sfepy.solvers.ls module

class sfepy.solvers.ls.CholeskySolver(conf, **kwargs)

Interface to scikit-sparse.cholesky solver.

Kind: ‘ls.cholesky’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

use_presolvebool (default: False)

If True, pre-factorize the matrix.

use_mtx_digestbool (default: True)

If True, determine automatically a reused matrix using its SHA1 digest. If False, .clear() has to be called manually whenever the matrix changes - expert use only!

name = 'ls.cholesky'

presolve(mtx, use_mtx_digest=True)

class sfepy.solvers.ls.MUMPSSolver(conf, **kwargs)

Interface to MUMPS solver.

Kind: ‘ls.mumps’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

use_presolvebool (default: False)

If True, pre-factorize the matrix.

use_mtx_digestbool (default: True)

If True, determine automatically a reused matrix using its SHA1 digest. If False, .clear() has to be called manually whenever the matrix changes - expert use only!

memory_relaxationint (default: 20)

The percentage increase in the estimated working space.

clear()

static coo_is_symmetric(mtx, tol=1e-09)

Symmetry check of the sparse matrix.

name = 'ls.mumps'

presolve(mtx, use_mtx_digest=True, factorize=True)

class sfepy.solvers.ls.MultiProblem(conf, context=None, **kwargs)

Conjugate multiple problems.

Allows to define conjugate multiple problems.

Kind: ‘ls.cm_pb’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

method{‘auto’, ‘umfpack’, ‘superlu’} (default: ‘auto’)

The actual solver to use.

use_presolvebool (default: False)

If True, pre-factorize the matrix.

use_mtx_digestbool (default: True)

If True, determine automatically a reused matrix using its SHA1 digest. If False, .clear() has to be called manually whenever the matrix changes - expert use only!

otherslist

The list of auxiliary problem definition files.

coupling_variableslist

The list of coupling variables.

init_subproblems(conf, **kwargs)

name = 'ls.cm_pb'

sparse_submat(Ad, Ar, Ac, gr, gc, S)

A[gr,gc] = S

class sfepy.solvers.ls.PETScKrylovSolver(conf, comm=None, context=None, **kwargs)

PETSc Krylov subspace solver.

The solver supports parallel use with a given MPI communicator (see comm argument of PETScKrylovSolver.__init__()) and allows passing in PETSc matrices and vectors. Returns a (global) PETSc solution vector instead of a (local) numpy array, when given a PETSc right-hand side vector.

The solver and preconditioner types are set upon the solver object creation. Tolerances can be overridden when called by passing a conf object.

Convergence is reached when rnorm < max(eps_r * rnorm_0, eps_a), where, in PETSc, rnorm is by default the norm of preconditioned residual.

Kind: ‘ls.petsc’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

methodstr (default: ‘cg’)

The actual solver to use.

setup_precondcallable

User-supplied function for the preconditioner initialization/setup. It is called as setup_precond(mtx, context), where mtx is the matrix, context is a user-supplied context, and should return an object with setUp(self, pc) and apply(self, pc, x, y) methods. Has precedence over the precond/sub_precond parameters.

precondstr (default: ‘icc’)

The preconditioner.

sub_precondstr (default: ‘none’)

The preconditioner for matrix blocks (in parallel runs).

precond_side{‘left’, ‘right’, ‘symmetric’, None}

The preconditioner side.

create_matrixcallable

User-defined function returning the linear system matrix and optionally a precoditioning matrix in a PETSc format. It is called as create_matrix(self, mtx, context, comm), where self is the solver instance, mtx is the matrix passed to self.__call__(), context is a user-supplied context and comm the PETSc communicator.

block_sizeint

The number of degrees of freedom per node.

i_maxint (default: 100)

The maximum number of iterations.

eps_afloat (default: 1e-08)

The absolute tolerance for the residual.

eps_rfloat (default: 1e-08)

The relative tolerance for the residual.

eps_dfloat (default: 100000.0)

The divergence tolerance for the residual.

force_reusebool (default: False)

If True, skip the check whether the KSP solver object corresponds to the mtx argument: it is always reused.

