*************************************************************************************** This code is meant to compare the convergence behaviour of PARALLEL and SERIAL implementation for selected Preconditioner-Solver combination **************** COMPILE TIME PARAMETERS ************** PARALLEL SOLVER TYPE : 2 PRECONDITIONER TYPE : 2 WRITE CONVERGENCE : 1 ******************************************************* *************** WORLD_SIZE : 4 Now setting up the matrices A and M process with rank : 0 is here Grid size: 32 Basis size: 33 MATRIX SETUP COMPLETE ***************************** PARALLEL SOLVER starts ******************************** Dispalying the complete intial solution vector by world_rank : 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Dispalying the complete matrix A by world_rank : 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 Dispalying the complete rhs vector by world_rank : 0 0 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0 Now Displaying the A matrix part from process with world_rank : 0 64 -32 0 0 0 0 0 0 -32 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 0 -32 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 The initial residual(2-norm) is 0.173993 The initial residual(inf-norm) is 0.03125 Employed pre-conditioner : SSOR with factor = 1 for pc_cycles = 1 Employed Iterative solver : parallel Restarted GMRES with restart=size and max_iter=size and tol = 1e-08 Now Displaying the A matrix part from process with world_rank : 3 64 -32 0 0 0 0 0 0 -32 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 0 -32 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 Now Displaying the A matrix part from process with world_rank : 1 1 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 1 Now Displaying the A matrix part from process with world_rank : 2 64 -32 0 0 0 0 0 0 0 -32 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 === RestartedGMResSolver Iter Defect Rate 0 8.68318185103925e-03 1 6.65733330303873e-03 7.66692834175982e-01 2 6.24239575126496e-03 9.37672107901766e-01 3 5.82057453531460e-03 9.32426390001807e-01 4 5.37150369024434e-03 9.22847677261813e-01 5 4.04331167251413e-03 7.52733667456571e-01 6 2.53198234171030e-03 6.26214980883707e-01 7 1.29750488744955e-03 5.12446262391038e-01 8 4.46561905145409e-04 3.44169728734661e-01 9 2.11534964045806e-04 4.73696841598986e-01 10 9.87535016294365e-05 4.66842453562676e-01 11 2.17352609919646e-05 2.20096104273083e-01 12 2.13067906702132e-06 9.80286856370862e-02 13 7.20257138618716e-07 3.38041120207575e-01 14 4.52302773301761e-07 6.27974023512174e-01 15 3.20236929544126e-07 7.08014516927304e-01 16 1.86687460742098e-07 5.82966683473569e-01 17 2.12773082415777e-08 1.13972883647347e-01 18 4.23257592655736e-09 1.98924407096125e-01 19 3.59214067076761e-10 8.48689009505695e-02 20 8.54242854009112e-11 2.37808853356115e-01 === rate=3.97781996234850e-01, T=3.51293300000000e-03, TIT=1.75646650000000e-04, IT=20 Convergence details for the selected solver and preconditioner combination convergence achieved : 1 iterations taken : 20 reduction achieved : 9.83790122864779e-09 convergence rate : 3.97781996234850e-01 time elapsed : 3.51293300000000e-03 Backward redistribution of the solution vector completed. The residual(inf_norm) for the selected solver and preconditioner combination is : 2.96282154366168e-09 The residual(2-norm) for the selected solver and preconditioner combination is : 6.62622483834134e-09 ***************************** PARALLEL SOLVER Completed !! ******************************** *************************************************************************************** *************************************************************************************** ***************************** SERIAL SOLVER starts ******************************** Dispalying the complete intial solution vector v 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Dispalying the complete matrix A 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -32 64 -32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 Dispalying the complete rhs vector b 0 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0.03125 0 The initial residual(2-norm) is 0.173993 The initial residual(inf-norm) is 0.03125 Employed pre-conditioner : SSOR with factor = 1 for pc_cycles = 1 Employed Iterative solver : Restated GMRES with restart=size and max_iter=size and tol = 1e-08 === RestartedGMResSolver Iter Defect Rate 0 0.0103623 1 0.00930749 0.89821 2 0.00810167 0.870447 3 0.0065647 0.81029 4 0.0046007 0.700823 5 0.00230585 0.501196 6 0.000671866 0.291375 7 0.000116192 0.17294 8 1.33489e-05 0.114886 9 1.93452e-06 0.144919 10 1.16505e-06 0.602243 11 6.22683e-07 0.534469 12 4.70373e-07 0.755398 13 2.65926e-07 0.565352 14 6.64779e-08 0.249986 15 1.31468e-08 0.197762 16 1.20503e-09 0.0916592 17 1.49984e-10 0.124465 18 8.32779e-12 0.0555244 === rate=0.312411, T=0.00202901, TIT=0.000112723, IT=18 Convergence details for the selected solver and preconditioner combination convergence achieved : 1 iterations taken : 18 reduction achieved : 8.03664626941521e-10 convergence rate : 3.12411045858427e-01 time elapsed : 2.02901400000000e-03 The residual(inf_norm) for the selected solver and preconditioner combination is : 3.01175973049794e-10 The residual(2-norm) for the selected solver and preconditioner combination is : 8.08217706120144e-10 ***************************** SERIAL SOLVER Completed !! ******************************** *************************************************************************************** *********** Now COmparing parallel and serial solutions ********************* Iter-parallel : 20 Iter-serial : 18 difference in inf-norm is sol_s : 1.25000000000590e-01 sol_p : 1.25000000157323e-01 diff : 1.79945322531516e-10 difference in normalized 2-norm is sol_s : 8.98932721306176e-02 sol_p : 8.98932721908264e-02 diff : 8.51559646730081e-11 *********************** Comparison Complete ************************** ***************************************************************************************