GetDDM: An open framework for testing optimized Schwarz methods for time-harmonic wave problems

Thierry, Bertrand; Vion, Alexandre; Tournier, Simon; Bouajaji, Mohamed El; Colignon, David; Marsic, Nicolas; Antoine, Xavier; Geuzaine, Christophe

doi:10.1016/j.cpc.2016.02.030

Cited by 20 publications

(28 citation statements)

References 44 publications

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“…However, this technique is known to perform poorly for wave problems, at least with classical preconditioners [42]. The design of good preconditioners for wave problems [43,44] and of memory efficient direct solvers [45] remains an active field of research.…”

Section: Memory Scalingmentioning

confidence: 99%

Modal analysis of the ultrahigh finesse Haroche QED cavity

et al. 2018

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View the article online for updates and enhancements. AbstractIn this paper, we study a high-order finite element approach to simulate an ultrahigh finesse FabryPérot superconducting open resonator for cavity quantum electrodynamics. Because of its high quality factor, finding a numerically converged value of the damping time requires an extremely high spatial resolution. Therefore, the use of high-order simulation techniques appears appropriate. This paper considers idealized mirrors (no surface roughness and perfect geometry, just to cite a few hypotheses), and shows that under these assumptions, a damping time much higher than what is available in experimental measurements could be achieved. In addition, this work shows that both high-order discretizations of the governing equations and high-order representations of the curved geometry are mandatory for the computation of the damping time of such cavities.

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Section: Memory Scalingmentioning

confidence: 99%

Modal analysis of the ultrahigh finesse Haroche QED cavity

et al. 2018

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“…The sweeping preconditioners presented in Section 3 will be derived directly using this operator form. The numerical results presented in Section 5 will use these preconditioners in combination with a finite element discretization of both Helmholtz (scalar) and Maxwell's (vector) equations: for a detailed presentation of the finite element formulations and their implementation in the context of Schwarz domain decomposition methods, see [15].…”

Section: Non-overlapping Schwarz Algorithmmentioning

confidence: 99%

“…Detailed expressions for the operators B i,j in the case of time-harmonic acoustic and electromagnetic wave problems can be found in [15]: they are respectively of the general form B i,j = ∂ ni + S for acoustics, and B i,j = (γ t ni curl + S) for electromagnetics, where S is called the transmission operator. The simplest, lowest order transmission operator for acoustics is S := −ik, and S := ikγ T ni = ikγ T nj for electromagnetics.…”

Section: Algorithm In Operator Formmentioning

confidence: 99%

Improved sweeping preconditioners for domain decomposition algorithms applied to time-harmonic Helmholtz and Maxwell problems

Vion

Geuzaine

2018

ESAIM: ProcS

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Sweeping-type algorithms have recently gained a lot of interest for the solution of highfrequency time-harmonic wave problems, in particular when used in combination with perfectly matched layers. However, an inherent problem with sweeping approaches is the sequential nature of the process, which makes them inadequate for efficient implementation on parallel computers. We propose several improvements to the double-sweep preconditioner originally presented in [18], which uses sweeping as a matrix-free preconditioner for a Schwarz domain decomposition method. Similarly, the improved preconditioners are based on approximations of the inverse of the Schwarz iteration operator: the general methodology is to apply well-known algebraic techniques to the operator seen as a matrix, which in turn is processed to obtain equivalent matrix-free routines that we use as preconditioners. A notable feature of the new variants is the introduction of partial sweeps that can be performed concurrently in order to make a better usage of the resources. As these modifications still leave some unexploited computational power, we also propose to combine them with right-hand side pipelining to further improve parallelism and achieve significant speed-ups. Examples are presented on high-frequency Helmholtz and Maxwell problems, in two and three dimensions, to demonstrate the properties of our improvements on parallel computer architectures.

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“…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].…”

Section: Numerical Implementationmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%