[petsc-users] 3D Model Coupled to 0D Model

Karabelas, Elias (elias.karabelas@uni-graz.at) elias.karabelas at uni-graz.at
Wed Aug 10 02:35:41 CDT 2022

Hey all,

so I have a nonlinear problem that can be abstractly written as

| F(u,P) |           | 0 |

|        |    =      |   |

| G(u,P) |           | 0 |

Here u is a variable that comes from a discretization of a PDE and P are four scalars that come from some coupled attached ODEs (P = (P1,P2,P3,P4) )

I know abstract how to apply Newton-Raphson in this context as the Jacobian is simply

d_u F   d_P F

d_u G   d_P G

where d_P F and d_u G are formed from 4 Vecs resp, and d_P G is a 4x4 matrix.

So what I have troubles with is how I could squeeze something like this into an SNES context, at the moment I'm doing a Schur-Complement for Solving this problem for each Newton solve. This however entails, that I'm, solving (d_u F)^-1 to a very low tolerance inside the SC.
In the End I want to have something that can work with an inexact Newton method, but I don't know which would be the correct tool (MATSHELL for the jacobian maybe?) to squeeze this into an SNES.

Any ideas?

Best regards

Dr. Elias Karabelas
Research Associate
University of Graz
Institute of Mathematics and Scientific Computing
Heinrichstraße 36
A-8010 Graz

Phone: +43 316 380 8546
Email: elias.karabelas at uni-graz.at<mailto:elias.karabelas at uni-graz.at>
Web:  https://ccl.medunigraz.at/
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