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

Tue Apr 2 09:54:39 CDT 2019

Your python implementation of the residual function and the Jacobian function is intended for solving ODEs in the form x' = f(t,x). So you should use ts.setRHSFunction() and ts.setRHSJacobian() instead of the implicit version.

Hong

> On Apr 2, 2019, at 3:18 AM, Nicola Creati via petsc-users <petsc-users at mcs.anl.gov> wrote:
> 
> Hello, I have run the two codes using: -pc_type lu -ts_monitor -snes_monitor -ksp_monitor -ts_max_steps 5. The codes start to diverge after the first time step:
> Python run :
> 
> 0 TS dt 0.01 time 0.
>     0 SNES Function norm 2.327405179696e+02
>       0 KSP Residual norm 1.939100379240e+00
>       1 KSP Residual norm 1.013760235597e-15
>     1 SNES Function norm 9.538686413612e-14
> 1 TS dt 0.01 time 0.01
>     0 SNES Function norm 8.565210784140e-14
>       0 KSP Residual norm 1.266678408555e-15
>       1 KSP Residual norm 2.663404219322e-31
>     1 SNES Function norm 5.528402779439e-29
> 2 TS dt 0.01 time 0.02
>     0 SNES Function norm 5.829656072531e-29
>       0 KSP Residual norm 3.805606380832e-31
>       1 KSP Residual norm 3.283104975114e-46
>     1 SNES Function norm 1.867771204856e-44
> 3 TS dt 0.01 time 0.03
>     0 SNES Function norm 1.644541571708e-44
>       0 KSP Residual norm 1.969573456719e-46
>       1 KSP Residual norm 1.297976290541e-61
>     1 SNES Function norm 1.780215821230e-59
> 4 TS dt 0.01 time 0.04
>     0 SNES Function norm 1.700894451833e-59
> 5 TS dt 0.01 time 0.05
> 
> ex13.c run:
> 
> 0 TS dt 0.01 time 0.
>     0 SNES Function norm 2.327405179696e+02
>       0 KSP Residual norm 9.158498731719e-01
>       1 KSP Residual norm 5.129005976821e-16
>     1 SNES Function norm 1.141297389434e-13
> 1 TS dt 0.01 time 0.01
>     0 SNES Function norm 9.158498731719e+01
>       0 KSP Residual norm 4.156347391374e-01
>       1 KSP Residual norm 1.996081836894e-16
>     1 SNES Function norm 3.609761734594e-14
> 2 TS dt 0.01 time 0.02
>     0 SNES Function norm 4.156347391374e+01
>       0 KSP Residual norm 2.203298795311e-01
>       1 KSP Residual norm 9.047356740098e-17
>     1 SNES Function norm 3.292648977280e-14
> 3 TS dt 0.01 time 0.03
>     0 SNES Function norm 2.203298795311e+01
>       0 KSP Residual norm 1.367458644503e-01
>       1 KSP Residual norm 5.055030661919e-17
>     1 SNES Function norm 1.272304808486e-14
> 4 TS dt 0.01 time 0.04
>     0 SNES Function norm 1.367458644503e+01
>       0 KSP Residual norm 9.695393464180e-02
>       1 KSP Residual norm 1.918401734795e-17
>     1 SNES Function norm 1.130247628824e-14
> 5 TS dt 0.01 time 0.05
> 
> I rechecked the Python code against the C one but I did not find the source of the issue.
> 
> # 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()
>     localU = da.getLocalVec()
> 
>     da.globalToLocal(X, localU)
> 
>     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)
> 
>     uarray = localU.getArray(readonly=1).reshape(8, 8, order='C')
>     f = F.getArray(readonly=0).reshape(8, 8, order='C')
> 
>     (xs, xm), (ys, ym) = da.getRanges()
>     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] = uarray[i,j]
>                 continue
>             u = uarray[i,j]
>             uxx = (-2.0 * u + uarray[i, j-1] + uarray[i, j+1]) * sx
>             uyy = (-2.0 * u + uarray[i-1, j] + uarray[i+1, j])* sy
>             f[i, j] = uxx + uyy
>     F.assemble()
>     #PETSc.Log.logFlops(11.0*xm*ym)
> 
> 
> 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.setOption(PETSc.Mat.Option.NEW_NONZERO_ALLOCATION_ERR, False)
>     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, j+1), sy),
>                     ((i,   j),  -2*sx - 2*sy)]:
>                     col.index = index
>                     col.field = 0
>                     B.setValueStencil(row, col, value)
> 
>     B.assemble()
>     #B.view()
>     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()
>     #U.view()
> 
> 
> 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, stencil_width=1, dof=1)
> 
> 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)
> 
> da.setMatType('aij')
> J = da.createMat()
> ts.setIJacobian(Jacobian_func, J, J)
> 
> 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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