The community working on the solution of boundary integral equations is way smaller than the one of finite element, finite differences or spectral methods. The originality at POEMS is to develop and implement fast and efficient solvers for wave propagation problems based on the discretization of boundary integral equations. There are three ways to discretize these equations and we consider all of them: the collocation, Galerkin and Nystrom approaches. To combine these expertises is quite unique in the world. All our developments are related to the possible level of improvements of the method: data-sparse approximations, preconditioning, definition of optimal quadratures, mesh adaptation procedures or coupling with other methods when needed. In all cases, parallel implementation is considered. Our goal is to confront these fast methods to real life and industrial applications. Various codes are developed in the team with different goals: from general codes for academics to application specific codes for industrial collaborations.
To our best knowledge the only other INRIA team working on fast solution of boundary integral equations is ALPINE.
