In this article we review recent progress on the design, analysis and implementation of numerical-asymptotic boundary integral methods for the computation of frequency-domain acoustic scattering in a homogeneous unbounded medium by a bounded obstacle. The main aim of the methods is to allow computation of scattering at arbitrarily high frequency with finite computational resources

Chandler-Wilde, Simon Neil

Graham, Ivan G.

CiteSeerX

English

A collocation method for high frequency scattering by convex polygons.

A fast multipole method for Maxwell equations stable at all frequencies,

A hybrid numericalasymptotic boundary integral method for high-frequency acoustic scattering,

A refined Galerkin error and stability analysis for highly indefinite variational problems,

A sparse discretisation for integral equation formulations of high-frequency scattering problems,

A wavenumber independent boundary element method for an acoustic scattering problem,

An asymptotically derived boundary element method for the Helmholtz equation,

An hp-BEM for high frequency scattering by convex polygons,

An inequality for the reduced wave equation and the justification of geometrical optics,

An O(1) integration scheme for threedimensional surface scattering problems,

Analysis of multiple scattering iterations for high-frequency scattering problems II: The three-dimensional scalar case, report 147, Max-Planck-Institut fu¨r Mathematik in den Naturwissenschaften,

Analysis of multiple scattering iterations for high-frequency scattering problems. I: The two dimensional case, report 137, Max-Planck-Institut fu¨r Mathematik in den Naturwissenschaften,

Approximation of high frequency wave propagation problems, this volume.

Asymptotically derived boundary elements for the Helmholtz equation in high frequencies,

Boundary integral solution of the exterior acoustic problem,

Condition number estimates for combined potential boundary integral operators in acoustic scattering,

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation, in preparation.

Construction de la parame´trix du proble`me mixte hyperbolique pour l’equation des ondes,

Convergence of moment-method solutions of the electric field integral equation for a 2-D open cavity,

Coupling of fast multipole method and microlocal discretization for the 3-D Helmholtz equation,

Creeping modes in a shadow,

Diffraction par un convexe.

Efficient evaluation of highly oscillatory acoustic scattering surface integrals.

Error analysis of the moment method,

Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals

High frequency scattering by convex curvilinear polygons,

Highly oscillatory quadrature, this volume.

Improvement of the integral equation method for high-frequency problems,

Integral equation formulations of electromagnetic and acoustic scattering problems: convergence of multiple scattering iterations and high-frequency asymptotic expansions.

Integral equation methods for the Helmholtz equation,

Me´thode des e´quations inte´grales pour les hautes fre´quencies.

Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering.

Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle,

Numerical evaluation of 2D partition of unity boundary integrals for Helmholtz problems,

Numerical steepest descent evaluation of 2D partition of unity boundary integrals for Helmholtz problems,

On quadrature methods for highly oscillatory integrals and their implementation,

On the acoustic single layer potential: Stabilisation and Fourier analysis,

On the choice of the coupling parameter in boundary integral formulations of the exterior acoustics problem.

On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation,

On the O(1) solution of multiplescattering problems,

On the question of the solvability of the exterior boundary-value problems for the wave eqaution and Maxwell’s equations,

On the spectrum of the electric field integral equation and the convergence of the moment method,

Plane-wave basis finite elements and boundary elements for three-dimensional wave scattering,

Potential techniques for boundary value problems on C1 domains,

Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: the convex case.

Quadrature methods for multivariate highly oscillatory integrals using derivatives”,

Re´gularite´ Gevrey 3 pour la diffraction,

Review of large scale computing in electromagnetics with fast integral equation solvers,

Rigorous justification of the shortwave asymptotic theory of diffraction in the shadow zone.

Schnelle Summationsverfahren zur numerischen Lo¨sung von Integralgleichungen fu¨r Streuprobleme im R3. PhD Thesis,

Short-wave asymptotic behaviour in the problem of diffraction by smooth convex contours (in

Short-wavelength Diffraction Theory (SpringerVerlag,

Some estimates of Green’s functions in the shadow,

Surface scattering in three dimensions: an accelerated high-order solver,

The asymptotic behavior of the spectral characteristics of exterior problems for the Schro¨dinger operator (in Russian).

The computation of conical diffraction coefficients in high frequency acoustic wave scattering,

The Numerical Solution of Integral Equations of the Second Kind,

U¨ber das Dirichletsche Außenraumproblem fu¨r die Helmholtzsche Schwingungsgleichung,

Wave-number-explicit bounds in timeharmonic scattering,

Zur Dirichtletschen Randwertaufgabe des Aussenraums der Schwingungsgleichung,

Boundary integral methods in high frequency scattering