Guillaume Sylvand
(Airbus Group)
04/02/2016 09:50
For the numerical simulation of wave propagation in acoustics, Airbus Group Innovations relies on integral
equations solved with the Boundary Elements Method. The advantages of this approach are well known: mainly
accuracy, and simpler (surfacic) mesh. The main algorithm drawback is the need to cope with a dense matrix
whose size can be quite large for wave propagation problems, where the...
Jérôme Simon
(Onera Palaiseau)
04/02/2016 11:20
The Surface Integral Equation is one of the most used methods in the simulation of electromagnetic problems. Its implementation combined with a fast multipole algorithm (MLFMM) and iterative solvers leads efficient and accurate methods for the analysis of radar cross section (RCS) for a target.
Different methods (MLFMM, ACA, Domain Decomposition Method …) and formulations EFIE...
Different methods (MLFMM, ACA, Domain Decomposition Method …) and formulations EFIE...
Christophe Geuzaine
(Université de Liège)
04/02/2016 11:55
In terms of computational methods, solving three-dimensional time-harmonic
acoustic or electromagnetic wave problems is known to be challenging, especially
in the high frequency regime and in the presence of inhomogenous media. The
brute-force application of the finite element method in this case leads to the
solution of very large, complex and possibly indefinite linear systems....
Jean-Claude Nédélec
(Ecole Polytechnique)
04/02/2016 14:15
Marion Darbas
(Université de Picardie)
04/02/2016 14:50
The numerical solution of time-harmonic scattering problems remains challenging in the high frequency regime due to its specific computational bottlenecks. The techniques based on integral equations lead to the resolution of linear systems where the involved matrices are dense and usually badly conditioned. The improvement of these methods is a timely research area. One possibility to reduce...
Stephen Langdon
(University of Reading)
04/02/2016 15:25
Linear wave scattering problems (e.g. for acoustic, electromagnetic and elastic waves) are ubiquitous in science and engineering applications. However, conventional numerical methods for such problems (e.g. FEM or BEM with piecewise polynomial basis functions) are prohibitively expensive when the wavelength of the scattered wave is small compared to typical lengthscales of the scatterer (the...
Catalin Turc
(New Jersey Institute of Technology)
04/02/2016 16:20
We present a new Windowed Green Function (WGF) method for the numerical integral-equation solution of problems of electromagnetic scattering by obstacles in presence of dielectric or conducting half-planes. The WGF method, which is based on use of integral kernels that can be expressed directly in terms of the free-space Green function, does not require evaluation of expensive Sommerfeld...
Matthieu Aussal
(Ecole Polytechnique)
04/02/2016 16:55
Fast convolution on unstructured grids have been developed for many
applications (e.g. electrostatics, magnetostatics, acoustics, electro-
magnetics, etc.). The goal is to reduce the complexity of matrix-vector
products, from O(N^2) to O(N log N ). In this presentation, we describe
a new efficient numerical method called Sparse Cardinal Sine Decomposition
(SCSD), based on a suitable...
Simon N. Chandler-Wilde
(University of Reading)
05/02/2016 09:00
In this talk we discuss the application of the unified transform method, due to A.S. Fokas and co-authors, to interior and exterior problems for time harmonic waves. Like integral equation methods, the method reduces to the solution of a problem on the boundary of the domain in question. We discuss numerical implementations, restricting the solution space to a finite-dimensional subspace, and...
Paul Soudais
(Dassault Aviation)
05/02/2016 09:35
Impedance Boundary Conditions (IBC) are widely used in computational
electromagnetics to model thin coatings on perfectly conducting (PEC) objects.
The IBC is used to reduce drastically the number of unknowns of the integral
equations models and to obtain a better conditioned linear system that can be
more efficiently iteratively solved.
Integral equations models can be built that...
Integral equations models can be built that...
Marc Bakry,
Sébastien Pernet
(Onera Toulouse)
05/02/2016 10:10
A posteriori error estimates are tools which enable a measure of the numerical error. They are required to be equivalent to the norm of the error and to be locally computable. They are norms of values which can be computed from the numerical solution and the problem parameters. In the context of BEM, there is a loss of locality of the norms and therefore of the estimates. Standard localization...
Abderrahmane Bendali
(INSA Toulouse)
05/02/2016 11:40
We first briefly present the dispersion phenomenon and show how it damages the numerical solution of wave problems over large distances of propagation. We then introduce a Trefftz Discontinuous Galerkin (TDG) symmetric formulation for the Helmholtz equation with piecewise constant coefficients. Recall that Trefftz methods are discretization processes based on the use of exact interior either...
Ralf Hiptmair
(ETH Zürich)
05/02/2016 14:00
For second-order linear transmission problems involving a single closed interface separating two homogeneous materials, a well-posed second-kind boundary integral formulation has been known for a long time. It arises from a straightforward combination of interior and exterior Calderon identities. Apparently, this simple approach cannot be extended to "composite" settings involving more than...
Francesco Andriulli
(Télécom Bretagne)
05/02/2016 15:10
Integral equation solvers are widely used for simulating electromagnetic scattering and radiation from metallic and penetrable objects. Long popular in academic circles, these solvers have been in recent years incorporated into several commercial electromagnetic analysis and design tools, after the advent of fast multipole and related algorithms. The effectiveness of these solvers...
