HELMHOLTZ C++/OpenMP version A program which solves the 2D Helmholtz equation. This program is being run in parallel. Number of processors available = 8 Number of threads = 1 The region is [-1,1] x [-1,1]. The number of nodes in the X direction is M = 500 The number of nodes in the Y direction is N = 500 Number of variables in linear system M * N = 250000 The scalar coefficient in the Helmholtz equation is ALPHA = 0.25 The relaxation value is OMEGA = 1.1 The error tolerance is TOL = 1e-08 The maximum number of Jacobi iterations is IT_MAX = 100 Right hand side l2 norm = 1458.46 1 Residual RMS 2.34289e-08 2 Residual RMS 2.34173e-08 3 Residual RMS 2.34096e-08 4 Residual RMS 2.34033e-08 5 Residual RMS 2.33978e-08 6 Residual RMS 2.33929e-08 7 Residual RMS 2.33884e-08 8 Residual RMS 2.33842e-08 9 Residual RMS 2.33802e-08 10 Residual RMS 2.33764e-08 11 Residual RMS 2.33729e-08 12 Residual RMS 2.33694e-08 13 Residual RMS 2.33661e-08 14 Residual RMS 2.33629e-08 15 Residual RMS 2.33598e-08 16 Residual RMS 2.33568e-08 17 Residual RMS 2.33538e-08 18 Residual RMS 2.3351e-08 19 Residual RMS 2.33482e-08 20 Residual RMS 2.33455e-08 21 Residual RMS 2.33428e-08 22 Residual RMS 2.33402e-08 23 Residual RMS 2.33376e-08 24 Residual RMS 2.33351e-08 25 Residual RMS 2.33326e-08 26 Residual RMS 2.33302e-08 27 Residual RMS 2.33278e-08 28 Residual RMS 2.33255e-08 29 Residual RMS 2.33231e-08 30 Residual RMS 2.33209e-08 31 Residual RMS 2.33186e-08 32 Residual RMS 2.33164e-08 33 Residual RMS 2.33142e-08 34 Residual RMS 2.3312e-08 35 Residual RMS 2.33098e-08 36 Residual RMS 2.33077e-08 37 Residual RMS 2.33056e-08 38 Residual RMS 2.33035e-08 39 Residual RMS 2.33015e-08 40 Residual RMS 2.32994e-08 41 Residual RMS 2.32974e-08 42 Residual RMS 2.32954e-08 43 Residual RMS 2.32934e-08 44 Residual RMS 2.32915e-08 45 Residual RMS 2.32895e-08 46 Residual RMS 2.32876e-08 47 Residual RMS 2.32857e-08 48 Residual RMS 2.32838e-08 49 Residual RMS 2.32819e-08 50 Residual RMS 2.32801e-08 51 Residual RMS 2.32782e-08 52 Residual RMS 2.32764e-08 53 Residual RMS 2.32746e-08 54 Residual RMS 2.32727e-08 55 Residual RMS 2.32709e-08 56 Residual RMS 2.32692e-08 57 Residual RMS 2.32674e-08 58 Residual RMS 2.32656e-08 59 Residual RMS 2.32639e-08 60 Residual RMS 2.32621e-08 61 Residual RMS 2.32604e-08 62 Residual RMS 2.32587e-08 63 Residual RMS 2.3257e-08 64 Residual RMS 2.32553e-08 65 Residual RMS 2.32536e-08 66 Residual RMS 2.32519e-08 67 Residual RMS 2.32502e-08 68 Residual RMS 2.32486e-08 69 Residual RMS 2.32469e-08 70 Residual RMS 2.32453e-08 71 Residual RMS 2.32437e-08 72 Residual RMS 2.3242e-08 73 Residual RMS 2.32404e-08 74 Residual RMS 2.32388e-08 75 Residual RMS 2.32372e-08 76 Residual RMS 2.32356e-08 77 Residual RMS 2.3234e-08 78 Residual RMS 2.32324e-08 79 Residual RMS 2.32309e-08 80 Residual RMS 2.32293e-08 81 Residual RMS 2.32277e-08 82 Residual