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A Refined Finite Element Convergence Theory for Highly Indefinite Helmholtz Problems

Sauter, S.

In: Computing, 2006, vol. 78, no. 2, p. 101-115

Vekua theory for the Helmholtz operator

Moiola, A. ; Hiptmair, R. ; Perugia, I.

In: Zeitschrift für angewandte Mathematik und Physik, 2011, vol. 62, no. 5, p. 779-807

Hierarchical matrix techniques for low- and high-frequency Helmholtz problems

Banjai, Lehel ; Hackbusch, Wolfgang

In: IMA Journal of Numerical Analysis, 2007, vol. 28, no. 1, p. 46-79

Asymptotics for Helmholtz and Maxwell Solutions in 3-D Open Waveguides

Jerez-Hanckes, Carlos ; Nédélec, Jean-Claude

In: Communications in Computational Physics, 2012, vol. 11, no. 2, p. 629-646

Domain decomposition preconditioning for the Helmholtz equation : a coarse space based on local Dirichlet-to-Neumann maps

Conen, Lea ; Krause, Rolf (Dir.)

Thèse de doctorat : Università della Svizzera italiana, 2015 ; 2015INFO001.

In this thesis, we present a two-level domain decomposition method for the iterative solution of the heterogeneous Helmholtz equation. The Helmholtz equation governs wave propagation and scattering phenomena arising in a wide range of engineering applications. Its discretization with piecewise linear finite elements results in typically large, ill-conditioned, indefinite, and non- Hermitian...