Computational model order reduction for systems with radiation damping

Abstract

Radiation of waves in an open domain is a common case for many applications in acoustics. Depending on the sys- tem, the damping effect introduced may not be negligi- ble. When using the finite element method to model such problems, appropriate techniques like absorbing boundary conditions or perfectly matched layers can be applied to achieve free field radiation despite the domain truncation. We show how the resulting quadratic eigenvalue problem of an acoustic system with free radiation boundary condi- tions can be solved. The resulting eigenmodes are clas- sified into physical modes and computational modes due to the domain truncation. A reduced-order model is con- structed by projection into a modal subspace. We suggest a selection criterion for modes to include in the basis using a similarity criterion with respect to selected full model solutions. We apply the model order reduction to a simple 2D ex- ample of a Helmholtz oscillator. Both the accuracy and performance of the strategy are evaluated, showing highly accurate results. Due to the high computational effort for solving the eigenvalue problem, significant performance improvements can only be expected from the reduction technique if many evaluations of the reduced order model are required.