On the Space-Time Discretization of Variational Retarded Potential Boundary Integral Equations

D. Pölz*, M. Schanz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper discusses the practical development of space-time boundary element methods for the wave equation in three spatial dimensions. The employed trial spaces stem from simplex meshes of the lateral boundary of the space-time cylinder. This approach conforms genuinely to the distinguished structure of the solution operators of the wave equation, so-called retarded potentials. Since the numerical evaluation of the arising integrals is intricate, the bulk of this work is constituted by ideas about quadrature techniques for retarded layer potentials and associated energetic bilinear forms. Finally, we glimpse at algorithmic aspects regarding the efficient implementation of retarded potentials in the space-time setting. The proposed methods are verified by means of numerical experiments, which illustrate their capacity.
Original languageEnglish
Pages (from-to)195-210
Number of pages16
JournalComputers & Mathematics with Applications
Publication statusPublished - 2021


  • Wave equation
  • Boundary element method
  • Bubnov-Galerkin
  • Light cone

ASJC Scopus subject areas

  • Computational Mathematics
  • Computational Theory and Mathematics
  • Modelling and Simulation

Fields of Expertise

  • Information, Communication & Computing


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