<div dir="ltr"><div dir="ltr">On Tue, Apr 2, 2019 at 4:19 AM Nicola Creati via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Hello, I have run the two codes using: -pc_type lu -ts_monitor <br>
-snes_monitor -ksp_monitor -ts_max_steps 5. The codes start to diverge <br>
after the first time step:<br></blockquote><div><br></div><div>In RHS_Function, you never use xdot, but this is an implicit TS. Thus, you are solving the Laplace</div><div>equation, not the heat equation, and you get the exact answer after one step.</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
Python run :<br>
<br>
0 TS dt 0.01 time 0.<br>
0 SNES Function norm 2.327405179696e+02<br>
0 KSP Residual norm 1.939100379240e+00<br>
1 KSP Residual norm 1.013760235597e-15<br>
1 SNES Function norm 9.538686413612e-14<br>
1 TS dt 0.01 time 0.01<br>
0 SNES Function norm 8.565210784140e-14<br>
0 KSP Residual norm 1.266678408555e-15<br>
1 KSP Residual norm 2.663404219322e-31<br>
1 SNES Function norm 5.528402779439e-29<br>
2 TS dt 0.01 time 0.02<br>
0 SNES Function norm 5.829656072531e-29<br>
0 KSP Residual norm 3.805606380832e-31<br>
1 KSP Residual norm 3.283104975114e-46<br>
1 SNES Function norm 1.867771204856e-44<br>
3 TS dt 0.01 time 0.03<br>
0 SNES Function norm 1.644541571708e-44<br>
0 KSP Residual norm 1.969573456719e-46<br>
1 KSP Residual norm 1.297976290541e-61<br>
1 SNES Function norm 1.780215821230e-59<br>
4 TS dt 0.01 time 0.04<br>
0 SNES Function norm 1.700894451833e-59<br>
5 TS dt 0.01 time 0.05<br>
<br>
ex13.c run:<br>
<br>
0 TS dt 0.01 time 0.<br>
0 SNES Function norm 2.327405179696e+02<br>
0 KSP Residual norm 9.158498731719e-01<br>
1 KSP Residual norm 5.129005976821e-16<br>
1 SNES Function norm 1.141297389434e-13<br>
1 TS dt 0.01 time 0.01<br>
0 SNES Function norm 9.158498731719e+01<br>
0 KSP Residual norm 4.156347391374e-01<br>
1 KSP Residual norm 1.996081836894e-16<br>
1 SNES Function norm 3.609761734594e-14<br>
2 TS dt 0.01 time 0.02<br>
0 SNES Function norm 4.156347391374e+01<br>
0 KSP Residual norm 2.203298795311e-01<br>
1 KSP Residual norm 9.047356740098e-17<br>
1 SNES Function norm 3.292648977280e-14<br>
3 TS dt 0.01 time 0.03<br>
0 SNES Function norm 2.203298795311e+01<br>
0 KSP Residual norm 1.367458644503e-01<br>
1 KSP Residual norm 5.055030661919e-17<br>
1 SNES Function norm 1.272304808486e-14<br>
4 TS dt 0.01 time 0.04<br>
0 SNES Function norm 1.367458644503e+01<br>
0 KSP Residual norm 9.695393464180e-02<br>
1 KSP Residual norm 1.918401734795e-17<br>
1 SNES Function norm 1.130247628824e-14<br>
5 TS dt 0.01 time 0.05<br>
<br>
I rechecked the Python code against the C one but I did not find the <br>
source of the issue.<br>
<br>
# Example 13 petsc TS<br>
import sys, petsc4py<br>
petsc4py.init(sys.argv)<br>
<br>
from petsc4py import PETSc<br>
from mpi4py import MPI<br>
import numpy as np<br>
import math<br>
<br>
def RHS_func(ts, t, X, xdot, F):<br>
da = ts.getDM()<br>
localU = da.getLocalVec()<br>
<br>
da.globalToLocal(X, localU)<br>
<br>
mx, my = da.getSizes()<br>
<br>
hx, hy = [1.0/(m-1) for m in [mx, my]]<br>
sx = 1.0/(hx*hx)<br>
sy = 1.0/(hy*hy)<br>
<br>
uarray = localU.getArray(readonly=1).reshape(8, 8, order='C')<br>
f = F.getArray(readonly=0).reshape(8, 8, order='C')<br>
<br>
(xs, xm), (ys, ym) = da.getRanges()<br>
for j in range(ys, ym):<br>
for i in range(xs, xm):<br>