RMS 2.32262e-08 83 Residual RMS 2.32247e-08 84 Residual RMS 2.32231e-08 85 Residual RMS 2.32216e-08 86 Residual RMS 2.32201e-08 87 Residual RMS 2.32185e-08 88 Residual RMS 2.3217e-08 89 Residual RMS 2.32155e-08 90 Residual RMS 2.3214e-08 91 Residual RMS 2.32125e-08 92 Residual RMS 2.3211e-08 93 Residual RMS 2.32096e-08 94 Residual RMS 2.32081e-08 95 Residual RMS 2.32066e-08 96 Residual RMS 2.32051e-08 97 Residual RMS 2.32037e-08 98 Residual RMS 2.32022e-08 99 Residual RMS 2.32008e-08 100 Residual RMS 2.31993e-08 Total number of iterations 101 Computed U l2 norm : 0.640273 Computed U_EXACT l2 norm : 266.133 Error l2 norm: 265.517 Wall clock time in seconds = 0.389149 HELMHOLTZ Normal end of execution. HELMHOLTZ C++/OpenMP version A program which solves the 2D Helmholtz equation. This program is being run in parallel. Number of processors available = 8 Number of threads = 2 The region is [-1,1] x [-1,1]. The number of nodes in the X direction is M = 500 The number of nodes in the Y direction is N = 500 Number of variables in linear system M * N = 250000 The scalar coefficient in the Helmholtz equation is ALPHA = 0.25 The relaxation value is OMEGA = 1.1 The error tolerance is TOL = 1e-08 The maximum number of Jacobi iterations is IT_MAX = 100 Right hand side l2 norm = 1458.46 1 Residual RMS 2.34289e-08 2 Residual RMS 2.34173e-08 3 Residual RMS 2.34096e-08 4 Residual RMS 2.34033e-08 5 Residual RMS 2.33978e-08 6 Residual RMS 2.33929e-08 7 Residual RMS 2.33884e-08 8 Residual RMS 2.33842e-08 9 Residual RMS 2.33802e-08 10 Residual RMS 2.33764e-08 11 Residual RMS 2.33729e-08 12 Residual RMS 2.33694e-08 13 Residual RMS 2.33661e-08 14 Residual RMS 2.33629e-08 15 Residual RMS 2.33598e-08 16 Residual RMS 2.33568e-08 17 Residual RMS 2.33538e-08 18 Residual RMS 2.3351e-08 19 Residual RMS 2.33482e-08 20 Residual RMS 2.33455e-08 21 Residual RMS 2.33428e-08 22 Residual RMS 2.33402e-08 23 Residual RMS 2.33376e-08 24 Residual RMS 2.33351e-08 25 Residual RMS 2.33326e-08 26 Residual RMS 2.33302e-08 27 Residual RMS 2.33278e-08 28 Residual RMS 2.33255e-08 29 Residual RMS 2.33231e-08 30 Residual RMS 2.33209e-08 31 Residual RMS 2.33186e-08 32 Residual RMS 2.33164e-08 33 Residual RMS 2.33142e-08 34 Residual RMS 2.3312e-08 35 Residual RMS 2.33098e-08 36 Residual RMS 2.33077e-08 37 Residual RMS 2.33056e-08 38 Residual RMS 2.33035e-08 39 Residual RMS 2.33015e-08 40 Residual RMS 2.32994e-08 41 Residual RMS 2.32974e-08 42 Residual RMS 2.32954e-08 43 Residual RMS 2.32934e-08 44 Residual RMS 2.32915e-08 45 Residual RMS 2.32895e-08 46 Residual RMS 2.32876e-08 47 Residual RMS 2.32857e-08 48 Residual RMS 2.32838e-08 49 Residual RMS 2.32819e-08 50 Residual RMS 2.32801e-08 51 Residual RMS 2.32782e-08 52 Residual RMS 2.32764e-08 53 Residual RMS 2.32746e-08 54 Residual RMS 2.32727e-08 55 Residual RMS 2.32709e-08 56 Residual RMS 2.32692e-08 