A Static Condensation Reduced Basis Element Approximation: Application To Three-Dimensional Acoustic Muffler Analysis

We apply the static condensation reduced basis element (scRBE) method to treat the class of parametrized complex Helmholtz partial differential equation. We construct a set of components of interoperable parametrized reference components in a Library to model a family of target models relevant to acoustic devices. The components in the Library are built upon the scRBE method by using reduced basis (RB) formulation, and are compatible to each other by a set of common interfaces, or port. We apply an offline online computational strategy to achieve rapid and accurate prediction of any parametric systems formed from a set of components in a Library. We demonstrate that the approach can handle large scale models with many parameters and/or topology variations efficiency in several numerical examples. We show that significant computational savings can be obtained by the scRBE method.