INTEGRAL-EQUATION METHOD FOR HIGH-FREQUENCIES

We are interested in the numerical approximation of the problem of the scattering of an electromagnetic plane wave by a bounded obstacle in R2 or R3, using the boundary integral equation method. A new choice of boundary finite element spaces leads to a good approximation with a number of degrees of freedom as 0 (k1/3) in dimension 2 and O (k2/3) in dimension 3, instead of O(k) and O(k2) respectively with a classical finite element method (k is the wave number). That makes the integral equation method more suitable for high frequency problems, and furthermore that works with rather general boundary conditions.