[Dune] Solving ODE-Systems in Dune

Firmbach, Max max.firmbach at tum.de
Fri May 22 21:06:45 CEST 2020


Hello Dune developers and users,


I'm currently working on a solver for linear elasticity problems and already

implemented a version for "static" loadcases in Dune that works well. Now, I'm in the process

of adding time dependency and thus need to solve a system of ODE's of

the form: y'-Ay = r, where all components are nested datatypes.

Matrix A for example is of type Matrix<BCRSMatrix<FieldMatrix<double, 3, 3>>>,

the other variables are of the corresponding nested block-vector type.

The FIeldMatrix represents the Elementmatrix, the BCRSMatrix the global system

matrix (both for Mass and Stiffness) and the outer Matrix is of size 2x2 that couples the

system matrices and resembles the second order ode transformed into the system

of first order ones.


My question is, if there is an interface in Dune that can solve ODE's and handle those

nested datatypes. For example, if i rewrite the system to y'=F(...):

F[0] = y[1];

F[1] = -M^-1*K*y[0]+M^-1*p

that the basic operations can be done with the BCRSMatrix and BlockVectors.

Or if someone has recommendations on how to solve this sytem in

Dune (in a simple way, that is still performing quite well concerning efficiency).

I've seen that there are implemented time stepping methods in the Dune-FEM and

Dune-PDELab modules, but I'm not sure what they are capable of.


Thanks for your help and best regards,

Max

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