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 eikona l equation, we will write that the solution is locally the product of an amplitude by an oscillating function whose phase gradient modulus i s the wave number. Discretizing in order to keep this relation, we wil l show that, is the limit of high frequencies, the matrices we obtain are sparse (as sparse as volumic finite-element methods, in fact), whi ch 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 pr ecisely, if N is the number of degrees of freedom, we lower the comple xity from O(N2) to O(N).