An open source domain decomposition solver for time-harmonic electromagnetic wave problems

Abstract

International audienceWe present a flexible finite element solver for testing optimized Schwarz domain decomposition techniques for the time-harmonic Maxwell equations. After a review of non-overlapping Schwarz domain decomposition methods and associated transmission conditions, we discuss the implementation, based on the open source software GetDP and Gmsh. The solver, along with ready-to-use examples, is available online for further testing

Acoustic multiple scattering using recursive algorithms

“…Each level considers the reflection and scattering from a single scatterer using the so-called wave based method for unbounded problems. Geuzaine et al [22] provided an open source finite element solver based on domain decomposition methods; the open source solver software available online, is suitable for solution of high frequency time-harmonic electromagnetic wave problems. Challa and Sini [23] studied the acoustic MS problem by many small rigid scatterers of arbitrary shapes using the Foldy-Lax approximation; they solved the inverse problem of scattering by the small obstacles.…”

Domain Decomposition Methods for Time-Harmonic Electromagnetic Waves With High-Order Whitney Forms

“…A short presentation of optimized boundary conditions can be found in [3]. Let us remark that, in its simplest form (zeroth order), the S operator is simply a complex value: S = k.…”

“…It is worth noticing [3] that solving iteratively (2) and (3) can be rewritten as the application of the iteration operator A:…”

Optimized Schwarz Domain Decomposition Methods for Scalar and Vector Helmholtz Equations

“…The domain decomposition methods analyzed above are all readily available for testing using finite element methods in the open source GetDDM software environment [33,48], [10,21]. e., f.: guided acoustic or electromagnetic waves in rectangular waveguides [51].…”

“…We analyze the behavior of these transmission operators on a model problem and derive generic weak formulations in view of their implementation in finite element codes. All the formulations are readily available for testing on several acoustic and electromagnetic cases using the open source GetDDM environment (http://onelab.info/wiki/GetDDM) [33,48], based on the finite element solver GetDP (http://getdp.info) [17,18,28] and the mesh generator Gmsh (http://gmsh.info) [31,32].…”