Past Event: Oden Institute Seminar

Fast Boundary Element solvers in the frequency domain to simulate coupled acoustic-elastic problems in the time domain

Dr. Stephanie Chaillat, CNRS/ENSTA Paris

Abstract

3D rapid transient acoustic problems are known to be difficult to solve numerically when dealing with large geometries. In a first part, I will present  a numerical method to efficiently deal with 3D rapid transient acoustic problems set in large exterior domains. Using the Z-transform and the convolution quadrature method (CQM), a straightforward way to reframe the problem to the solving of a large amount of frequency-domain BEMs is derived. Then, taking advantage of a well-designed high-frequency approximation, the number of frequency-domain BEMs to be solved is drastically reduced, with little loss of accuracy. 

In a second part, I will discuss how to consider the coupled, i.e. Fluid Structure Interaction, problem. A first approach  consists in iteratively solving the BEM-FEM coupling by alternating Neumann solutions in each domain. Unfortunately this simple approach fails. We can show that the transient BEM-FEM coupling based on Neumann-Neumann iterations is problematic since energy estimates indicate that each iteration degrades the regularity of boundary traces (unlike in the elliptic case). To avoid this issue, an iterative algorithm based on Robin boundary conditions for the coupled elastodynamic/acoustic problem will be presented and proved to converge. The efficiency of these numerical methods will be demonstrated in the context of the simulation of underwater explosions.

Biography

Dr. Stephanie Chaillat is a CNRS researcher in computational mechanics (CNRS Section 9) since 2011. She is part of the POEMS team which is a joint team between CNRS/ENSTA ParisTech/INRIA. Before joining CNRS, she was a post-doctorate associate at Georgia Tech, College of Computing, in the team of George Biros. She did her PhD at Ecole Polytechnique with Marc Bonnet and Jean-François Semblat. She has a twofold background in computational mechanics and applied mathematics.

Dr. Chaillat's research concerns the proposition and study of fast algorithms and numerical methods to study wave propagation problems in large scale domains, e.g., acoustic wave propagation or seismic wave propagation. Her research is always driven by realistic physical problems.  Her expertise concerns numerical methods for PDEs, fast algorithms and efficient (including parallel) programming. To simulate seismic waves in the soil, she proposes fast Boundary Element Methods. All her research advances are used to develop the fast solver COFFEE (available for free for research purpose).

In addition to her research activites, she teachs at ENSTA ParisTech, mainly on the introduction of numerical methods (Finite Element Method, Finite Difference Method or Boundary Element Method).