de La Bourdonnaye, Armel High frequency methods for integral equations. (English) Zbl 0883.65090 Z. Angew. Math. Mech. 76, Suppl. 1, 263-266 (1996). Summary: We present a review of some methods which intend to diminish the complexity of the numerical treatment of integral equations arising in scattering phenomena. Indeed, it is a well-known point that for integral equations discretized with classical finite elements the complexity grows as the fourth power of the frequency. The methods reviewed here try to use a priori informations coming from asymptotic analysis and to include them into the discretization. MSC: 65N38 Boundary element methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 65Y20 Complexity and performance of numerical algorithms Keywords:integral equation method; Helmholtz problem; high frequency methods; complexity; integral equations; scattering; finite elements; asymptotic analysis PDFBibTeX XMLCite \textit{A. de La Bourdonnaye}, Z. Angew. Math. Mech. 76, 263--266 (1996; Zbl 0883.65090) Full Text: DOI