[petsc-users] Vector form of TS solvers

Chris Bradley c.bradley at auckland.ac.nz
Wed Jul 8 18:25:02 CDT 2015

Dear PETSc,
I was wondering if you had any advice for using PETSc TS solvers to
solve a vector of ODEs. PETSc TS solvers solve DAEs of the form

f(t,u,u^dot,a) = g(u,t) = 0 (for my case)

where f is a user provided function, u is a vector of state variables,
u^dot a vector of the derivatives of state variables and a is a vector
of parameters (passed through the context).

I need to solve a large number of these DAEs (one for every node in a
bigger finite element problem). Is there a vector form of the TS solvers
that can solve

F(t,U,U^dot) = G(U,t) = 0

where F is now a vector, U is a matrix of state variables and U^dot is a
matrix of the derivatives of U. Each row of the system corresponds to
the standard PETSc TS problem above and is independent of every other row.

If I understand the TS manual correctly then if I wanted to do this in
PETSc I would have to create a TS object and state and derivative
vectors objects for each row? All these PETSc objects for each row would
seem like a big overhead if there was a very large number of rows
(potentially tens of millions for my problem).

Thanks for your help
Chris Bradley
Auckland Bioengineering Institute,
University of Auckland,
Private Bag 92019,
New Zealand.

Tel: +64 9 373 7599 xtn 89924
Fax: +64 9 367 7157

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