# [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
Elias

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

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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