A 3D DPG Maxwell approach to nonlinear Raman gain in fiber laser amplifiers

Nagaraj, Sriram; Grosek, Jacob; Petrides, Socratis; Demkowicz, Leszek; Mora, Jaime

doi:10.1016/j.jcpx.2019.100002

Cited by 12 publications

(9 citation statements)

References 59 publications

(112 reference statements)

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“…This in turn gives a pollution free method for one-space dimension problems (see [44,16,56,26] for additional details). Additionally, we emphasize that other equivalent (in terms of stability) formulations can be explored [35,14,21,34], however, especially for wave operators, the ultraweak formulation is provably superior because of its approximability properties [56,16,43,40,32,31].…”

Section: The Dpg Methods and Linear Acousticsmentioning

confidence: 99%

An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics

Petrides¹,

Demkowicz²

2020

Preprint

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We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov-Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces defined on the mesh skeleton, and it is suitable for adaptive hp-meshes. The key point of the construction is the integration of the iterative solver with a fully automatic and reliable mesh refinement process provided by the DPG technology. The efficacy of the solution technique is showcased with numerous examples of linear acoustics and electromagnetic simulations, including simulations in the high-frequency regime, problems which otherwise would be intractable. Finally, we analyze the one-level preconditioner (smoother) for uniform meshes and we demonstrate that theoretical estimates of the condition number of the preconditioned linear system can be derived based on well established theory for self-adjoint positive definite operators.

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Section: The Dpg Methods and Linear Acousticsmentioning

confidence: 99%

An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics

Petrides¹,

Demkowicz²

2020

Preprint

Self Cite

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“…Let U 0 h ⊂ H 0 (curl ; ), and V h ⊂ V be finite-dimensional subspaces (as usual, h > 0 denotes a typical mesh size parameter). For details about the finite element subspaces, curl-conforming and div-conforming elements see, e.g., the spatial discretization in [50, Section IV, equations (19)- (23)]. For the equations (8)-(10), the semi-discrete problem involves the determination of elements…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…This scheme was applied to second-and third-order nonlinear phenomena including spatial soliton propagation [14], [15], linear and nonlinear interface scattering [16], and pulse propagation through nonlinear wave guides [17]. A lot of interesting modeling and simulation results for linear and nonlinear Lorentz dispersion with nonlinear Kerr response in case of 1D, 2D and 3D can be found in [15], [18]- [23]. Among non-standard difference methods, pseudospectral spatial domain schemes have been employed for optical carrier shock [24] and linear Lorentz dispersion with nonlinear response [25] simulation.…”

Section: Introductionmentioning

confidence: 99%

Energy-Stable Time-Domain Finite Element Methods for the 3D Nonlinear Maxwell's Equations

Anees

Angermann

2020

IEEE Photonics J.

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In this paper, time-domain finite element methods for the full system of Maxwell's equations with cubic nonlinearities in 3D are presented, including a selection of computational experiments. The new capabilities of these methods are to efficiently model linear and nonlinear effects of the electrical polarization. The novel strategy has been developed to bring under control the discrete nonlinearity model in space and time. It results in energy stable discretizations both at the semi-discrete and the fully discrete levels, with spatial discretization using edge and face elements (Nédeléc-Raviart-Thomas formulation). In particular, the proposed time discretization schemes are unconditionally stable with respect to a specially defined nonlinear electromagnetic energy, which is an upper bound of the electromagnetic energy commonly used. The approaches presented prove to be robust and allow the modeling of 3D optical problems that can be directly derived from the full system of Maxwell's nonlinear equations, and allow the treatment of complex nonlinearities and geometries of various physical systems coupled with electromagnetic fields.

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“…In the case of a distributed-memory parallel simulation, we emphasize the importance of dynamic load balancing for this particular problem. 25,18], compressible fluid dynamics [6], and linear elasticity [21]. Its stability properties make it particularly applicable to high-frequency wave propagation problems, where pre-asymptotic stability is essential for driving efficient hp-adaptivity [26].…”

Section: Introductionmentioning

confidence: 99%

A numerical study of the pollution error and DPG adaptivity for long waveguide simulations

Henneking

Demkowicz

2021

Computers & Mathematics with Applications

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High-frequency wave propagation has many important applications in acoustics, elastodynamics, and electromagnetics. Unfortunately, the finite element discretization for these problems suffer from significant numerical pollution errors that increase with the wavenumber. It is critical to control these errors to obtain a stable and accurate method. We study the effect of pollution for very long waveguide problems in the context of robust discontinuous Petrov-Galerkin (DPG) finite element discretizations. Our numerical experiments show that the pollution primarily has a diffusive effect causing energy loss in the DPG method while phase errors appear less significant. We report results for 3D vectorial timeharmonic Maxwell problems in waveguides with more than 8000 wavelengths. Our results corroborate previous analysis for the Galerkin discretization of the Helmholtz operator by Melenk and Sauter ("Wavenumber explicit convergence analysis for Galerkin discretizations of the Helmholtz equation". In: SIAM J. Numer. Anal. 49.3 (2011Anal. 49.3 ( ), pp. 1210Anal. 49.3 ( -1243. Additionally, we discuss adaptive refinement strategies for multi-mode fiber waveguides where the propagating transverse modes must be resolved sufficiently. Our study shows the applicability of the DPG error indicator to this class of problems. Finally, we illustrate the importance of load balancing in these simulations for distributed-memory parallel computing. arXiv:1912.05716v1 [math.NA] 12 Dec 2019 2 The DPG methodologyThe DPG method of Demkowicz and Gopalakrishnan [7,9,8] has been used to solve applications in viscoelasticity [15], acoustic and electromagnetic wave propagation [27,

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A 3D DPG Maxwell approach to nonlinear Raman gain in fiber laser amplifiers

Cited by 12 publications

References 59 publications

An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics

An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics

Energy-Stable Time-Domain Finite Element Methods for the 3D Nonlinear Maxwell's Equations

A numerical study of the pollution error and DPG adaptivity for long waveguide simulations

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