[petsc-users] petsc4py - Convert c example code to Python

[Nicola Creati]

Hello, I'm trying to write in Python one of the TS PETSc tutorial example:

https://www.mcs.anl.gov/petsc/petsc-current/src/ts/examples/tutorials/ex13.c.html 


I'm not able to fill the Jacobian matrix in the right way in Python. 
Maybe there are some other conversion errors.
Might someone help, please?

This is my code:

# Example 13 petsc TS
import sys, petsc4py
petsc4py.init(sys.argv)

from petsc4py import PETSc
from mpi4py import MPI
import numpy as np
import math

def RHS_func(ts, t, X, xdot, F):
     da = ts.getDM()

     mx, my = da.getSizes()

     hx, hy = [1.0/(m-1) for m in [mx, my]]
     sx = 1.0/(hx*hx)
     sy = 1.0/(hy*hy)

     x = X.getArray(readonly=1).reshape(8, 8, order='C')
     f = F.getArray(readonly=0).reshape(8, 8, order='C')

     (xs, xm), (ys, ym) = da.getRanges()
     aa = np.zeros((8,8))
     for j in range(ys, ym):
         for i in range(xs, xm):
             if i == 0 or j == 0 or i == (mx-1) or j == (my-1):
                 f[i,j] = x[i,j]
                 continue
             u = x[i,j]
             uxx = (-2.0 * u + x[i, j-1] + x[i, j+1]) * sx
             uyy = (-2.0 * u + x[i-1, j] + x[i+1, j])* sy
             f[i, j] = uxx + uyy
     F.assemble()

def Jacobian_func(ts, t, x, xdot, a, A, B):
     mx, my = da.getSizes()
     hx = 1.0/(mx-1)
     hy = 1.0/(my-1)
     sx = 1.0/(hx*hx)
     sy = 1.0/(hy*hy)

     B.zeroEntries()
     (i0, i1), (j0, j1) = da.getRanges()
     row = PETSc.Mat.Stencil()
     col = PETSc.Mat.Stencil()

     for i in range(j0, j1):
         for j in range(i0, i1):
             row.index = (i,j)
             row.field = 0
             if i == 0 or j== 0 or i==(my-1) or j==(mx-1):
                 B.setValueStencil(row, row, 1.0)
             else:
                 for index, value in [
                     ((i-1, j),   sx),
                     ((i+1, j),   sx),
                     ((i,   j-1), sy),
                     ((i-1, j+1), sy),
                     ((i,   j),  -2*sx - 2*sy)]:
                     col.index = index
                     col.field = 0
                     B.setValueStencil(row, col, value)

     B.assemble()
     if A != B: B.assemble()
     return PETSc.Mat.Structure.SAME_NONZERO_PATTERN

def make_initial_solution(da, U, c):
     mx, my = da.getSizes()
     hx = 1.0/(mx-1)
     hy = 1.0/(my-1)
     (xs, xm), (ys, ym) = da.getRanges()

     u = U.getArray(readonly=0).reshape(8, 8, order='C')

     for j in range(ys, ym):
         y = j*hy
         for i in range(xs, xm):
             x = i*hx
             r = math.sqrt((x-0.5)**2+(y-0.5)**2)
             if r < (0.125):
                 u[i, j] = math.exp(c*r*r*r)
             else:
                 u[i, j] = 0.0
     U.assemble()

def monitor(ts, i, t, x):
     xx = x[:].tolist()
     history.append((i, t, xx))

history = []
nx = 8
ny = 8
da = PETSc.DMDA().create([nx, ny], stencil_type= PETSc.DA.StencilType.STAR)
da.setFromOptions()
da.setUp()

u = da.createGlobalVec()
f = u.duplicate()

c = -30.0

ts = PETSc.TS().create()
ts.setDM(da)
ts.setType(ts.Type.BEULER)

ts.setIFunction(RHS_func, f)
ts.setIJacobian(Jacobian_func)

ftime = 1.0
ts.setMaxTime(ftime)
ts.setExactFinalTime(PETSc.TS.ExactFinalTime.STEPOVER)

make_initial_solution(da, u, c)
dt = 0.01
ts.setMonitor(monitor)
ts.setTimeStep(dt)
ts.setFromOptions()
ts.solve(u)

ftime = ts.getSolveTime()
steps = ts.getStepNumber()

Thanks.

Nicola

-- 

Nicola Creati
Istituto Nazionale di Oceanografia e di Geofisica Sperimentale - OGS www.inogs.it
Dipartimento di Geofisica della Litosfera Geophysics of Lithosphere Department
CARS (Cartography and Remote Sensing) Research Group http://www.inogs.it/Cars/
Borgo Grotta Gigante 42/c 34010 Sgonico - Trieste - ITALY ncreati at ogs.trieste.it
off.   +39 040 2140 213
fax.   +39 040 327307

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