Fast BEM solution for scattering problems using Quantized Tensor Train format

International audienceIt is common to accelerate the boundary element method by compression methods (FMM, H-Matrix / ACA) that enable a more accurate solution or a solution in higher frequency. In this work, we present a compression method based on a transformation of the linear system into Tensor-Train format by the quantization technique. The method is applied to a scattering problem by a canonical object with a regular mesh and improves the performance obtained by the previous methods

Prise en compte des symétries dans la méthode des moments magnétostatiques

Dans ce travail, nous présentons une stratégie pour prendre en compte les symétries dans la méthode des moments magnétostatique (MoM). Ceci permet de réduire les dimensions de la matrice d’interaction, difficulté principale de la méthode

Physically-based preconditioner for the WCIP

International audienceA physically-based preconditioner for the 1d and 2d Wave Concept Iterative Procedure is introduced in this paper. Numerical results are provided to assess the efficiency of this technique

Boundary element method for 3D conductive thin layer in eddy current problems

International audiencePurpose-Thin conducting sheets are used in many electric and electronic devices. Solving numerically the eddy current problems in presence of these thin conductive sheets requires a very fine mesh which leads to a large system of equations, and it becomes more problematic in case of higher frequencies. The purpose of this paper is to show the numerical pertinence of equivalent models for 3D eddy current problems with a conductive thin layer of small thickness e based on the replacement of the thin layer by its mid-surface with equivalent transmission conditions that satisfy the shielding purpose, and by using an efficient discretization using the Boundary Element Method (BEM) in order to reduce the computational work. Design/methodology/approach-These models are solved numerically using the BEM and some numerical experiments are performed to assess the accuracy of our models. The results are validated by comparison with an analytical solution and a numerical solution by the commercial software Comsol. Findings-The error between the equivalent models and the analytical and numerical solutions confirms the theoretical approach. In addition to this accuracy, the time consumption is reduced by considering a discretization method that requires only a surface mesh. Originality/Value-Based on an hybrid formulation, we present briefly a formal derivation of impedance transmission conditions for 3D thin layers in eddy current problems where non-conductive materials are considered in the interior and the exterior domain of the sheet. BEM is adopted to discretize the problem as there is no need for a volume discretization

Adaptive cross approximation for scattering by periodic surfaces

Full text is available at the following URL: http://www.jpier.org/PIERM/pierm35/11.14011505.pdfInternational audienceThe adaptive cross approximation is applied to boundary element matrices coming from 2D scattering problems by an infinite periodic surface. This compression technique has the advantage to be applied before the assembly of the matrix. As a result, the computational times for both assembly and solution phases are reduced. Numerical results assess the efficacy of the method on scattering problems with several periodic surfaces

Homogenization Techniques for Improving the Calculations of Scattering by 1-D Fast Oscillating Periodic Surfaces

International audienceThis paper deals with the efficient computation of scattering problems by fast oscillating periodic surfaces using two-scale expansion homogenization techniques. The proposed method splits the field between an effective field and a boundary layer corrector and applies an asymptotic expansion. Then, the evaluation of these boundary layers leads to the extraction of effective parameters, modeling the effects of the highly oscillating surface on the scattered field. A previous paper has already presented such a technique to deal with TM polarization. First, this paper extends the approach to TE polarization and completes it by pointing out all the key points. Especially it shows the map of the split fields underlining the physical contribution of each term. Second, this paper exposes and compares two different uses of these computed effective parameters. Numerical examples show the validity of the method, especially by justifying the asymptotic expansion ansatz. Computational efficiency is discussed

Application of the ACA compression technique for the scattering of Periodic Surfaces

International audienceThe computation of scattering by an infinite periodic structure by an integral equation technique is accelerated by the use of a the ACA method. This compression technique has the advantage to be applied before the building of the matrix. As a result, both assembly and solution phases benefit from the acceleration of computation times. Numerical results assess the e cacy on a problem with a simple periodic surface

Fast BEM Solution for 2-D Scattering Problems Using Quantized Tensor-Train Format

International audienceIt is common to accelerate the boundary element method (BEM) by compression techniques [fast multipole method (FMM), H-matrix/adaptive cross approximation (ACA)] that enable a more accurate solution or a solution in higher frequency. In this article, we present a compression method based on a transformation of the linear system into the tensor-train format by the quantization technique. The method is applied to a scattering problem on a canonical object with a regular mesh and improves the performance obtained from existing methods