57 Residual RMS 2.32674e-08 58 Residual RMS 2.32656e-08 59 Residual RMS 2.32639e-08 60 Residual RMS 2.32621e-08 61 Residual RMS 2.32604e-08 62 Residual RMS 2.32587e-08 63 Residual RMS 2.3257e-08 64 Residual RMS 2.32553e-08 65 Residual RMS 2.32536e-08 66 Residual RMS 2.32519e-08 67 Residual RMS 2.32502e-08 68 Residual RMS 2.32486e-08 69 Residual RMS 2.32469e-08 70 Residual RMS 2.32453e-08 71 Residual RMS 2.32437e-08 72 Residual RMS 2.3242e-08 73 Residual RMS 2.32404e-08 74 Residual RMS 2.32388e-08 75 Residual RMS 2.32372e-08 76 Residual RMS 2.32356e-08 77 Residual RMS 2.3234e-08 78 Residual RMS 2.32324e-08 79 Residual RMS 2.32309e-08 80 Residual RMS 2.32293e-08 81 Residual RMS 2.32277e-08 82 Residual RMS 2.32262e-08 83 Residual RMS 2.32247e-08 84 Residual RMS 2.32231e-08 85 Residual RMS 2.32216e-08 86 Residual RMS 2.32201e-08 87 Residual RMS 2.32185e-08 88 Residual RMS 2.3217e-08 89 Residual RMS 2.32155e-08 90 Residual RMS 2.3214e-08 91 Residual RMS 2.32125e-08 92 Residual RMS 2.3211e-08 93 Residual RMS 2.32096e-08 94 Residual RMS 2.32081e-08 95 Residual RMS 2.32066e-08 96 Residual RMS 2.32051e-08 97 Residual RMS 2.32037e-08 98 Residual RMS 2.32022e-08 99 Residual RMS 2.32008e-08 100 Residual RMS 2.31993e-08 Total number of iterations 101 Computed U l2 norm : 0.640273 Computed U_EXACT l2 norm : 266.133 Error l2 norm: 265.517 Wall clock time in seconds = 0.212966 HELMHOLTZ Normal end of execution. HELMHOLTZ C++/OpenMP version A program which solves the 2D Helmholtz equation. This program is being run in parallel. Number of processors available = 8 Number of threads = 4 The region is [-1,1] x [-1,1]. The number of nodes in the X direction is M = 500 The number of nodes in the Y direction is N = 500 Number of variables in linear system M * N = 250000 The scalar coefficient in the Helmholtz equation is ALPHA = 0.25 The relaxation value is OMEGA = 1.1 The error tolerance is TOL = 1e-08 The maximum number of Jacobi iterations is IT_MAX = 100 Right hand side l2 norm = 1458.46 1 Residual RMS 2.34289e-08 2 Residual RMS 2.34173e-08 3 Residual RMS 2.34096e-08 4 Residual RMS 2.34033e-08 5 Residual RMS 2.33978e-08 6 Residual RMS 2.33929e-08 7 Residual RMS 2.33884e-08 8 Residual RMS 2.33842e-08 9 Residual RMS 2.33802e-08 10 Residual RMS 2.33764e-08 11 Residual RMS 2.33729e-08 12 Residual RMS 2.33694e-08 13 Residual RMS 2.33661e-08 14 Residual RMS 2.33629e-08 15 Residual RMS 2.33598e-08 16 Residual RMS 2.33568e-08 17 Residual RMS 2.33538e-08 18 Residual RMS 2.3351e-08 19 Residual RMS 2.33482e-08 20 Residual RMS 2.33455e-08 21 Residual RMS 2.33428e-08 22 Residual RMS 2.33402e-08 23 Residual RMS 2.33376e-08 24 Residual RMS 2.33351e-08 25 Residual RMS 2.33326e-08 26 Residual RMS 2.33302e-08 27 Residual RMS 2.33278e-08 28 Residual RMS 2.33255e-08 29 Residual RMS 2.33231e-08 30 Residual RMS 2.33209e-08 31 Residual