Over recent times we have gradually made various development steps that last week enabled us to solve solid-shell coupling as an eigenmode problem in parallel. The feature set that enabled this is rather generic and enables also other kind of strong coupling in steady-state, transient or harmonic. So far structural equations (plate, shell, solid) have been coupled with linear fluid solvers (mainly acoustics) and now also shell-solid coupling has been introduced.
As an example here is an 8th eigenmode of a cylindrical piece of solid/plate.
- SolidShellEigenmode8.PNG (97.61 KiB) Viewed 1745 times
The machinery uses just the standard solvers. One of the solvers takes the lead while the other acts as a slave that only assembles its matrix. The master solver then creates a 2x2 block matrix of the two. There are some library features that create the coupling matrices (1,2) and (2,1). The master block is naturally (1,1) and the slave one is (2,2).
The 2x2 block matrix may be solved either by block preconditioning techniques when it is easier to apply ideal strategies for the subproblems. But we may also use this as a monolithic system resulting to more robust solution of coupled problems utilizing for example the direct solver MUMPS.
These features have not been fully documented. If there is somebody wanting to study some strongly coupled problem then we are happy to have test users, and also ideas where this machinery could be utilized. When weak coupling works it is usually more efficient but sometimes that does not lead convergence. Then strong coupling may be the only option. And for some problems, like the solution of common eigenmodes, the loose coupling is not even an option.
-Peter