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High frequency methods for integral equations. (English) Zbl 0883.65090

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
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