On the efficiency of an H-matrix based direct solver for the Boundary Element Method in 3D elastodynamics

The main advantage of the Boundary Element Method (BEM) is that only the domain boundaries are discretized leading to a drastic reduction of the total number of degrees of freedom. In traditional BE implementation the dimensional advantage with respect to domain discretization methods is offset by the fully-populated nature of the BEM coefficient matrix. In the present work, we propose a fast method to solve the BEM system in 3-D frequency-domain elastodynamics. Using the H-matrix arithmetic and low-rank approximations (performed with Adaptive Cross Approximation), we derive a fast direct solver. We assess the numerical efficiency and accuracy on the basis of numerical results obtained for problems having known solutions. In particular, we study the efficiency of low-rank approximations when the frequency is increased. 

Bio :
Dr Stéphanie Chaillat is a CNRS research scientist in the POEMS group in the Applied Mathematics department of ENSTA (Ecole Nationale Superieure des Techniques Avancées) in Palaiseau, France. Her research interests notably span boundary integral equations and boundary elements, inverse problems for elastodynamics with applications in seismology and mechanics.  She graduated in 2006 as a civil engineer from Ecole Nationale des Travaux Publics de l'Etat, Lyon, France, and got her PhD at the Laboratoire de Mécanique des Solides of Ecole Polytechnique, Palaiseau France in 2008. She has received the National PhD Award from the French Computational Mechanics Association, and the European PhD Award from the European Community on Computational Methods in Applied Sciences (ECCOMAS) for her work on Fast Multipole Method for 3-D elastodynamic boundary integral equations.