Computational Wave Propagation

Computational Wave Propagation

The modeling of acoustics and elastic wave fields by numerically approximating the characterizing partial differential equations is a difficult problem. Due to the oscillatory behavior of the fields, standard numerical tools (e.g. finite difference (FD), finite element (FE), and boundary element (BE) methods) need several discretization points per wavelength to lead to sufficient accuracy. Hence, the computational complexity of the methods rapidly becomes intolerable when the field extends over several wavelengths.

Discontinuous Galerkin method

A promising approach for accurately approximating wave fields is the discontinuous Galerkin (DG) method. The approach is originally published by Reed and Hill in 1973 for approximating neutron transport equation. The DG method has several features that make it an attractive candidate for large-scale wave simulations. The variational formulation reduces each element of the computational mesh to a subproblem. With the DG method, the communication between adjacent elements is handled using the numerical flux. On the other hand, the variational form allows for easier parallelization of the solver code and the material parameters, the order of the polynomial basis functions, and the length of the time step can be chosen individually for each subproblem.


Timo Lähivaara

Past and present collaborators

  • P. Monk, University of Delaware, Department of Mathematical Sciences
  • J. S. Hesthaven, A. Buffa, Ecole Polytechnique Fédérale de Lausanne
  • O. Dazel, J-P. Groby, A. Duclos, G. Gabard, Université du Maine, Laboratoire d’Acoustique de l’Université du Maine
  • J. Astley, University of Southampton, Institute of Sound and Vibration Research
  • P. Göransson, KTH Royal Institute of Technology, Department of Aeronautical and Vehicle Engineering
  • J. Cuenca, LMS International / Siemens Industry Software
  • N. F. Dudley Ward, University of Canterbury, Civil and Natural Resources Engineering
  • T. Huttunen, IDA
  • S-P. Simonaho, School of Pharmacy, University of Eastern Finland
  • Nokia Bell Labs