if i == 0 or j == 0 or i == (mx-1) or j == (my-1):<br>
f[i,j] = uarray[i,j]<br>
continue<br>
u = uarray[i,j]<br>
uxx = (-2.0 * u + uarray[i, j-1] + uarray[i, j+1]) * sx<br>
uyy = (-2.0 * u + uarray[i-1, j] + uarray[i+1, j])* sy<br>
f[i, j] = uxx + uyy<br>
F.assemble()<br>
#PETSc.Log.logFlops(11.0*xm*ym)<br>
<br>
<br>
def Jacobian_func(ts, t, x, xdot, a, A, B):<br>
mx, my = da.getSizes()<br>
hx = 1.0/(mx-1)<br>
hy = 1.0/(my-1)<br>
sx = 1.0/(hx*hx)<br>
sy = 1.0/(hy*hy)<br>
<br>
B.setOption(PETSc.Mat.Option.NEW_NONZERO_ALLOCATION_ERR, False)<br>
B.zeroEntries()<br>
<br>
(i0, i1), (j0, j1) = da.getRanges()<br>
row = PETSc.Mat.Stencil()<br>
col = PETSc.Mat.Stencil()<br>
<br>
for i in range(j0, j1):<br>
for j in range(i0, i1):<br>
row.index = (i,j)<br>
row.field = 0<br>
if i == 0 or j== 0 or i==(my-1) or j==(mx-1):<br>
B.setValueStencil(row, row, 1.0)<br>
else:<br>
for index, value in [<br>
((i-1, j), sx),<br>
((i+1, j), sx),<br>
((i, j-1), sy),<br>
((i, j+1), sy),<br>
((i, j), -2*sx - 2*sy)]:<br>
col.index = index<br>
col.field = 0<br>
B.setValueStencil(row, col, value)<br>
<br>
B.assemble()<br>
#B.view()<br>
if A != B: B.assemble()<br>
<br>
return PETSc.Mat.Structure.SAME_NONZERO_PATTERN<br>
<br>
def make_initial_solution(da, U, c):<br>
mx, my = da.getSizes()<br>
hx = 1.0/(mx-1)<br>
hy = 1.0/(my-1)<br>
(xs, xm), (ys, ym) = da.getRanges()<br>
<br>
u = U.getArray(readonly=0).reshape(8, 8, order='C')<br>
<br>
for j in range(ys, ym):<br>
y = j*hy<br>
for i in range(xs, xm):<br>
x = i*hx<br>
r = math.sqrt((x-0.5)**2+(y-0.5)**2)<br>
if r < (0.125):<br>
u[i, j] = math.exp(c*r*r*r)<br>
else:<br>
u[i, j] = 0.0<br>
U.assemble()<br>
#U.view()<br>
<br>
<br>
def monitor(ts, i, t, x):<br>
xx = x[:].tolist()<br>
history.append((i, t, xx))<br>
<br>
<br>
history = []<br>
nx = 8<br>
ny = 8<br>
da = PETSc.DMDA().create([nx, ny], stencil_type= <br>
PETSc.DA.StencilType.STAR, stencil_width=1, dof=1)<br>
<br>
da.setFromOptions()<br>
da.setUp()<br>
<br>
u = da.createGlobalVec()<br>
f = u.duplicate()<br>
<br>
c = -30.0<br>
<br>
ts = PETSc.TS().create()<br>
ts.setDM(da)<br>
ts.setType(ts.Type.BEULER)<br>
<br>
ts.setIFunction(RHS_func, f)<br>
<br>
da.setMatType('aij')<br>
J = da.createMat()<br>
ts.setIJacobian(Jacobian_func, J, J)<br>
<br>
ftime = 1.0<br>
ts.setMaxTime(ftime)<br>
ts.setExactFinalTime(PETSc.TS.ExactFinalTime.STEPOVER)<br>
<br>
make_initial_solution(da, u, c)<br>
dt = 0.01<br>
<br>
ts.setMonitor(monitor)<br>
ts.setTimeStep(dt)<br>
ts.setFromOptions()<br>
ts.solve(u)<br>
<br>
ftime = ts.getSolveTime()<br>
steps = ts.getStepNumber()<br>
<br>
Thanks.<br>
<br>
Nicola<br>
<br>
<br>
-- <br>
<br>
Nicola Creati<br>
Istituto Nazionale di Oceanografia e di Geofisica Sperimentale - OGS <a href="http://www.inogs.it" rel="noreferrer" target="_blank">www.inogs.it</a><br>
Dipartimento di Geofisica della Litosfera Geophysics of Lithosphere Department<br>
CARS (Cartography and Remote Sensing) Research Group <a href="http://www.inogs.it/Cars/" rel="noreferrer" target="_blank">http://www.inogs.it/Cars/</a><br>
Borgo Grotta Gigante 42/c 34010 Sgonico - Trieste - ITALY <a href="mailto:ncreati@ogs.trieste.it" target="_blank">ncreati@ogs.trieste.it</a><br>
off. +39 040 2140 213<br>
fax. +39 040 327307<br>
<br>
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</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>