Solve the Matrix stored in mtx format

The code for this example is located in examples/MatSolve

Brief

This example solves the linear system using different solvers.

Description

This example may run in both serial and parallel modes with NP processes.

The code loads the matrix and right-hand side from files. If right-hand side is omitted, the artificial rhs=(1,1,...,1) is used. The specific solver is defined by user. User may also provide options file to alter default solver options.

Arguments

Usage: ./MatSolve method_number<0:INNER_ILU2,1:INNER_MLILUC,2:PETSc,3:Trilinos_Aztec,4:Trilinos_Belos,5:Trilinos_Ifpack,6:Trilinos_ML,7:ANI> matrix.mtx [right_hand_side.rhs] [solver_options.txt]

• First parameter is the Solver type:
  • 0 – INNER_ILU2, inner Solver based on BiCGStab(L) solver with second order ILU factorization as preconditioner;
  • 1 – INNER_MLILUC, inner Solver based on BiCGStab(L) solver with second order Crout-ILU with inversed-based condition estimation and unsymmetric reordering for diagonal dominance as preconditioner;
  • 2 – PETSc, external Solver AztecOO from Trilinos package;
  • 3 – Trilinos_Aztec, external Solver Belos from Trilinos package, currently without preconditioner;
  • 4 – Trilinos_Belos, external Solver AztecOO with ML preconditioner;
  • 5 – Trilinos_Ifpack, external Solver AztecOO with Ifpack preconditioner;
  • 6 – Trilinos_ML, external Solver PETSc;
  • 7 – ANI, external Solver from ANI3D based on ILU2 (sequential Fortran version).
• Second parameter is the file with matrix in mtx format.
• Third optional parameter is the file with right-hand side in mtx format.
• Fourth optional parameter is the file with solver parameters, see examples/MatSolve/database.txt as example.

Running example

FVDiscr/tmp/A.mtx and right-hand side /tmp/b.rhsFVDiscr example

$ cd examples/MatSolve
$ mpirun -np 4 ./MatSolve 0 /tmp/A.mtx /tmp/b.rhs 
load matrix: 0.346156
load vector: 0.0542159
preconditioner: 0.516358
solver: 0.0345631.37095e-06 | 0
||Ax-b|| 1.37095e-06 ||b|| 2.14884 ||Ax-b||/||b|| 6.37997e-07
norms: 0.00276518
4 processors solved in 0.95183 secs with 4 iterations to 1.37095e-06 norm matrix "/tmp/A.mtx" vector "/tmp/b.rhs" true residual ||Ax-b||/||b|| 6.37997e-07
reason: converged due to relative tolerance