-05 1.44e-15 WATHEN_GB 4 16 65 3185 4.60e-05 3.53e-03 3.89e-15 WATHEN_SPARSE 4 16 65 817 1.80e-03 1.03e-04 1.49e+00 WATHEN_DAVIS 4 16 65 817 1.48e-04 8.40e-05 8.89e-01 WATHEN_GE 8 64 225 50625 9.40e-05 3.23e-04 1.78e-15 WATHEN_GB 8 64 225 19125 1.00e-04 2.08e-02 4.55e-15 WATHEN_SPARSE 8 64 225 3137 8.31e-03 2.67e-04 5.66e+01 WATHEN_DAVIS 8 64 225 3137 1.38e-03 2.58e-04 2.74e+01 WATHEN_GE 16 256 833 693889 7.39e-04 5.58e-03 1.67e-15 WATHEN_GB 16 256 833 130781 4.41e-04 1.46e-01 6.55e-15 WATHEN_SPARSE 16 256 833 12289 3.42e-02 1.27e-03 2.28e+01 WATHEN_DAVIS 16 256 833 12289 6.98e-04 1.16e-03 9.83e+00 WATHEN_GE 32 1024 3201 10246401 8.58e-03 1.53e-01 2.55e-15 WATHEN_GB 32 1024 3201 963501 3.01e-03 1.12e+00 1.11e-14 WATHEN_SPARSE 32 1024 3201 48641 2.10e-01 3.96e-03 2.52e+01 WATHEN_DAVIS 32 1024 3201 48641 1.73e-03 3.88e-03 1.56e+01 wathen_test09(): For various problem sizes, time the assembly and factorization of a Wathen system using the wathen_sparse() and wathen_davis() functions. NX Elements Nodes Storage Assembly Factor Error WATHEN_SPARSE 32 1024 3201 48641 2.11e-01 3.91e-03 2.89e-15 WATHEN_DAVIS 32 1024 3201 48641 1.78e-03 3.87e-03 2.33e-15 WATHEN_SPARSE 64 4096 12545 193537 3.36e+00 1.71e-02 4.44e-15 WATHEN_DAVIS 64 4096 12545 193537 6.81e-03 1.52e-02 7.11e-15 WATHEN_SPARSE 128 16384 49665 772097 5.12e+01 8.18e-02 4.44e-15 WATHEN_DAVIS 128 16384 49665 772097 3.34e-02 7.64e-02 4.77e-15 wathen_test10() 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 5.38235e-07 wathen_test11() 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 1.44329e-15 wathen_test115() Assemble, factor and solve a Wathen system using wathen_gb() and cg_gb(). Elements in X direction NX = 2 Elements in Y direction NY = 2 Number of elements = 4 Number of nodes N = 21 Lower bandwidth ML = 10 Lower bandwidth MU = 10 Maximum solution error is 1.43409e-05 wathen_test12(): Assemble, factor and solve a Wathen system defined by wathen_davis() and cg_sparse(). Elements in X direction NX = 1 Elements in Y direction NY = 1 Number of elements = 1 Number of nodes N = 8 Maximum solution error is 5.55112e-16 wathen_spy_test Use spy() to display the sparsity of the Wathen matrix. Graphics file saved as "wathen_spy.png" wathen_xy_test(): wathen_xy() returns the (X,Y) coordinates of nodes. N was not supplied. N = 96 Graphics saved as "wathen_xy_test.png" wathen_matrix_test(): Normal end of execution. 13-May-2025 19:22:34