Tailoring unstructured meshes for use with a 3D time domain co‐volume algorithm for computational electromagnetics

Xie, Zhong Qiu; Hassan, O.; Morgan, K.

doi:10.1002/nme.2970

Cited by 13 publications

(38 citation statements)

References 27 publications

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“…In fact, the Voronoï grid can always be of quite low quality with Voronoï edge sizes being close to zero. Several methods exist for generating grids with high Voronoï cell qualities (see, for example, Du and Wang, 2006;Xie et al, 2011). However, these methods are either not automatic or they do not support the local refinement that we need in our application.…”

Section: Mesh Generation Considerationsmentioning

confidence: 98%

“…FV schemes based on these grids possess the simplicity of Yee's scheme. The use of these grids has been presented in the electric engineering literature for the solution of Maxwell's equations in the time domain (Hermeline, 1993;Sazonov et al, 2006;Xie et al, 2011). In this scheme, the magnetic field remains divergence free, the method is nondissipative, and it has been shown to be first-order convergent (Nicolaides and Wang, 1998;Hermeline et al, 2008).…”

Section: Introductionmentioning

confidence: 96%

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A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids

2014

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The application of unstructured grids can improve the solution of total field electromagnetic problems because these grids allow efficient local refinement of the mesh at the locations of high field gradients. Unstructured grids also provide the flexibility required for representing arbitrary topography and subsurface interfaces. We investigated the generalization of the standard Yee's staggered scheme to unstructured tetrahedral-Voronoï grids using a finite-volume approach. We discretized the Helmholtz equation for the electric field in the frequency domain and solved the problem to find the projection of the total electric field along the edges of the tetrahedral elements. To compute the electric and magnetic fields at the observation points, an interpolation technique was employed, which uses the edge vector interpolation functions of the tetrahedral elements. To verify the presented scheme, two examples were evaluated, which revealed the computation of the total and secondary fields due to electric and magnetic sources in half-spaces that contain anomalous bodies. The results had good agreement with those from the literature. For the second example, accuracy studies were conducted to better understand the relative importance of different refinements in the grid and also the effect of the general quality of the grid. The results revealed the utmost importance of the quality of the tetrahedral grid and refinement at the observation locations. To validate the versatility of the approach, we synthesized helicopter-borne data for a model of the Ovoid ore body at Voisey's Bay, Labrador, Canada, which had good agreement with real data.

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Section: Mesh Generation Considerationsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 96%

A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids

2014

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“…This allows us to use unstructured meshes and to model electromagnetic scattering, even for objects of arbitrary shape. Full details of the mesh generating process that is employed, to ensure Delaunay and Voronoi meshes with the correct properties, may be found elsewhere [8][9][10]. Here, the additional challenge that is faced, is that we have no direct access to the full field vectors B, H D and E at a given location.…”

Section: Discrete Equationsmentioning

confidence: 99%

“…The integral form of Maxwell's equations is employed [8]. For a three dimensional lossy dielectric medium, Ampère's and Faraday's Laws are expressed, in a scattered field form, as…”

Section: Problem Formulationmentioning

confidence: 99%

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EM modelling of arbitrary shaped anisotropic dielectric objects using an efficient 3D leapfrog scheme on unstructured meshes

et al. 2016

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The standard Yee algorithm is widely used in computational electromagnetics because of its simplicity and divergence free nature. A generalization of the classical Yee scheme to 3D unstructured meshes is adopted, based on the use of a Delaunay primal mesh and its high quality Voronoi dual. This allows the problem of accuracy losses, which are normally associated with the use of the standard Yee scheme and a staircased representation of curved material interfaces, to be circumvented. The 3D dual mesh leapfrog-scheme which is presented has the ability to model both electric and magnetic anisotropic lossy materials. This approach enables the modelling of problems, of current practical interest, involving structured composites and metamaterials.

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Delaunay–Voronoi surface integration: a full‐wave electromagnetics discretization for electronic device simulation

Miller

Albrecht

Grupen³

2016

Int J Numerical Modelling

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A promising time domain electromagnetics numerical method for treating the highly nonlinear problem of charge transport in electronic devices called Delaunay-Voronoi surface integration is presented. This method couples the rotational electric and magnetic fields governed by Ampere's and Faraday's laws with the electrostatic potential dictated by Poisson's equation in a simultaneous solution. Discretization of the governing equations using dual meshes and the relevant boundary conditions are presented. The engineering application details specific to electronic device simulation are treated, and an example calculation is shown to compare with an analytical solution for propagation in a waveguide. Benchmark results are presented for the rotational equations, Poisson's equation, and the complete set of electromagnetic equations. the computational domain, and electric and magnetic fields are computed through scalar and vector potentials. An IE is most often derived from Maxwell's equations using the Green's function approach [2]. The crux of the approach is deriving a Green's function that satisfies the linear Helmholtz equation subject to point sources. IEs are then built upon the principle of linear superposition. Although this method is a staple of antenna design and other radiation (free-space) applications, the Green's function method cannot be applied when the point source is inherently nonlinear and is very limited when the dielectric medium is inhomogeneous. Other methods for deriving IEs from Maxwell's equations may produce viable options for coupling to electronic transport, but they are unknown to the authors. For a more detailed discussion of IEs, please see [2] and the references therein. Time-domain differential equation methods are much better suited for representing and solving full-wave EM phenomena in electronic devices. Unlike IE methods, DE methods seek EM solutions directly from Maxwell's equations in differential form. The two most common TD-DE categories can be classified as unstructured and structured grid methods. Even though these two methods are both DE solvers, they differ greatly in their computational approach and sophistication. Unstructured grid (mesh) methods first decompose the computational domain into a collection of elements that are typically tetrahedra. The governing equations are then written in a form suitable for discretization. This amounts to writing Maxwell's equations in curl-curl form for the well-known finite element method TD [2] or adding flux terms to Maxwell's equations for the discontinuous Galerkin TD (DGTD) method [3]. Both of these methods seek a variational solution by approximating the quantities of interest with collections of basis functions, which are carefully tailored to satisfy the governing equations and boundary conditions (BCs), for example, vector finite elements. When coupling these discretization methods to charge transport, it is not clear to the authors how to construct a basis set that approximates an equation with exponentially nonlinear depend...

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Tailoring unstructured meshes for use with a 3D time domain co‐volume algorithm for computational electromagnetics

Cited by 13 publications

References 27 publications

A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids

A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids

EM modelling of arbitrary shaped anisotropic dielectric objects using an efficient 3D leapfrog scheme on unstructured meshes

Delaunay–Voronoi surface integration: a full‐wave electromagnetics discretization for electronic device simulation

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