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A question about NDSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112020] A question about NDSolve
  • From: pratip <pratip.chakraborty at gmail.com>
  • Date: Wed, 25 Aug 2010 06:03:39 -0400 (EDT)

Dear group,

If we use NDSolve to solve a PDE then normally mathematica uses a
method of lines discretization and form a system of coupled ODE or
DAE. Then the default ODE/DAE solver is used. Now I want to ask if
there is any way one can access this system of ODE/DAE generated after
the spatial discretization of the give PDE. In the documentation there
is some very simple example with 1D Burger's equation where these
system of ODE is generated. I want to do the same for 2D and 3D
problem in space. If thee is any easy way to achieve this please help.
I guess may be from the NDSolveState or ProcessEquation or in general
from the data structure of NDSolve one can recover this system. So in
that case NDSolve is just used for discretizing the PDE. If we can get
the discretized system we can also take advantage of other external
solvers to simulate the system. Specially one can deal with really
large scale problems if one has a parallel linear (for example using
CUDA or MPI) solver implemented with in his external ODE/DAE solver. I
guess Mathematica can proved to be a great preprocessor to perform the
discretization of the PDE. If I can get access to this system it will
be an immense help that will simplify my project. I plan to port a
open source parallel ODE/DAE solver to Mathematica so that we can deal
with large scale problems. Hope some of you may give a helping hand.

Regards

pratip


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