27-Sep-2022 14:53:30 wathen_matrix_test(): MATLAB/Octave version 4.2.2. 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 8.60423e-16 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: -329.655 2: 1335 3: -613.726 4: 1015.91 5: -18.3654 6: -238.149 7: -5.85668 8: 1187.91 9: -235.988 10: 1304.57 11: 2071.28 12: 249.915 13: 903.821 14: 1252.07 15: -792.495 16: 2773.23 17: -1025.92 18: 1282.43 19: -289.245 20: -87.8617 21: -170.786 22: 1345.99 23: -273.179 24: 1367.55 25: 1962.85 26: 1051.99 27: 688.723 28: 343.103 29: -371.728 30: 1115.48 31: -755.242 32: 984.454 33: -607.332 34: 1313.9 35: -375.226 36: 854.128 37: -64.8874 38: 68.2512 39: 338.595 40: 1306.95 41: 942.502 42: 521.565 43: -274.833 44: 1198.5 45: -533.891 46: 1144.38 47: -576.312 48: 1537.68 49: -632.005 50: 419.056 51: -148.317 52: 929.839 53: 1731.09 54: 1550.8 55: 993.874 56: 223.169 57: -301.11 58: 1039.67 59: -411.488 60: 750.989 61: -345.124 62: 815.743 63: -240.158 64: 216.332 65: -34.8802 Maximum solution error is 2.42167e-15 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 2.16493e-15 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 8.88178e-16 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 1.41e-03 6.60e-05 8.88e-16 2 4 21 441 3.79e-03 2.29e-05 9.44e-16 4 16 65 4225 1.58e-02 1.77e-04 9.44e-16 8 64 225 50625 8.37e-02 1.02e-03 9.99e-16 16 256 833 693889 2.89e-01 1.37e-02 1.33e-15 32 1024 3201 10246401 1.03e+00 2.83e-01 2.11e-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 1.55e-03 3.94e-03 8.88e-16 2 4 21 651 5.74e-03 1.83e-02 2.70e-15 4 16 65 3185 2.25e-02 6.42e-02 9.99e-16 8 64 225 19125 6.73e-02 3.78e-01 2.33e-15 16 256 833 130781 2.55e-01 2.22e+00 5.11e-15 32 1024 3201 963501 9.91e-01 1.78e+01 1.08e-14 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 1.02e-03 2.79e-05 1.33e-15 WATHEN_GB 1 1 8 176 1.10e-03 2.99e-03 2.11e-15 WATHEN_SPARSE 1 1 8 64 1.30e-03 5.10e-02 2.59e-01 WATHEN_DAVIS 1 1 8 64 1.12e-03 1.10e-05 1.92e-01 WATHEN_GE 2 4 21 441 3.92e-03 3.41e-05 5.83e-16 WATHEN_GB 2 4 21 651 4.12e-03 1.32e-02 1.33e-15 WATHEN_SPARSE 2 4 21 221 5.18e-03 1.81e-05 5.71e-01 WATHEN_DAVIS 2 4 21 221 3.74e-03 1.69e-05 4.36e+00 WATHEN_GE 4 16 65 4225 1.55e-02 1.55e-04 9.99e-16 WATHEN_GB 4 16 65 3185 2.26e-02 8.41e-02 4.66e-15 WATHEN_SPARSE 4 16 65 817 2.44e-02 1.03e-04 3.59e+00 WATHEN_DAVIS 4 16 65 817 1.54e-02 8.92e-05 1.61e+00 WATHEN_GE 8 64 225 50625 6.21e-02 7.14e-04 1.44e-15 WATHEN_GB 8 64 225 19125 9.02e-02 3.66e-01 3.77e-15 WATHEN_SPARSE 8 64 225 3137 8.20e-02 2.93e-04 3.08e+01 WATHEN_DAVIS 8 64 225 3137 6.09e-02 2.67e-04 3.33e+00 WATHEN_GE 16 256 833 693889 2.49e-01 1.03e-02 1.72e-15 WATHEN_GB 16 256 833 130781 3.05e-01 2.50e+00 8.88e-15 WATHEN_SPARSE 16 256 833 12289 3.60e-01 1.19e-03 3.68e+01 WATHEN_DAVIS 16 256 833 12289 2.44e-01 1.51e-03 1.66e+01 WATHEN_GE 32 1024 3201 10246401 1.01e+00 2.79e-01 1.83e-15 WATHEN_GB 32 1024 3201 963501 1.09e+00 1.77e+01 1.97e-14 WATHEN_SPARSE 32 1024 3201 48641 1.85e+00 4.59e-01 1.04e+02 WATHEN_DAVIS 32 1024 3201 48641 9.83e-01 8.46e-03 4.00e+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 1.89e+00 4.99e-01 2.12e-15 WATHEN_DAVIS 32 1024 3201 48641 1.03e+00 6.61e-01 1.89e-15 WATHEN_SPARSE 64 4096 12545 193537 1.49e+01 1.38e+00 2.72e-15 WATHEN_DAVIS 64 4096 12545 193537 3.74e+00 3.33e-02 3.72e-15 WATHEN_SPARSE 128 16384 49665 772097 4.48e+02 2.88e+00 4.39e-15 WATHEN_DAVIS 128 16384 49665 772097 1.56e+01 2.25e+00 2.86e-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 4.56114e-06 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 1.60982e-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 8.13653e-07 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 1.08247e-15 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. 27-Sep-2022 15:04:16