**

Additional parameters supported by the method. Can be used to pass all PETSc options supported by petsc.Options().

create_ksp(options=None, comm=None)

create_petsc_matrix(mtx, comm=None)

init_ksp(conf=None, comm=None)

name = 'ls.petsc'

set_field_split(field_ranges, comm=None)

Setup local PETSc ranges for fields to be used with ‘fieldsplit’ preconditioner.

This function must be called before solving the linear system.

class sfepy.solvers.ls.PyAMGKrylovSolver(conf, context=None, **kwargs)

Interface to PyAMG Krylov solvers.

Kind: ‘ls.pyamg_krylov’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

methodstr (default: ‘cg’)

The actual solver to use.

setup_precondcallable (default: <function PyAMGKrylovSolver.<lambda> at 0x73b12e8470a0>)

User-supplied function for the preconditioner initialization/setup. It is called as setup_precond(mtx, context), where mtx is the matrix, context is a user-supplied context, and should return one of {sparse matrix, dense matrix, LinearOperator}.

callbackcallable

User-supplied function to call after each iteration. It is called as callback(xk), where xk is the current solution vector, except the gmres method, where the argument is the residual norm.

i_maxint (default: 100)

The maximum number of iterations.

eps_rfloat (default: 1e-08)

The relative tolerance for the residual.

**

Additional parameters supported by the method.

name = 'ls.pyamg_krylov'

class sfepy.solvers.ls.PyAMGSolver(conf, **kwargs)

Interface to PyAMG solvers.

The method parameter can be one of: ‘smoothed_aggregation_solver’, ‘ruge_stuben_solver’. The accel parameter specifies the Krylov solver name, that is used as an accelerator for the multigrid solver.

Kind: ‘ls.pyamg’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

methodstr (default: ‘smoothed_aggregation_solver’)

The actual solver to use.

accelstr

The accelerator.

callbackcallable

User-supplied function to call after each iteration. It is called as callback(xk), where xk is the current solution vector, except the gmres accelerator, where the argument is the residual norm.

i_maxint (default: 100)

The maximum number of iterations.

eps_rfloat (default: 1e-08)

The relative tolerance for the residual.

force_reusebool (default: False)

If True, skip the check whether the MG solver object corresponds to the mtx argument: it is always reused.

**

Additional parameters supported by the method. Use the ‘method:’ prefix for arguments of the method construction function (e.g. ‘method:max_levels’ : 5), and the ‘solve:’ prefix for the subsequent solver call.

name = 'ls.pyamg'

class sfepy.solvers.ls.PyPardisoSolver(conf, method=None, **kwargs)

PyPardiso direct solver.

PyPardiso (https://github.com/haasad/PyPardiso) is a python package to solve large sparse linear systems of equations with the Intel oneAPI Math Kernel Library PARDISO solver, a shared-memory multiprocessing parallel direct sparse solver. PyPardiso is not a python interface to the PARDISO Solver Project (https://panua.ch/pardiso).

Kind: ‘ls.pypardiso’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

use_presolvebool (default: False)

If True, pre-factorize the matrix. It is not needed for performance here, as it just calls pypardiso.spsolve() on zeros.

name = 'ls.pypardiso'

presolve(mtx, use_mtx_digest=True)

class sfepy.solvers.ls.RMMSolver(conf, context=None, **kwargs)

Special solver for explicit transient elastodynamics.

The solver uses the reciprocal mass matrix algorithm [1], [2] to directly construct a sparse inverse mass matrix. Instead of solving a linear system, calling the solver simply performs a sparse matrix multiplication.

Limitations:

• Assumes that the density is constant in time.

• Uses the direct EBC application, i.e., no EBC projection matrix.

