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AbstractLinSolver

AbstractLinSolver_ is an abstract class for solving system of linear equation.

note

It is important to note that AbstractLinSolver_ is created to build an interface between EASIFEM library and other existing open-source and powerful linear solver libraries.

Structure​

TYPE, ABSTRACT :: AbstractLinSolver_
  LOGICAL(LGT) :: isInitiated = .FALSE.
  !! is object initiated?
  TYPE(String) :: engine
  !! Name of the engine
  !! NATIVE-SERIAL
  !! NATIVE-OMP
  !! NATIVE-ACC
  !! NATIVE-MPI
  !! PETSC
  !! LIS-OMP
  !! LIS-MPI
  INTEGER(I4B) :: solverName = 0
  !! Solver name
  INTEGER(I4B) :: ierr = 0
  !! Error code returned by the solver
  INTEGER(I4B) :: preconditionOption = 0
  !! Name of preconditioner;
  !! NO_PRECONDITION
  !! LEFT_PRECONDITION
  !! RIGHT_PRECONDITION
  !! LEFT_RIGHT_PRECONDITON
  INTEGER(I4B) :: iter = 0
  !! Current iteration number
  INTEGER(I4B) :: maxIter = 0
  !! Maximum iteration number
  REAL(DFP) :: atol = 0.0_DFP
  !! absolute tolerance
  REAL(DFP) :: rtol = 1.0E-8
  !! relative tolerance
  REAL(DFP) :: tol = 0.0_DFP
  !! Tolerance for testing convergence
  REAL(DFP) :: normRes = 0.0_DFP
  !! norm Residual
  REAL(DFP) :: error0 = 0.0_DFP
  !! initial error res or sol
  REAL(DFP) :: error = 0.0_DFP
  !! final error in res of sol
  INTEGER(I4B) :: convergenceIn = convergenceInRes
  !! convergence in residual or solution
  INTEGER(I4B) :: convergenceType = relativeConvergence
  !! relative/ absolute convergence
  LOGICAL(LGT) :: relativeToRHS = .FALSE.
  !! In case of relative convergence
  !! is convergence
  !! is relative to
  !! right hand side
  INTEGER(I4B) :: KrylovSubspaceSize = 15
  !! Useful for GMRES type algorithm
  INTEGER(I4B) :: globalNumRow = 0, globalNumColumn = 0
  !! Size of the global problem;
  INTEGER(I4B) :: localNumRow = 0, localNumColumn = 0
  !! Size of the problem on a single process
  REAL(DFP), ALLOCATABLE :: RES(:)
  !! Residual in each iteration
  CLASS(AbstractMatrixField_), POINTER :: Amat => NULL()
  !! Pointer to child of [[AbstractMatrixField_]]
  • isInitiated = .FALSE. is object initiated
  • engine is the name of the engine, following options are possible:
    • NATIVE-SERIAL
    • NATIVE-OMP
    • NATIVE-ACC
    • NATIVE-MPI
    • PETSC
    • LIS-OMP
    • LIS-MPI
  • solverName=0 is the name of solver
  • ierr = 0 denotes the error code returned by the solver
  • preconditionOption = 0 is the name of preconditioner, following options are possible:
    • NO_PRECONDITION
    • LEFT_PRECONDITION
    • RIGHT_PRECONDITION
    • LEFT_RIGHT_PRECONDITON
  • iter = 0 denotes the current iteration number, and total numbe of iterations taken by the solver
  • maxIter = 0, is the maximum iteration number allowed for the solver.
  • atol = 0.0_DFP denotes the absolute tolerance.
  • rtol = 1.0E-8 denotes the relative tolerance.
  • tol = 0.0_DFP is the tolerance for testing convergence.
  • normRes = 0.0_DFP is the norm of Residual.
  • error0 = 0.0_DFP, initial error in residual or solution.
  • error = 0.0_DFP, final error in residual or solution.
  • convergenceIn = convergenceInRes, convergence in residual or solution
  • convergenceType = relativeConvergence, relative or absolute convergence
  • relativeToRHS = .FALSE., in case of relative convergence, if relativeToRHS is true, then convergence is relative to right-hand side.
  • KrylovSubspaceSize = 15, useful for GMRES type algorithm
  • globalNumRow = 0, globalNumColumn = 0, size of the global problem;
  • localNumRow = 0, localNumColumn = 0, size of the problem on a single process
  • dbcIndx(:), Indices where Dirichlet boundary conditions is prescribed
  • RES(:), Residual in each iteration
  • Amat => NULL(), Pointer to child of AbstractMatrixField_

Convergence criteria​

If convergenceIn is equal to convergenceInSol​

For convergenceType equals to relativeConvergence, and relativeToRHS=.FALSE., we use following convergence criteria:

∥x∥≤εr∥x∥0+εa\Vert x\Vert\le\varepsilon_{r}\Vert x\Vert_{0}+\varepsilon_{a}

For convergenceType equals to relativeConvergence, and relativeToRHS=.TRUE., we use following convergence criteria:

∥x∥≤εr∥rhs∥0+εa\Vert x\Vert\le\varepsilon_{r}\Vert rhs\Vert_{0}+\varepsilon_{a}

Note that for convergenceType equals to absoluteConvergence, we have rtol=0.0, therefore, relativeToRHS options is not used, and the resultant criteria becomes:

∥x∥≤εa\Vert x\Vert\le\varepsilon_{a}

If convergenceIn is equal to convergenceInRes​

For convergenceType equals to relativeConvergence, and relativeToRHS=.FALSE., we use following convergence criteria:

∥res∥≤εr∥res∥0+εa\Vert res\Vert\le\varepsilon_{r}\Vert res\Vert_{0}+\varepsilon_{a}

For convergenceType equals to relativeConvergence, and relativeToRHS=.TRUE., we use following convergence criteria:

∥res∥≤εr∥rhs∥0+εa\Vert res\Vert\le\varepsilon_{r}\Vert rhs\Vert_{0}+\varepsilon_{a}

Note that for convergenceType equals to absoluteConvergence, we have rtol=0.0, therefore, relativeToRHS options is not used, and the resultant criteria becomes:

∥res∥≤εa\Vert res\Vert\le\varepsilon_{a}

Methods​