26 febbraio Seminario di Analisi Numerica: dott.ssa Stéphanie Chaillat-Loseille "A new Analytic Preconditioner for the Fast Multipole accelerated Boundary Element Method in 3-D elastodynamics"
la dott.ssa Stéphanie Chaillat-Loseille, Dipartimento di Matematica Applicata
ENSTA Paristech - PARIGI
terra un seminario dal titolo:
A new Analytic Preconditioner for the Fast Multipole accelerated Boundary Element Method in 3-D elastodynamics
When considering the solution of scattering problems of time-harmonic elastic waves by a three-dimensional rigid obstacle, the main difficulty in the numerical simulation comes from the unbounded characteristic of the computational domain.
The boundary element method (BEM) is one possible approach to overcome this issue. The method results from the discretization of boundary integral equations (BIE). In traditional boundary element (BE) implementations, the
dimensional advantage with respect to domain discretization methods is offset by the fully-populated nature of the BEM coefficient matrix. The Fast Multipole Method (FMM) permits to overcome the drawback of the fully-
populated matrix by introducing a fast and approximate method to compute the linear integral operator in conjunction with the use of an iterative solver (e.g. GMRES).
In 3D elastodynamics the FM-BEM has been shown to be efficient with solution times of order O(N log N) per iteration (where N is the number of BE degrees of freedom). However, the number of iterations in GMRES can significantly hinder the overall efficiency of the FM-BEM even though an algebraic preconditioner is applied. Preconditioning the FM-BEM is therefore an
important practical issue. A possible approach consists in exploiting mathematical properties of the relevant continuous integral operators. In a first part, I will present the Fast Multipole accelerated Boundary Element Method for 3D elastodynamics. In a second part, I will show how to define an efficient analytic preconditioner for the FM-BEM in elastodynamics based on the On-Surface Radiation Condition (OSRC).
Gli interessati sono invitati a partecipare.