NGSolve - PETSc interface

105. NGSolve - PETSc interface#

We use the ngs2petsc interface (shipped with NGSolve) to map vectors and matrices between NGSolve and PETSc

An extended interface to PETSc is available by Stefano Zampini and Umberto Zerbinati from https://ngspetsc.readthedocs.io/en/latest/ngsPETSc.html

from ipyparallel import Cluster
c = await Cluster(engines="mpi").start_and_connect(n=4, activate=True)
c.ids

Starting 4 engines with <class 'ipyparallel.cluster.launcher.MPIEngineSetLauncher'>

[0, 1, 2, 3]

%%px
from ngsolve import *
comm = MPI.COMM_WORLD
ngmesh = unit_square.GenerateMesh(maxh=0.1, comm=comm)
    
for l in range(3):
    ngmesh.Refine()
mesh = Mesh(ngmesh)

The Python-module ngsolve.ngs2petsc provides functionality to transfer vectors and matrices between NGSolve and Python.

%%px
import ngsolve.ngs2petsc as n2p
import petsc4py.PETSc as psc

%%px
fes = H1(mesh, order=1, dirichlet="left|bottom")
u,v = fes.TnT()
a = BilinearForm(grad(u)*grad(v)*dx+u*v*ds).Assemble()
f = LinearForm(x*v*dx).Assemble()
gfu = GridFunction(fes)

The function CreatePETScMatrix takes an NGSolve matrix, and creates a PETSc matrix from it. A VectorMapping object can map vectors between NGSolve and PETSc.

%%px
psc_mat = n2p.CreatePETScMatrix(a.mat, fes.FreeDofs())
vecmap = n2p.VectorMapping (a.mat.row_pardofs, fes.FreeDofs())

%%px
# psc_mat.view()

Create PETSc-vectors fitting to the matrix

%%px
psc_f, psc_u = psc_mat.createVecs()

setting up the parallel Krylov-space solver ….

%%px
ksp = psc.KSP()
ksp.create()
ksp.setOperators(psc_mat)
ksp.setType(psc.KSP.Type.CG)
ksp.setNormType(psc.KSP.NormType.NORM_NATURAL)
ksp.getPC().setType("gamg")
ksp.setTolerances(rtol=1e-6, atol=0, divtol=1e16, max_it=400)

moving vectors between NGSolve and PETSc, and solve:

%%px
vecmap.N2P(f.vec, psc_f)
ksp.solve(psc_f, psc_u)   
vecmap.P2N(psc_u, gfu.vec);

gfu = c[:]["gfu"]
from ngsolve.webgui import Draw

Draw (gfu[0]);

105.1. PETSc preconditioner for NGSolve#

Next we create a PETSc preconditioner, and wrap it into an NGSolve preconditioner:

%%px
a = BilinearForm(grad(u)*grad(v)*dx+u*v*ds)
pre = Preconditioner(a, "gamg")
a.Assemble();

and use it in an NGSolve - CGSolver:

%%px
from ngsolve.krylovspace import CGSolver
inv = CGSolver(a.mat, pre, printrates=comm.rank==0)
gfu.vec.data = inv * f.vec

[stdout:0] CG iteration 1, residual = 0.1566964029283152     
CG iteration 2, residual = 0.030192900198026517     
CG iteration 3, residual = 0.004851540898218855     
CG iteration 4, residual = 0.0008155136133605194     
CG iteration 5, residual = 0.00012290564477014334     
CG iteration 6, residual = 2.024986973253222e-05     
CG iteration 7, residual = 3.253472013629693e-06     
CG iteration 8, residual = 5.127897790833774e-07     
CG iteration 9, residual = 8.564297519064976e-08     
CG iteration 10, residual = 1.4038894412092944e-08     
CG iteration 11, residual = 2.3492707399620672e-09     
CG iteration 12, residual = 3.7670723474767985e-10     
CG iteration 13, residual = 6.24527644130138e-11     
CG iteration 14, residual = 9.644250760453501e-12     
CG iteration 15, residual = 1.538704195556293e-12     
CG iteration 16, residual = 2.546662863901983e-13     
CG iteration 17, residual = 3.7841019811145543e-14     

gfu = c[:]["gfu"]
Draw (gfu[0]);

c.shutdown(hub=True)
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