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'''
This module contains all the function and class needed to wrap a PETSc Preconditioner in NGSolve
'''
from petsc4py import PETSc
from ngsolve import BaseMatrix, comp
from ngsPETSc import Matrix, VectorMapping
class PETScPreconditioner(BaseMatrix):
'''
This class creates a Netgen/NGSolve BaseMatrix corresponding to a PETSc PC
:arg mat: NGSolve Matrix one would like to build the PETSc preconditioner for.
:arg freeDofs: not constrained degrees of freedom of the finite element space over
which the BilinearForm corresponding to the matrix is defined.
:arg solverParameters: parameters to be passed to the KSP solver
:arg optionsPrefix: special solver options prefix for this specific Krylov solver
:arg matType: type of sparse matrix, i.e. PETSc sparse: aij,
MKL sparse: mklaij or CUDA: aijcusparse
'''
def __init__(self, mat, freeDofs, solverParameters=None, optionsPrefix="", nullspace=None,
matType="aij"):
BaseMatrix.__init__(self)
if hasattr(solverParameters, "ToDict"):
solverParameters = solverParameters.ToDict()
self.ngsMat = mat
if hasattr(self.ngsMat, "row_pardofs"):
dofs = self.ngsMat.row_pardofs
else:
dofs = None
self.vecMap = VectorMapping((dofs,freeDofs,{"bsize":self.ngsMat.local_mat.entrysizes}))
petscMat = Matrix(self.ngsMat, (dofs, freeDofs, None), matType).mat
self.lgmap = petscMat.getLGMap()[0]
if nullspace is not None:
if nullspace.near:
petscMat.mat.setNearNullSpace(nullspace.nullspace)
self.petscPreconditioner = PETSc.PC().create(comm=petscMat.getComm())
self.petscPreconditioner.setOperators(petscMat)
options_object = PETSc.Options()
if solverParameters is not None:
for optName, optValue in solverParameters.items():
options_object[optName] = optValue
self.petscPreconditioner.setOptionsPrefix(optionsPrefix)
self.petscPreconditioner.setFromOptions()
self.petscPreconditioner.setUp()
self.petscVecX, self.petscVecY = petscMat.createVecs()
def Shape(self):
'''
Shape of the BaseMatrix
'''
return self.ngsMat.shape
def CreateVector(self,col):
'''
Create vector corresponding to the matrix
:arg col: True if one want a column vector
'''
return self.ngsMat.CreateVector(not col)
def Mult(self,x,y):
'''
BaseMatrix multiplication Ax = y
:arg x: vector we are multiplying
:arg y: vector we are storeing the result in
'''
self.vecMap.petscVec(x,self.petscVecX)
self.petscPreconditioner.apply(self.petscVecX, self.petscVecY)
self.vecMap.ngsVec(self.petscVecY, y)
def MultTrans(self,x,y):
'''
BaseMatrix multiplication A^T x = y
:arg x: vector we are multiplying
:arg y: vector we are storeing the result in
'''
self.vecMap.petscVec(x,self.petscVecX)
self.petscPreconditioner.applyTranspose(self.petscVecX, self.petscVecY)
self.vecMap.ngsVec(self.petscVecY, y)
def setActingDofs(self, dofs):
'''
Set the acting dofs of the preconditioner
:arg dofs: dofs that the preconditioner is acting on
'''
self.actingDofs = dofs
def createPETScPreconditioner(mat, freeDofs, solverParameters):
'''
Create PETSc PC that can be accessed by NGSolve.
:arg mat: NGSolve Matrix one would like to build the PETSc preconditioner for.
:arg freeDofs: not constrained degrees of freedom of the finite element space over
which the BilinearForm corresponding to the matrix is defined.
:arg solverParameters: parameters to be passed to the KSP solver
'''
return PETScPreconditioner(mat, freeDofs, solverParameters)
class ASMPreconditioner(PETScPreconditioner):
'''
This class creates a Netgen/NGSolve BaseMatrix corresponding to a PETSc ASM PC
'''
def __init__(self, mat, freeDofs, solverParameters=None, optionsPrefix="",
nullspace=None, matType="aij", blocks=None):
if "sub_pc_type" not in solverParameters:
solverParameters["sub_pc_type"] = "lu"
if "sub_pc_factor_mat_ordering_type" not in solverParameters:
solverParameters["sub_pc_factor_mat_ordering_type"] = "natural"
super().__init__(mat, freeDofs, solverParameters, optionsPrefix, nullspace, matType)
self.asmpc = None
if blocks is not None:
if len (blocks) == 0:
self.ises = [PETSc.IS().createGeneral([0], comm=PETSc.COMM_SELF)]
else:
if self.petscPreconditioner.getComm().size > 1:
self.ises = [self.lgmap.applyIS(PETSc.IS().createGeneral(list(block),
comm=PETSc.COMM_SELF)) for block in blocks]
else:
self.ises = [PETSc.IS().createGeneral(list(block),
comm=PETSc.COMM_SELF) for block in blocks]
self.asmpc = PETSc.PC().create(comm=self.petscPreconditioner.getComm())
self.asmpc.incrementTabLevel(1, parent=self.petscPreconditioner)
self.asmpc.setOptionsPrefix(optionsPrefix)
self.asmpc.setFromOptions()
self.asmpc.setOperators(*self.petscPreconditioner.getOperators())
self.asmpc.setType(self.asmpc.Type.ASM)
self.asmpc.setASMType(PETSc.PC.ASMType.BASIC)
self.asmpc.setASMLocalSubdomains(len(self.ises), self.ises)
self.asmpc.setUp()
def Mult(self,x,y):
'''
BaseMatrix multiplication Ax = y
:arg x: vector we are multiplying
:arg y: vector we are storeing the result in
'''
self.vecMap.petscVec(x,self.petscVecX)
if self.asmpc is not None:
self.asmpc.apply(self.petscVecX, self.petscVecY)
else:
self.petscPreconditioner.apply(self.petscVecX, self.petscVecY)
self.vecMap.ngsVec(self.petscVecY, y)
def MultTrans(self,x,y):
'''
BaseMatrix multiplication A^T x = y
:arg x: vector we are multiplying
:arg y: vector we are storeing the result in
'''
self.vecMap.petscVec(x,self.petscVecX)
if self.asmpc is not None:
self.asmpc.applyTranspose(self.petscVecX, self.petscVecY)
else:
self.petscPreconditioner.applyTranspose(self.petscVecX, self.petscVecY)
self.vecMap.ngsVec(self.petscVecY, y)
comp.RegisterPreconditioner ("PETScPC", createPETScPreconditioner)
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