Schedule (modified 6/25/2012)

S (in alphabetic order by speaker surname) Speaker: Nathan Albin (Kansas State University) Title: Fourier Continuation Methods for Long-Range Propagation and Transport Abstract: The Fourier Continuation (FC) method is a numerical technique for expressing nonperiodic functions as restrictions of rapidly converging Fourier series, thus avoiding the Gibbs phenomenon and enabling the use of Fourier-based methods to accurately evaluate derivatives of nonperiodic functions. The spectral properties of the FC derivative operator make it especially well-suited for use in numerical solvers for long-range wave propagation and transport problems. This talk will present the basic constructions The Fourier Continuation (FC) method is a numerical technique for expressing nonperiodic functions as restrictions of rapidly converging Fourier series, thus avoiding the Gibbs phenomenon and enabling the use of Fourier-based methods to accurately evaluate derivatives of nonperiodic functions. The spectral properties of the FC derivative operator make it especially well-suited for use in numerical solvers for long-range wave propagation and transport problems. This talk will present the basic constructions underlying FC-based PDE solvers and will summarize some of the most interesting properties of these solvers, including exceptional accuracy, e cient parallelization, and optimal CFL scaling. Several applications to which FC solvers have been successfully applied, including models for ultrasound cancer therapies, scattering of chirped radar signals, and complex fluid flows, will be presented. Speaker: Xavier Antoine (Université de Lorraine) Title: High-Order Shifted Laplace Preconditioners for Wave Equations Abstract: Solving linear systems arising from wave scattering is generally a di cult and challenging problem. During these last decades some preconditioning technics have been proposed to provide satisfactory convergence for iterative solvers. The aim of this talk is to propose a generalization of the so-called Shifted Laplace preconditioning methods [Erlangga & al., Appl. Numer. Math. 2004] by using operator representation combined with complex Pad approximants. We will show that the resulting High-order Shifted Laplace preconditioners are highly e cient and robust for twoand three-dimensional scattering problems that exhibit complex geometrical features (e.g. resonant structures). Furthermore, the convergence is proved to be weakly frequency dependent. The low order of this class of preconditioning method corresponds to the Shifted Laplace one in the symbolic calculus of pseudodi↵erential operators meaning. Some numerical examples and comparison to the Shifted Laplace methods will be presented for illustration. Speaker: Timo Betcke (University College London) Title: Nonnormality of boundary integral operators in acoustic scattering Abstract: Nonnormality is a well studied subject in the context of partial di↵erential operators. Yet, only little is known for boundary integral operators. The only well studied case is the unit ball, where the standard single layer, double layer and conjugate double layer potential operators in acoustic scattering diagonalise in a unitary basis. In this talk we present recent results for the analysis of spectral decompositions and nonnormality of boundary integral operators on more general domains. One particular application is the analysis of stability constants for boundary element discretisations. We demonstrate how these are e↵ected by nonnormality and give several numerical examples, illustrating these issues on various domains. Speaker: Simon Chandler-Wilde, Steve Langdon, Euan Spence (University of Reading and University of Bath) Title: Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering Abstract: n this talk we will describe recent progress on the design and analysis of hybrid numericalasymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. This work combines new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and