[ZRZ]

There are many examples of applying MPI to explicit discretization, but can MPI be used for fully implicit discretization?
If possible， how to implement MPI in full implicit discretization?
If not，how to accelerate in Parallel in fully implicit discretization except OpenMP.
Thanks.

[aerosayan]

Fully implicit solvers are simple linear solvers.

Look up parallelization of Gauss-Siedel elimination, Least Squares method, etc. Because that's what's used to solve the Ax=b set of linear equations. Rest of the solver is just creating and organizing the matrices.

Those are the two main methods that I know, if you would need names of more methods, I could look it up for you.

Best of luck.

[naffrancois]

Hello,

You can apply domain decomposition MPI to a fully implicit discretization. As aerosayan said, implicit discretization computational work is mostly about solving linear systems.

This is easier in my opinion with iterative solvers where you usually end up doing matrix-vector products and dot products. Broadly speaking, you work with an extended matrix and RHS containing extra entries associated to flux and flux derivatives at the cpu boundaries. This is a piece of work though, and it should be done very incrementally, starting from pen and paper with a simple equation set.

But short answer yes you can