Structure

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.

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:

$$\Vert x\Vert\le\varepsilon_{r}\Vert x\Vert_{0}+\varepsilon_{a}$$

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

$$\Vert x\Vert\le\varepsilon_{r}\Vert rhs\Vert_{0}+\varepsilon_{a}$$

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

$$\Vert x\Vert\le\varepsilon_{a}$$

If convergenceIn is equal to convergenceInRes

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

$$\Vert res\Vert\le\varepsilon_{r}\Vert res\Vert_{0}+\varepsilon_{a}$$

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

$$\Vert res\Vert\le\varepsilon_{r}\Vert rhs\Vert_{0}+\varepsilon_{a}$$

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

$$\Vert res\Vert\le\varepsilon_{a}$$