[1]

González, J.A., Kolman, R., Cho, S.S., Felippa, C.A., Park, K.C., 2018. Inverse mass matrix via the method of localized Lagrange multipliers. International Journal for Numerical Methods in Engineering 113, 277–295. https://doi.org/10.1002/nme.5613

[2]

González, J.A., Kopačka, J., Kolman, R., Cho, S.S., Park, K.C., 2019. Inverse mass matrix for isogeometric explicit transient analysis via the method of localized Lagrange multipliers. International Journal for Numerical Methods in Engineering 117, 939–966. https://doi.org/10.1002/nme.5986

Kind: ‘ls.rmm’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

rmm_termstr

The RMM term definition, see MassTerm.

debugbool (default: False)

If True, run in debug mode.

init_rmm(mtx)

name = 'ls.rmm'

class sfepy.solvers.ls.SchurMumps(conf, **kwargs)

Mumps Schur complement solver.

Kind: ‘ls.schur_mumps’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

use_presolvebool (default: False)

If True, pre-factorize the matrix.

use_mtx_digestbool (default: True)

If True, determine automatically a reused matrix using its SHA1 digest. If False, .clear() has to be called manually whenever the matrix changes - expert use only!

memory_relaxationint (default: 20)

The percentage increase in the estimated working space.

schur_variableslist

The list of Schur variables.

name = 'ls.schur_mumps'

class sfepy.solvers.ls.ScipyDirect(conf, method=None, **kwargs)

Direct sparse solver from SciPy.

Kind: ‘ls.scipy_direct’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

method{‘auto’, ‘umfpack’, ‘superlu’} (default: ‘auto’)

The actual solver to use.

use_presolvebool (default: False)

If True, pre-factorize the matrix.

use_mtx_digestbool (default: True)

If True, determine automatically a reused matrix using its SHA1 digest. If False, .clear() has to be called manually whenever the matrix changes - expert use only!

clear()

name = 'ls.scipy_direct'

presolve(mtx, use_mtx_digest=True)

class sfepy.solvers.ls.ScipyIterative(conf, context=None, **kwargs)

Interface to SciPy iterative solvers.

The eps_r tolerance is both absolute and relative - the solvers stop when either the relative or the absolute residual is below it.

Kind: ‘ls.scipy_iterative’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

methodstr (default: ‘cg’)

The actual solver to use.

setup_precondcallable (default: <function ScipyIterative.<lambda> at 0x73b12e846a70>)

User-supplied function for the preconditioner initialization/setup. It is called as setup_precond(mtx, context), where mtx is the matrix, context is a user-supplied context, and should return one of {sparse matrix, dense matrix, LinearOperator}.

callbackcallable

User-supplied function to call after each iteration. It is called as callback(xk), where xk is the current solution vector, except the gmres method, where the argument is the residual.

i_maxint (default: 100)

The maximum number of iterations.

eps_afloat (default: 1e-08)

The absolute tolerance for the residual.

eps_rfloat (default: 1e-08)

The relative tolerance for the residual.

**

Additional parameters supported by the method.

name = 'ls.scipy_iterative'

class sfepy.solvers.ls.ScipySuperLU(conf, **kwargs)

SuperLU - direct sparse solver from SciPy.

Kind: ‘ls.scipy_superlu’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

use_presolvebool (default: False)

If True, pre-factorize the matrix.

use_mtx_digestbool (default: True)

If True, determine automatically a reused matrix using its SHA1 digest. If False, .clear() has to be called manually whenever the matrix changes - expert use only!

name = 'ls.scipy_superlu'

class sfepy.solvers.ls.ScipyUmfpack(conf, **kwargs)

UMFPACK - direct sparse solver from SciPy.

Kind: ‘ls.scipy_umfpack’

For common configuration parameters, see Solver.

Specific configuration parameters:

Parameters:

use_presolvebool (default: False)

If True, pre-factorize the matrix.

use_mtx_digestbool (default: True)

If True, determine automatically a reused matrix using its SHA1 digest. If False, .clear() has to be called manually whenever the matrix changes - expert use only!

name = 'ls.scipy_umfpack'

sfepy.solvers.ls.petsc_call(call)

Decorator handling argument preparation and timing for PETSc-based linear solvers.

sfepy.solvers.ls.solve(mtx, rhs, solver_class=None, solver_conf=None)

Solve the linear system with the matrix mtx and the right-hand side rhs.

Convenience wrapper around the linear solver classes below.

sfepy.solvers.ls.standard_call(call)

Decorator handling argument preparation and timing for linear solvers.