Efficient wave propagation simulation on quadtree meshes using SBFEM with reduced modal basis

Abstract

SummaryWe apply a combination of the transient scaled boundary finite element method (SBFEM) and quadtree‐based discretization to model dynamic problems at high frequencies. We demonstrate that the current formulation of the SBFEM for dynamics tends to require more degrees of freedom than a corresponding spectral element discretization when dealing with smooth problems on regular domains. Thus, we improve the efficiency of the SBFEM by proposing a novel approach to reduce the number of auxiliary variables for transient analyses. Based on this improved SBFEM, we present a modified meshing procedure, which creates a quadtree mesh purely based on the geometry and allows arbitrary sizes and orders of elements, as well as an arbitrary number of different materials. The discretization of each subdomain is created automatically based on material parameters and the highest frequency of interest. The transition between regions of different properties is straightforward when using the SBFEM. The proposed approach is applied to image‐based analysis with a particular focus on geological models. Copyright © 2016 John Wiley & Sons, Ltd.