17 August 2018 10:11:54 PM MGMRES_TEST: C++ version Test the MGMRES library. TEST01 Test MGMRES_ST on the simple -1,2-1 matrix. Test 1 Matrix order N = 20 Inner iteration limit = 20 Outer iteration limit = 1 Initial X_ERROR = 53.5724 ITR = 1 Residual = 21 K = 1 Residual = 9.39149 K = 2 Residual = 5.61249 K = 3 Residual = 3.83406 K = 4 Residual = 2.83164 K = 5 Residual = 2.2014 K = 6 Residual = 1.77482 K = 7 Residual = 1.47029 K = 8 Residual = 1.24393 K = 9 Residual = 1.07026 K = 10 Residual = 0.933564 K = 11 Residual = 0.823688 K = 12 Residual = 0.733799 K = 13 Residual = 0.659153 K = 14 Residual = 0.59636 K = 15 Residual = 0.542942 K = 16 Residual = 0.49705 K = 17 Residual = 0.457279 K = 18 Residual = 0.422543 K = 19 Residual = 0.391993 K = 20 Residual = 0 MGMRES_ST Number of iterations = 20 Final residual = 0 Final X_ERROR = 3.76207e-14 Test 2 Matrix order N = 20 Inner iteration limit = 10 Outer iteration limit = 2 Initial X_ERROR = 53.5724 ITR = 1 Residual = 21 K = 1 Residual = 9.39149 K = 2 Residual = 5.61249 K = 3 Residual = 3.83406 K = 4 Residual = 2.83164 K = 5 Residual = 2.2014 K = 6 Residual = 1.77482 K = 7 Residual = 1.47029 K = 8 Residual = 1.24393 K = 9 Residual = 1.07026 K = 10 Residual = 0.933564 ITR = 2 Residual = 0.933564 K = 1 Residual = 0.870799 K = 2 Residual = 0.805248 K = 3 Residual = 0.738292 K = 4 Residual = 0.671495 K = 5 Residual = 0.606584 K = 6 Residual = 0.545422 K = 7 Residual = 0.489961 K = 8 Residual = 0.442132 K = 9 Residual = 0.403607 K = 10 Residual = 0.352454 MGMRES_ST Number of iterations = 20 Final residual = 0.352454 Final X_ERROR = 12.2128 Test 3 Matrix order N = 20 Inner iteration limit = 4 Outer iteration limit = 5 Initial X_ERROR = 53.5724 ITR = 1 Residual = 21 K = 1 Residual = 9.39149 K = 2 Residual = 5.61249 K = 3 Residual = 3.83406 K = 4 Residual = 2.83164 ITR = 2 Residual = 2.83164 K = 1 Residual = 2.42224 K = 2 Residual = 1.99652 K = 3 Residual = 1.60097 K = 4 Residual = 1.28892 ITR = 3 Residual = 1.28892 K = 1 Residual = 1.16868 K = 2 Residual = 1.06683 K = 3 Residual = 0.949296 K = 4 Residual = 0.851935 ITR = 4 Residual = 0.851935 K = 1 Residual = 0.792114 K = 2 Residual = 0.740289 K = 3 Residual = 0.693 K = 4 Residual = 0.645403 ITR = 5 Residual = 0.645403 K = 1 Residual = 0.612411 K = 2 Residual = 0.584505 K = 3 Residual = 0.552767 K = 4 Residual = 0.522552 MGMRES_ST Number of iterations = 20 Final residual = 0.522552 Final X_ERROR = 21.7238 TEST02 Test MGMRES_ST on matrix that is not quite the -1,2,-1 matrix, of order N = 9 First try, use zero initial vector: Before solving, X_ERROR = 16.5831 ITR = 1 Residual = 3 K = 1 Residual = 2.23607 K = 2 Residual = 1.91485 K = 3 Residual = 1.29099 K = 4 Residual = 0.377964 K = 5 Residual = 2.64365e-16 MGMRES_ST Number of iterations = 5 Final residual = 2.64365e-16 After solving, X_ERROR = 3.01605e-15 Final solution estimate: 0 3.5 1 1 2 1 3 6 4 7.5 5 8 6 7.5 7 6 8 3.5 Second try, use random initial vector: Before solving, X_ERROR = 15.8935 ITR = 1 Residual = 2.69846 K = 1 Residual = 2.29822 K = 2 Residual = 1.76549 K = 3 Residual = 1.11318 K = 4 Residual = 0.3694 K = 5 Residual = 0.168095 K = 6 Residual = 0.0623144 K = 7 Residual = 0.0227188 K = 8 Residual = 0.00504869 ITR = 2 Residual = 0.00504869 K = 1 Residual = 0.00112195 K = 2 Residual = 0.000409042 K = 3 Residual = 0.000151636 K = 4 Residual = 6.90017e-05 K = 5 Residual = 2.28977e-05 K = 6 Residual = 1.44375e-05 K = 7 Residual = 1.10909e-05 K = 8 Residual = 9.44583e-06 ITR = 3 Residual = 9.44583e-06 K = 1 Residual = 8.04479e-06 K = 2 Residual = 6.17999e-06 K = 3 Residual = 3.89663e-06 K = 4 Residual = 1.29307e-06 K = 5 Residual = 5.88408e-07 K = 6 Residual = 2.18128e-07 K = 7 Residual = 7.95259e-08 K = 8 Residual = 1.76727e-08 ITR = 4 Residual = 1.76727e-08 K = 1 Residual = 3.92731e-09 MGMRES_ST Number of iterations = 25 Final residual = 3.92731e-09 After solving, X_ERROR = 4.39551e-09 Final solution estimate: 0 3.5 1 1 2 1 3 6 4 7.5 5 8 6 7.5 7 6 8 3.5 TEST03 Test PMGMRES_ILU_CR on the simple -1,2-1 matrix. ia[0] = 0 ia[1] = 2 ia[2] = 5 ia[3] = 8 ia[4] = 11 ia[5] = 14 ia[6] = 17 ia[7] = 20 ia[8] = 23 ia[9] = 26 ia[10] = 29 ia[11] = 32 ia[12] = 35 ia[13] = 38 ia[14] = 41 ia[15] = 44 ia[16] = 47 ia[17] = 50 ia[18] = 53 ia[19] = 56 ia[20] = 58 Test 1 Matrix order N = 20 Inner iteration limit = 20 Outer iteration limit = 1 Initial X_ERROR = 53.5724 PMGMRES_ILU_CR Number of unknowns = 20 ITR = 0 Residual = 53.5724 K = 0 Residual = 1.26434e-14 PMGMRES_ILU_CR: Iterations = 1 Final residual = 1.26434e-14 Final X_ERROR = 8.29924e-15 Test 2 Matrix order N = 20 Inner iteration limit = 10 Outer iteration limit = 2 Initial X_ERROR = 53.5724 PMGMRES_ILU_CR Number of unknowns = 20 ITR = 0 Residual = 53.5724 K = 0 Residual = 1.26434e-14 PMGMRES_ILU_CR: Iterations = 1 Final residual = 1.26434e-14 Final X_ERROR = 8.29924e-15 Test 3 Matrix order N = 20 Inner iteration limit = 4 Outer iteration limit = 5 Initial X_ERROR = 53.5724 PMGMRES_ILU_CR Number of unknowns = 20 ITR = 0 Residual = 53.5724 K = 0 Residual = 1.26434e-14 PMGMRES_ILU_CR: Iterations = 1 Final residual = 1.26434e-14 Final X_ERROR = 8.29924e-15 TEST04 Test PMGMRES_ILU_CR on a simple 5 x 5 matrix. ia[0] = 0 ia[1] = 3 ia[2] = 4 ia[3] = 6 ia[4] = 7 ia[5] = 9 ia[6] = 0 Test 1 Matrix order N = 5 Inner iteration limit = 20 Outer iteration limit = 1 Initial X_ERROR = 7.4162 PMGMRES_ILU_CR Number of unknowns = 5 ITR = 0 Residual = 12.083 K = 0 Residual = 3.67696 K = 1 Residual = 2.46137e-15 PMGMRES_ILU_CR: Iterations = 2 Final residual = 2.46137e-15 Final X_ERROR = 1.9984e-15 Test 2 Matrix order N = 5 Inner iteration limit = 10 Outer iteration limit = 2 Initial X_ERROR = 7.4162 PMGMRES_ILU_CR Number of unknowns = 5 ITR = 0 Residual = 12.083 K = 0 Residual = 3.67696 K = 1 Residual = 2.46137e-15 PMGMRES_ILU_CR: Iterations = 2 Final residual = 2.46137e-15 Final X_ERROR = 1.9984e-15 Test 3 Matrix order N = 5 Inner iteration limit = 4 Outer iteration limit = 5 Initial X_ERROR = 7.4162 PMGMRES_ILU_CR Number of unknowns = 5 ITR = 0 Residual = 12.083 K = 0 Residual = 3.67696 K = 1 Residual = 2.46137e-15 PMGMRES_ILU_CR: Iterations = 2 Final residual = 2.46137e-15 Final X_ERROR = 1.9984e-15 MGMRES_TEST: Normal end of execution. 17 August 2018 10:11:54 PM