Sparse Blocked Equation Solving Techniques in Boundary Element Analysis

Abstract

Multi-zone boundary element analysis (BEA) is known to produce overall system matrices with a sparse blocked character. Recent advancements in the direct and iterative solution of these special sets of algebraic equations are discussed. Static condensation is shown to dramatically reduce the computational burden associated with matrix fill-in during both the direct matrix factorization step and the subsequent forward reduction and backward substitution process for multiply connected BEA models. Preconditioned block iterative unsymmetric equation solution schemes are shown to generally out-perform direct approaches for single- and multi-zone models. Plots of matrix populations associated with multi-zone BEA models are depicted to aid in the explanation of the impact of preconditioning on the convergence of the iterative methods. Numerical examples are given with timing, storage, and accuracy statistics presented. A relatively extensive literature survey is given to help provide a general characterization of the state of the art in equation solving for BEA.