RMS 2.33186e-08 32 Residual RMS 2.33164e-08 33 Residual RMS 2.33142e-08 34 Residual RMS 2.3312e-08 35 Residual RMS 2.33098e-08 36 Residual RMS 2.33077e-08 37 Residual RMS 2.33056e-08 38 Residual RMS 2.33035e-08 39 Residual RMS 2.33015e-08 40 Residual RMS 2.32994e-08 41 Residual RMS 2.32974e-08 42 Residual RMS 2.32954e-08 43 Residual RMS 2.32934e-08 44 Residual RMS 2.32915e-08 45 Residual RMS 2.32895e-08 46 Residual RMS 2.32876e-08 47 Residual RMS 2.32857e-08 48 Residual RMS 2.32838e-08 49 Residual RMS 2.32819e-08 50 Residual RMS 2.32801e-08 51 Residual RMS 2.32782e-08 52 Residual RMS 2.32764e-08 53 Residual RMS 2.32746e-08 54 Residual RMS 2.32727e-08 55 Residual RMS 2.32709e-08 56 Residual RMS 2.32692e-08 57 Residual RMS 2.32674e-08 58 Residual RMS 2.32656e-08 59 Residual RMS 2.32639e-08 60 Residual RMS 2.32621e-08 61 Residual RMS 2.32604e-08 62 Residual RMS 2.32587e-08 63 Residual RMS 2.3257e-08 64 Residual RMS 2.32553e-08 65 Residual RMS 2.32536e-08 66 Residual RMS 2.32519e-08 67 Residual RMS 2.32502e-08 68 Residual RMS 2.32486e-08 69 Residual RMS 2.32469e-08 70 Residual RMS 2.32453e-08 71 Residual RMS 2.32437e-08 72 Residual RMS 2.3242e-08 73 Residual RMS 2.32404e-08 74 Residual RMS 2.32388e-08 75 Residual RMS 2.32372e-08 76 Residual RMS 2.32356e-08 77 Residual RMS 2.3234e-08 78 Residual RMS 2.32324e-08 79 Residual RMS 2.32309e-08 80 Residual RMS 2.32293e-08 81 Residual RMS 2.32277e-08 82 Residual RMS 2.32262e-08 83 Residual RMS 2.32247e-08 84 Residual RMS 2.32231e-08 85 Residual RMS 2.32216e-08 86 Residual RMS 2.32201e-08 87 Residual RMS 2.32185e-08 88 Residual RMS 2.3217e-08 89 Residual RMS 2.32155e-08 90 Residual RMS 2.3214e-08 91 Residual RMS 2.32125e-08 92 Residual RMS 2.3211e-08 93 Residual RMS 2.32096e-08 94 Residual RMS 2.32081e-08 95 Residual RMS 2.32066e-08 96 Residual RMS 2.32051e-08 97 Residual RMS 2.32037e-08 98 Residual RMS 2.32022e-08 99 Residual RMS 2.32008e-08 100 Residual RMS 2.31993e-08 Total number of iterations 101 Computed U l2 norm : 0.640273 Computed U_EXACT l2 norm : 266.133 Error l2 norm: 265.517 Wall clock time in seconds = 0.111136 HELMHOLTZ Normal end of execution. HELMHOLTZ C++/OpenMP version A program which solves the 2D Helmholtz equation. This program is being run in parallel. Number of processors available = 8 Number of threads = 8 The region is [-1,1] x [-1,1]. The number of nodes in the X direction is M = 500 The number of nodes in the Y direction is N = 500 Number of variables in linear system M * N = 250000 The scalar coefficient in the Helmholtz equation is ALPHA = 0.25 The relaxation value is OMEGA = 1.1 The error tolerance is TOL = 1e-08 The maximum number of Jacobi iterations is IT_MAX = 100 Right hand side l2 norm = 1458.46 1 Residual RMS 2.34289e-08 2 Residual RMS 2.34173e-08 3 Residual RMS 2.34096e-08 4 Residual RMS 2.34033e-08 5 Residual RMS 