Documentation: Overview Solvers

Solving with Mumps

Installation

You can find installation information for Mumps here.

Edit in Jamfile

If the library paths for Mumps package installation is in the standard paths /usr/lib, /usr/lib64, then you do not need to edit anything in Jamfile.

If it is outside the standard paths /usr/lib, /usr/lib64, then in $CONCEPTS_PATH/boost-build.jam file, you need to add,

• MUMPS_PATH
• MUMPS_INCLPATH
• MUMPS_SUFFIX

Documentation

The documentation for the class Mumps can be found here.

Syntax

Considering, A to be a system matrix, rhs be a right hand side vector, and sol be a solution vector.

The syntax to use sequential version of Mumps:

For C++

concepts::Mumps<Real> solver(A)
concepts::Vector<Real> sol(spc)
solver(rhs, sol)

Note that, you have to add MPI_INIT, MPI_FINALIZE (see parallelizationTutorial.cc) in your main program, if MPI is installed in your machine.

For Python

To use a MUMPS solver, first import MPI libary,

from mpi4py import MPI

then, use a sequential version of Mumps linear solver in the following way:

solver = MUMPS_r(A = A)
sol = concepts.Vector_r(spc = space)
solver(fncY = rhs, fncX = sol)

Solving with SuperLU

Installation

You can find the installation information for SuperLU library here.

Documentation

The documentation for the class SuperLU can be found here.

Syntax

Considering, A to be a system matrix, rhs be a right hand side vector, and sol be a solution vector.

For C++

concepts::SuperLU<Real> solver(A)
concepts::Vector<Real> sol(spc)
solver(rhs, sol)

For Python

solver = SuperLU _r(A = A)
sol = concepts.Vector_r(spc = space)
solver(fncY = rhs, fncX = sol)

Solving with Conjugate Gradient (CG) method

Documentation

The documentation for the class CG can be found here.

Syntax

Considering, A to be a system matrix, rhs be a right hand side vector, and sol be a solution vector.

We use CG method with a tolerance of 1e-6 and a maximum number of iterations of 200.

For C++

concepts::CG<Real> solver(A,1e-6, 200);
concepts::Vector<Real> sol(spc)
solver(rhs, sol)

For Python

solver = CG_r(A = A, maxeps=1e-6, maxit=200)
sol = concepts.Vector_r(spc = space)
solver(fncY = rhs, fncX = sol)

Other Solvers

Other solvers with similar syntax are:

• General minimal residuals (GMRES)
• BiConjugate Gradient Stabilized (BiCGStab)

For the complete list of available linear solvers, please see here.