Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: the singular complement method

Assous, Franck; Ciarlet, Patrick; Labrunie, Simon; Segré, J.

doi:10.1016/s0021-9991(03)00309-7

Cited by 50 publications

(47 citation statements)

References 17 publications

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“…Numerical results are shown. This extends the numerical results obtained in two-dimensional cartesian [5] or axisymetric domains [6]. See also [7] for an extension to prismatic domains based on a Fourier expansion.…”

Section: Introductionsupporting

confidence: 81%

A Multiscale Approach for Solving Maxwell’s Equations in Waveguides with Conical Inclusions

Assous

Ciarlet

2008

Computational Science – ICCS 2008

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Abstract. This paper is devoted to the numerical solution of the instationary Maxwell equations in waveguides with metallic conical inclusions on its internal boundary. These conical protuberances are geometrical singularities that generate in their neighborhood, strong electromagnetic fields. Using some recent theoretical and practical results on curl-free singular fields, we have built a method which allows to compute the instationary electromagnetic field. It is based on a splitting of the spaces of solutions into a regular part and a singular one. The singular part is computed with the help of a multiscale representation, written in the vicinity of the geometrical singularities. As an illustration, numerical results in a rectangular waveguide are shown.

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Section: Introductionsupporting

confidence: 81%

A Multiscale Approach for Solving Maxwell’s Equations in Waveguides with Conical Inclusions

Assous

Ciarlet

2008

Computational Science – ICCS 2008

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“…In the literature, some developments have been suggested to approach such problems. Among them, numerical solutions have been proposed to resolve the time-dependent material behaviour with Maxwell equations [10]. Also, according to nondependent integrals, a generalization of the M integral [11] and T and A integrals to viscoelastic materials have been proposed in order to resolve the axisymmetric problem submitted to environmental loading [12].…”

Section: Introductionmentioning

confidence: 99%

Stress Intensity Factors for Viscoelastic Axisymmetric Problems Applied to Wood

Pitti

Chazal

Labesse-Jied

et al. 2012

Conference Proceedings of the Society for Experimental Mechanics Series

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ABSTRACT. Many materials used in engineering applications obey to time-dependent behaviours and the mechanical fields are affected by the time effects. As a result, the evolution of the stresses and strains in these materials appear still very complex and difficult to study. Among such cases is the situation when the material has an axisymmetric shape and when it is submitted to a complex fracture loading. In this paper, the creep loading is applied on an axisymmetric viscoelastic orthotropic material and the stress intensity factors are computed in the opening mode, in the shear mode and in the mixed mode using to a finite element approach. The uncoupling method is based on M integral, combining the virtual and real mechanical fields. In the same time, the viscoelastic effects are introduced according to the generalized Kelvin-Voigt model composed by four branches. The numerical solution is obtained with an incremental viscoelastic formulation in the time domain. Using a Compact Tension Shear (CTS) specimen, the evolutions of stress intensity factor versus time are posted in each fracture mode configuration. The obtained results demonstrate the efficiency of the proposed model.

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“…In plasma physics, fields computed by discontinuous FE Maxwell solvers create a considerable numerical noise when embedded in a plasma code, e.g. using the particle-in-cell method (see [2]). Furthermore, nodal approximations are particularly well-suited for time-dependent electromagnetic problems because the mass matrix can be consistently lumped without loss of accuracy, leading to inexpensive transient solvers.…”

mentioning

confidence: 99%

“…In the negative side, it clearly complicates the numerical integration (of the weighted term), loses computational efficiency and complicates the automatization of the simulations. An alternative approach to solve the Maxwell problem is the decomposition of the solution into singular and smooth part (see [2,26]) but this method is harder to generalize, specially in three dimensions. Very recently, Duan et al have designed in [19] a method based on local projections that uses a FE space composed of cubic nodal elements enriched with edge and element bubbles.…”

mentioning

confidence: 99%

A Nodal-based Finite Element Approximation of the Maxwell Problem Suitable for Singular Solutions

Badia¹,

Codina²

2012

SIAM J. Numer. Anal.

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Abstract.A new mixed finite element approximation of Maxwell's problem is proposed, its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term, which yields a very weak control on the divergence of the unknown. The method is shown to be stable and convergent in the natural H(curl; Ω) norm for this unknown. In particular, convergence also applies to singular solutions, for which classical nodal based interpolations are known to suffer from spurious convergence upon mesh refinement.1. Introduction. The simulation of electromagnetic phenomena with increasing complexity demands accurate and efficient numerical methods suitable for large-scale computing. Finite element (FE) methods are commonly used in this context because they can easily handle complicated geometries by using unstructured grids, provide a rigorous mathematical framework and allow adaptation.In many applications of current interest, the electromagnetic problem is coupled to other physical processes. Salient examples of multiphysics phenomena that include electromagnetics are magnetohydrodynamics (MHD) and plasma physics. These two problems have experienced increasing attention due to the need to develop numerical laboratories in fusion technology design. The simulation of these problems (and many others) would benefit of an all-purpose FE method that would be suitable for the different sub-problems at hand, simplifying the implementation issues and the enforcement of the coupling conditions. In particular, an all-purpose continuous nodal-based formulation would be a favored candidate. E.g. the Navier-Stokes equations are commonly solved with stabilized FE approximations that can deal with the singularly perturbed nature of the system for high Reynolds numbers and circumvent the restrictions related to the corresponding inf-sup condition (see e.g. [13,14]). In plasma physics, fields computed by discontinuous FE Maxwell solvers create a considerable numerical noise when embedded in a plasma code, e.g. using the particle-in-cell method (see [2]). Furthermore, nodal approximations are particularly well-suited for time-dependent electromagnetic problems because the mass matrix can be consistently lumped without loss of accuracy, leading to inexpensive transient solvers.The Maxwell operator has a saddle-point structure, with the particularity that the Lagrange multiplier introduced to enforce the divergence-free constraint is identically zero. Existing FE methods that satisfy the discrete counterpart of the inherent inf-sup condition for this problem are based on Nedelec's or edge elements (see e.g. [27,33]); edge elements lead to fields with discontinuous normal component on element edges or faces. We also refer to alternative formulations based on discontinuous Galerkin approximations [28,24,23,34]. With the aim to solve the Maxwell problem with Lagrangian finite elements (FEs), the differential operator of the problem can be transformed into an elliptic on...

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Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: the singular complement method

Cited by 50 publications

References 17 publications

A Multiscale Approach for Solving Maxwell’s Equations in Waveguides with Conical Inclusions

A Multiscale Approach for Solving Maxwell’s Equations in Waveguides with Conical Inclusions

Stress Intensity Factors for Viscoelastic Axisymmetric Problems Applied to Wood

A Nodal-based Finite Element Approximation of the Maxwell Problem Suitable for Singular Solutions

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