2.33978e-08 6 Residual RMS 2.33929e-08 7 Residual RMS 2.33884e-08 8 Residual RMS 2.33842e-08 9 Residual RMS 2.33802e-08 10 Residual RMS 2.33764e-08 11 Residual RMS 2.33729e-08 12 Residual RMS 2.33694e-08 13 Residual RMS 2.33661e-08 14 Residual RMS 2.33629e-08 15 Residual RMS 2.33598e-08 16 Residual RMS 2.33568e-08 17 Residual RMS 2.33538e-08 18 Residual RMS 2.3351e-08 19 Residual RMS 2.33482e-08 20 Residual RMS 2.33455e-08 21 Residual RMS 2.33428e-08 22 Residual RMS 2.33402e-08 23 Residual RMS 2.33376e-08 24 Residual RMS 2.33351e-08 25 Residual RMS 2.33326e-08 26 Residual RMS 2.33302e-08 27 Residual RMS 2.33278e-08 28 Residual RMS 2.33255e-08 29 Residual RMS 2.33231e-08 30 Residual RMS 2.33209e-08 31 Residual RMS 2.33186e-08 32 Residual RMS 2.33164e-08 33 Residual RMS 2.33142e-08 34 Residual RMS 2.3312e-08 35 Residual RMS 2.33098e-08 36 Residual RMS 2.33077e-08 37 Residual RMS 2.33056e-08 38 Residual RMS 2.33035e-08 39 Residual RMS 2.33015e-08 40 Residual RMS 2.32994e-08 41 Residual RMS 2.32974e-08 42 Residual RMS 2.32954e-08 43 Residual RMS 2.32934e-08 44 Residual RMS 2.32915e-08 45 Residual RMS 2.32895e-08 46 Residual RMS 2.32876e-08 47 Residual RMS 2.32857e-08 48 Residual RMS 2.32838e-08 49 Residual RMS 2.32819e-08 50 Residual RMS 2.32801e-08 51 Residual RMS 2.32782e-08 52 Residual RMS 2.32764e-08 53 Residual RMS 2.32746e-08 54 Residual RMS 2.32727e-08 55 Residual RMS 2.32709e-08 56 Residual RMS 2.32692e-08 57 Residual RMS 2.32674e-08 58 Residual RMS 2.32656e-08 59 Residual RMS 2.32639e-08 60 Residual RMS 2.32621e-08 61 Residual RMS 2.32604e-08 62 Residual RMS 2.32587e-08 63 Residual RMS 2.3257e-08 64 Residual RMS 2.32553e-08 65 Residual RMS 2.32536e-08 66 Residual RMS 2.32519e-08 67 Residual RMS 2.32502e-08 68 Residual RMS 2.32486e-08 69 Residual RMS 2.32469e-08 70 Residual RMS 2.32453e-08 71 Residual RMS 2.32437e-08 72 Residual RMS 2.3242e-08 73 Residual RMS 2.32404e-08 74 Residual RMS 2.32388e-08 75 Residual RMS 2.32372e-08 76 Residual RMS 2.32356e-08 77 Residual RMS 2.3234e-08 78 Residual RMS 2.32324e-08 79 Residual RMS 2.32309e-08 80 Residual RMS 2.32293e-08 81 Residual RMS 2.32277e-08 82 Residual RMS 2.32262e-08 83 Residual RMS 2.32247e-08 84 Residual RMS 2.32231e-08 85 Residual RMS 2.32216e-08 86 Residual RMS 2.32201e-08 87 Residual RMS 2.32185e-08 88 Residual RMS 2.3217e-08 89 Residual RMS 2.32155e-08 90 Residual RMS 2.3214e-08 91 Residual RMS 2.32125e-08 92 Residual RMS 2.3211e-08 93 Residual RMS 2.32096e-08 94 Residual RMS 2.32081e-08 95 Residual RMS 2.32066e-08 96 Residual RMS 2.32051e-08 97 Residual RMS 2.32037e-08 98 Residual RMS 2.32022e-08 99 Residual RMS 2.32008e-08 100 Residual RMS 2.31993e-08 Total number of iterations 101 Computed U l2 norm : 0.640273 Computed U_EXACT l2 norm : 266.133 Error l2 norm: 265.517 Wall clock time in seconds = 0.107322 HELMHOLTZ Normal end of execution.