CA08 exercise · Method-selection and coupling exercise
Choose suitable hybrid method combinations for multi-region acoustic problems and compare weak iterative coupling with a monolithic coupled reference.
Aim
Hybrid methods combine solvers because one method is rarely optimal everywhere. This exercise asks you to classify subregions and then run a toy weak-coupling iteration.
A vibrating machine housing radiates into an unbounded exterior fluid. A natural method split is structural FEM for the housing and BEM/Rayleigh radiation for the exterior acoustic field.
What is one-way FEM–BEM radiation coupling?
For the toy system in the Python code, the monolithic solution is approximately x = 0.3261 and y = 0.2536.
Python exercise
The code compares a monolithic coupled solution with a sequential fixed-point iteration.
Expected observation
The weak iteration approaches the monolithic solution when feedback is moderate. Strong coupling can slow convergence or destabilise the iteration.
Teaching note
This is a numerical analogy for partitioned hybrid methods. Real hybrid acoustic coupling also needs physical interface consistency and validation.
Written submission
Interface checks
List three checks you would perform before trusting a hybrid FEM–BEM or FEM–SEA result.
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