HIGH-FREQUENCY APPROXIMATION OF INTEGRAL-EQUATIONS MODELING SCATTERING PHENOMENA

In this paper, we present a new way of discretizing integral equations coming from high frequency wave propagation. Indeed, using the eikonal equation, we will write that the solution is locally the product of an amplitude by an oscillating function whose phase gradient modulus is the wave number. Discretizing in order to keep this relation, we will show that, is the limit of high frequencies, the matrices we obtain are sparse (as sparse as volumic finite-element methods, in fact), which is not the case with the classical way of discretizing for example with P1-Lagrange or H(div) (see [11] or [13]) finite elements. More precisely, if N is the number of degrees of freedom, we lower the complexity from O(N2) to O(N).