Unstructured Grid-Based Discontinuous Galerkin Method for Broadband Electromagnetic Simulations

Kabakian, Adour V.; Shankar, Vijaya; Hall, William J.

doi:10.1023/b:jomp.0000025932.17082.18

Cited by 26 publications

(19 citation statements)

References 27 publications

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“…Based on the upwinding flux theory introduced in [42], the proper expression for the tangential surface fields are Using the above definition, the inter-element coupling terms are obtained based on the fields at the local and adjacent elements. For the surfaces corresponding to particular boundary conditions such as open, perfect electric or perfect magnetic conductors, proper definitions are available and introduced in [31][32][33][34].…”

Section: Dgtd Methodsmentioning

confidence: 99%

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Field-based DGTD/PIC technique for general and stable simulation of interaction between light and electron bunches

Fallahi¹,

Kärtner²

2014

J. Phys. B: At. Mol. Opt. Phys.

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We introduce a hybrid technique based on the discontinuous Galerkin time domain (DGTD) and the particle in cell (PIC) simulation methods for the analysis of interaction between light and charged particles. The DGTD algorithm is a three-dimensional, dual-field and fully explicit method for efficiently solving Maxwell equations in the time domain on unstructured grids. On the other hand, the PIC algorithm is a versatile technique for the simulation of charged particles in an electromagnetic field. This paper introduces a novel strategy for combining both methods to solve for the electron motion and field distribution when an optical beam interacts with an electron bunch in a very general geometry. The developed software offers a complete and stable numerical solution of the problem for arbitrary charge and field distributions in the time domain on unstructured grids. For this purpose, an advanced search algorithm is developed for fast calculation of field data at charge points and for later importing to the PIC simulations. In addition, we propose a field-based coupling between the two methods resulting in a stable and precise time marching scheme for both fields and charged particle motion. To benchmark the solver, some examples are numerically solved and compared with analytical solutions. Eventually, the developed software is utilized to simulate the field emission from a flat metal plate and a silicon nano-tip. In the future, we will use this technique for the simulation and design of ultrafast compact x-ray sources.

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Section: Dgtd Methodsmentioning

confidence: 99%

“…To achieve a stable time marching process the time step for the update must be less than a limit. This limit is empirically set according to the criterion introduced in [33] …”

Section: Dgtd Methodsmentioning

confidence: 99%

Field-based DGTD/PIC technique for general and stable simulation of interaction between light and electron bunches

Fallahi¹,

Kärtner²

2014

J. Phys. B: At. Mol. Opt. Phys.

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“…17. For a stretching factor of 100, a higher number of load increments is required (approximately 40) compared to previous examples and a value of the Poisson's ratio near the incompressible limit is mandatory to obtain the best quality meshes. It is also worth noting that this example shows, for the first time, a subtle difference between the ILE isotropic and CIL neo-Hookean approaches.…”

Section: Mesh Around the Sd7003 Aerofoilmentioning

confidence: 99%

“…acoustics and electromagnetics) due to their low dispersion and dissipation compared to low-order methods [2,7,31,46,47,64]. In particular, the high-order discontinuous Galerkin method has become popular in this area due to its ability to propagate waves over long periods of time with a reduced computational cost compared to alternative low-order methods [13,15,38,40,42].…”

Section: Introductionmentioning

confidence: 99%

A unified approach for a posteriori high-order curved mesh generation using solid mechanics

2016

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The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh

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“…Our implementation of the RKDG method [3] for integrating MaxwellÕs equations has been described elsewhere [23]. Essentially, each field component in each cell is expanded in general polynomials of the spatial coordinates up to some defined order, and the coefficients in these expansions are taken to be time dependent.…”

mentioning

confidence: 99%

A sequence of absorbing boundary conditions for Maxwell’s equations

Hall

Kabakian

2004

Journal of Computational Physics

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Unstructured Grid-Based Discontinuous Galerkin Method for Broadband Electromagnetic Simulations

Cited by 26 publications

References 27 publications

Field-based DGTD/PIC technique for general and stable simulation of interaction between light and electron bunches

Field-based DGTD/PIC technique for general and stable simulation of interaction between light and electron bunches

A unified approach for a posteriori high-order curved mesh generation using solid mechanics

A sequence of absorbing boundary conditions for Maxwell’s equations

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