Development and Application of Compatible Discretizations of Maxwell’s Equations

White, Daniel A.; Koning, Joseph; Rieben, Robert N.

doi:10.1007/0-387-38034-5_11

Cited by 10 publications

(6 citation statements)

References 48 publications

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“…For these simulations we use the 3D electromagnetic code EMSolve, which has been used for a wide range of applications. [8][9][10][11][12][13][14] However, to simulate EMP in the Titan chamber we had to change from the standard E/B formulation for solving Maxell equations to a D/H formulation as discussed below.…”

Section: Simulations Of Empmentioning

confidence: 99%

Mitigation of Electromagnetic Pulse (EMP) Effects from Short-Pulse Lasers and Fusion Neutrons

Eder¹,

Throop²,

Brown³

et al. 2009

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Our research focused on obtaining a fundamental understanding of the source and properties of EMP at the Titan PW(petawatt)-class laser facility. The project was motivated by data loss and damage to components due to EMP, which can limit diagnostic techniques that can be used reliably at short-pulse PW-class laser facilities. Our measurements of the electromagnetic fields, using a variety of probes, provide information on the strength, time duration, and frequency dependence of the EMP. We measure electric field strengths in the 100's of kV/m range, durations up to 100 ns, and very broad frequency response extending out to 5 GHz and possibly beyond. This information is being used to design shielding to mitigate the effects of EMP on components at various laser facilities. We showed the need for well-shielded cables and oscilloscopes to obtain high quality data. Significant work was invested in data analysis techniques to process this data. This work is now being transferred to data analysis procedures for the EMP diagnostics being fielded on the National Ignition Facility (NIF). In addition to electromagnetic field measurements, we measured the spatial and energy distribution of electrons escaping from targets. This information is used as input into the 3D electromagnetic code, EMSolve, which calculates time dependent electromagnetic fields. The simulation results compare reasonably well with data for both the strength and broad frequency bandwidth of the EMP. This modeling work required significant improvements in EMSolve to model the fields in the Titan chamber generated by electrons escaping the target. During dedicated Titan shots, we studied the effects of varying laser energy, target size, and pulse duration on EMP properties. We also studied the effect of surrounding the target with a thick conducting sphere and cube as a potential mitigation approach. System generated EMP (SGEMP) in coaxial cables does not appear to be a significant at Titan. Our results are directly relevant to planned short-pulse ARC (advanced radiographic capability) operation on NIF.

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Section: Simulations Of Empmentioning

confidence: 99%

Mitigation of Electromagnetic Pulse (EMP) Effects from Short-Pulse Lasers and Fusion Neutrons

Eder¹,

Throop²,

Brown³

et al. 2009

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“…The DeRham complex (1) and its dual relative to d * are exterior calculus notions that can encode the structure of a large class of PDEs composed from d, d * , and their higher-order products such as dd * and d * d. Consequently, building finite-dimensional "exterior calculus" structures for FEM, FVM and FDM is now the standard approach to design and analyze compatible discretization methods for PDEs [1,6,30,43].…”

Section: Exterior Calculusmentioning

confidence: 99%

“…math.ttu.edu/~kelong/Sundance/html/), MFEM (code. google.com/p/mfem), FEMSTER [13], EMSolve [43] and FEniCS (www.fenicsproject.org) support primarily FEM, based on weak variational forms of the PDEs.…”

Section: Introductionmentioning

confidence: 99%

Solving PDEs with Intrepid

Bochev

Edwards

Kirby

et al. 2012

Scientific Programming

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Intrepid is a Trilinos package for advanced discretizations of Partial Differential Equations (PDEs). The package provides a comprehensive set of tools for local, cell-based construction of a wide range of numerical methods for PDEs. This paper describes the mathematical ideas and software design principles incorporated in the package. We also provide representative examples showcasing the use of Intrepid both in the context of numerical PDEs and the more general context of data analysis.

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“…High-order finite element methods posed on the discrete de Rham complex (cf. [5,6]) are of increasing relevance for a wide range of computational applications [1,7,27,42,74]. Problems such as electromagnetic diffusion (Maxwell's equations), radiation-diffusion transport, and porous media flow require the solution of finite element problems posed in H(curl) and H(div) spaces (using Nédélec and Raviart-Thomas elements, respectively) [16,60,68].…”

Section: Introductionmentioning

confidence: 99%

Low-order preconditioning for the high-order finite element de Rham complex

Pazner¹,

Kolev²,

Dohrmann³

2022

Preprint

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In this paper we present a unified framework for constructing spectrally equivalent low-orderrefined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in H 1 , H(curl), and H(div), and is based on combining a low-order discretization posed on a refined mesh with a high-order basis for Nédélec and Raviart-Thomas elements that makes use of the concept of polynomial histopolation (polynomial fitting using prescribed mean values over certain regions). This spectral equivalence, coupled with algebraic multigrid methods constructed using the low-order discretization, results in highly scalable matrix-free preconditioners for high-order finite element problems in the full de Rham complex. Additionally, a new lowest-order (piecewise constant) preconditioner is developed for highorder interior penalty discontinuous Galerkin (DG) discretizations, for which spectral equivalence results and convergence proofs for algebraic multigrid methods are provided. In all cases, the spectral equivalence results are independent of polynomial degree and mesh size; for DG methods, they are also independent of the penalty parameter. These new solvers are flexible and easy to use; any "black-box" preconditioner for low-order problems can be used to create an effective and efficient preconditioner for the corresponding high-order problem. A number of numerical experiments are presented, using the finite element library MFEM, with which the construction of such preconditioners requires only one or two lines of code. The theoretical properties of these preconditioners are corroborated, and the flexibility and scalability of the method are demonstrated on a range of challenging three-dimensional problems.

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Development and Application of Compatible Discretizations of Maxwell’s Equations

Cited by 10 publications

References 48 publications

Mitigation of Electromagnetic Pulse (EMP) Effects from Short-Pulse Lasers and Fusion Neutrons

Mitigation of Electromagnetic Pulse (EMP) Effects from Short-Pulse Lasers and Fusion Neutrons

Solving PDEs with Intrepid

Low-order preconditioning for the high-order finite element de Rham complex

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