Boundary Integral Equation and Domain Decomposition Methods
Abstract
Boundary integral equations (BIE) are a reformulation of partial differential equations with non-local integral operators. It has the advantage to reduce the dimension of the geometric domain and to be able to naturally formulate problems on open domains. This kind of reformulation is widely used in acoustic, electromagnetic and mechanics. The matrices obtained after discretisation of these equations have the disadvantage to be fully populated, which leads us to use iterative linear solvers such as conjugated gradient or GMRes to solve the associated linear systems. To stabilize the number of iterations of these solvers with respect to the mesh size, a classical technique is to use a preconditioner. In this talk, after introducing BIE, we will present a method to precondition these matrices using domain decompositions methods and its analysis. This is a joint work with Xavier Claeys and Frédéric Nataf.
