wathen_test 09-Feb-2019 19:24:28 wathen_test MATLAB version Test wathen. 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 1.33227e-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: -61.0176 2: 539.483 3: -250.613 4: 1760.23 5: -276.364 6: 637.406 7: -857.118 8: 1709 9: -647.263 10: 448.354 11: 1520.36 12: 2464.89 13: 2916.37 14: 2227.21 15: 196.604 16: -289.071 17: -28.4923 18: 1556.32 19: -750.157 20: 828.401 21: -537.695 22: 2784.07 23: -661.145 24: -525.486 25: -201.404 26: 746.345 27: 513.839 28: 283.744 29: 267.318 30: -266.48 31: -187.305 32: 2040.89 33: -398.485 34: 538.486 35: -510.74 36: 1985.37 37: -596.66 38: 120.145 39: 1860.56 40: 1629.6 41: 1922.59 42: 1527.78 43: -220.482 44: 958.733 45: -1430.9 46: 4191.91 47: -2125.18 48: 2923.88 49: -1109.14 50: 1836.74 51: -514.863 52: 1194.37 53: 2517.28 54: 5877.56 55: 3199.62 56: 7.52859 57: -146.537 58: 1187.51 59: -782.29 60: 2183.43 61: -1054.54 62: 3186.03 63: -997.315 64: 7.87855 65: -2.67162 Maximum solution error is 6.77236e-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 9.99201e-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 9.99201e-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 3.07e-04 1.05e-03 3.33e-16 2 4 21 441 1.18e-04 1.09e-04 1.44e-15 4 16 65 4225 1.85e-04 1.76e-04 1.33e-15 8 64 225 50625 1.82e-04 3.10e-03 2.66e-15 16 256 833 693889 1.39e-03 1.29e-02 2.00e-15 32 1024 3201 10246401 1.59e-02 7.87e-01 3.55e-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 3.61e-03 5.54e-03 9.16e-16 2 4 21 651 4.40e-04 3.15e-03 1.23e-15 4 16 65 3185 2.96e-04 8.00e-03 6.77e-15 8 64 225 19125 1.86e-03 3.10e-02 2.16e-15 16 256 833 130781 9.30e-04 1.86e-01 4.35e-13 32 1024 3201 963501 7.94e-03 1.30e+00 1.42e-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 8.90e-05 8.40e-05 3.33e-16 WATHEN_GB 1 1 8 176 1.33e-04 3.18e-03 9.16e-16 WATHEN_SPARSE 1 1 8 64 4.85e-03 3.70e-04 9.99e-16 WATHEN_DAVIS 1 1 8 64 2.28e-03 4.50e-05 9.99e-16 WATHEN_GE 2 4 21 441 1.18e-04 7.60e-05 1.44e-15 WATHEN_GB 2 4 21 651 5.70e-05 1.54e-03 1.23e-15 WATHEN_SPARSE 2 4 21 221 2.82e-03 6.40e-05 3.66e-15 WATHEN_DAVIS 2 4 21 221 1.79e-03 4.90e-05 3.39e-15 WATHEN_GE 4 16 65 4225 6.20e-05 1.05e-04 1.33e-15 WATHEN_GB 4 16 65 3185 6.30e-05 7.51e-03 6.77e-15 WATHEN_SPARSE 4 16 65 817 3.33e-03 1.89e-04 9.99e-16 WATHEN_DAVIS 4 16 65 817 6.32e-04 2.15e-04 9.99e-16 WATHEN_GE 8 64 225 50625 1.56e-04 6.79e-04 2.66e-15 WATHEN_GB 8 64 225 19125 1.73e-04 2.82e-02 2.16e-15 WATHEN_SPARSE 8 64 225 3137 1.18e-02 2.95e-04 1.67e-15 WATHEN_DAVIS 8 64 225 3137 2.41e-03 5.15e-04 1.67e-15 WATHEN_GE 16 256 833 693889 8.47e-04 8.37e-03 2.00e-15 WATHEN_GB 16 256 833 130781 4.16e-04 1.69e-01 4.35e-13 WATHEN_SPARSE 16 256 833 12289 4.46e-02 1.28e-03 2.11e-15 WATHEN_DAVIS 16 256 833 12289 2.13e-03 2.29e-03 2.11e-15 WATHEN_GE 32 1024 3201 10246401 1.08e-02 1.82e-01 3.55e-15 WATHEN_GB 32 1024 3201 963501 2.31e-03 1.30e+00 1.42e-14 WATHEN_SPARSE 32 1024 3201 48641 2.75e-01 5.65e-03 3.11e-15 WATHEN_DAVIS 32 1024 3201 48641 6.67e-03 4.16e-03 3.11e-15 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 2.67e-01 4.14e-03 3.11e-15 WATHEN_DAVIS 32 1024 3201 48641 5.26e-03 4.48e-03 3.14e-15 WATHEN_SPARSE 64 4096 12545 193537 2.55e+00 1.65e-02 4.72e-15 WATHEN_DAVIS 64 4096 12545 193537 2.60e-02 1.68e-02 5.05e-15 WATHEN_SPARSE 128 16384 49665 772097 5.47e+01 8.35e-02 5.22e-15 WATHEN_DAVIS 128 16384 49665 772097 1.06e-01 7.22e-02 5.11e-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 4.80389e-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 1.20737e-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 4.63067e-06 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 1.20737e-15 WATHEN_TEST13 Display the sparsity of the Wathen matrix. Graphics file saved as "wathen_spy.png" wathen_test: Normal end of execution. 09-Feb-2019 19:25:34 diary off