Fictitious Domain Solution of Frequency Response Problems

This paper discusses an alternative solution strategy for frequency response problems in elasticity. This strategy uses a meshless method, derived in a periodic domain setting, extended to allow the analysis of arbitrary geometries with the use of a fictitious domain. This solution technique is designed to solve problems with a large number of degrees of freedom and it requires the use of iterative solvers where preconditioning is necessary for reasonable convergence rates. Two dimensional examples illustrating this approach are provided.