High-order methods for computational wave propagation and scattering

September 10 to September 14, 2007

at the

American Institute of Mathematics, Palo Alto, California

organized by

Oscar P. Bruno and Rainer Kress

This workshop, sponsored by AIM and the NSF, will address numerical methods for wave propagation with a focus on high-order convergence for general scattering configurations (with applicability to complex and singular geometries and high frequency problems); they include a significant focus on integral equation methods, with reference to finite-difference and finite-element algorithms, spectral and Fourier based approaches, hybrids of asymptotic and numerical methods, as well as the closely related field of inverse scattering problems. In particular, this workshop will have an emphasis on spectral methods concerning the following topics:

  1. High frequency approximations;
  2. Geometric singularities; and,
  3. Generalized impedance boundary conditions.
Significant progress in the field of computational wave scattering in recent years has resulted from use of sophisticated mathematical techniques and insights, arising from the fields of approximation theory, pseudo-differential operator theory, asymptotics and special functions, in conjunction with the classical methods of numerical analysis. It now appears the time is ripe for these emerging methods to evolve into fast and accurate algorithms, capable of evaluating accurately and efficiently wave scattering for low, intermediate and high frequencies, and applicable to scatterers which may contain geometrically complicated scattering surfaces and volumes, including geometric singularities such as edges, corners and cusps and impedance boundary conditions.

A number of recent individual efforts have furthered our capabilities in computational wave scattering. It is hoped this workshop will accelerate progress by allowing for exchanges of ideas beyond those that would occur through direct study of the published literature or occasional encounters in large yearly conferences.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email workshops@aimath.org

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