A high order hybrid finite element method applied to the solution of electromagnetic wave scattering problems in the time domain

Davies, Richard Wyn; Morgan, K.; Hassan, O.

doi:10.1007/s00466-009-0377-4

Cited by 32 publications

(26 citation statements)

References 37 publications

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“…This principle is applicable throughout a variety of fields, notably in static stress analysis when modelling stress concentrations, e.g. Davies et al [9] implement a hybrid mesh technique -uniform for the background medium and conforming for the complex geometry of the scatterer -in an attempt to benefit from the advantages of each. Similarly in the field of ocean modelling, Rao [7] concludes that a conforming mesh FE model is an improvement over FD (which is limited to a uniform mesh) for its ability to model the detailed shoreline accurately while retaining a sparse mesh for the open sea.…”

Section: Meshingmentioning

confidence: 99%

On the Convergence of Finite Element Scattering Simulations

Huthwaite¹,

Simonetti²,

Lowe³

et al. 2010

AIP Conference Proceedings

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The ability to produce accurate scattering data for imaging is important in the field of NDT for both the development of new algorithms and iterative methods which improve the scatterer reconstruction by trial and error. Error analysis for FE simulations is typically performed for plane wave propagation in a homogeneous space. In this paper it is demonstrated that the mesh refinement must be significantly improved to achieve the same accuracy for scattering problems. A study of meshing techniques suggests that a uniform mesh is necessary to obtain a suitable dynamic range.

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Section: Meshingmentioning

confidence: 99%

On the Convergence of Finite Element Scattering Simulations

Huthwaite¹,

Simonetti²,

Lowe³

et al. 2010

AIP Conference Proceedings

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“…in the DG method [11,23,24,29,31,35,43] and in the finite element method [5,8,16,20,26,27]. This paper exploits the version the discontinuous Galerkin method where the continuity and boundary conditions are enforced by the finite difference rule.…”

Section: Introductionmentioning

confidence: 99%

Very high order discontinuous Galerkin method in elliptic problems

Jaśkowiec

2017

Comput Mech

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The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

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“…The discussion above begs the question as to whether one could formulate a hybrid CDG technique that exploits the advantages of both formulations. In [38] a hybrid method is formulated in 2-D. For it, the CG formalism is applied in a large structured region formed of squares, coupled to a DG scheme applied to another region consisting on an unstructured mesh of triangles. The use of a continuous formalism in the large region thus requires the solution of a large global system of equations that reduces the performance of such an approach, especially for large problems.…”

Section: Cgtd Versus Dgtd: the Cdgtd Methodsmentioning

confidence: 99%

“…The proposed method is aimed at taking advantage of a reduced number of DOF and smaller spectral radius in CG while benefiting from the spurious-free and block-diagonal properties of DG. Previous attempts exist [38], employing a two-dimensional (2-D) multi-element hybrid continuous-discontinuous scheme: CG in a structured grid of square elements, and DG in a unstructured triangular grid. In our approach, rather than applying a CG formalism over large regions, we apply it only on small clusters of elements, thus maintaining the easily invertible block-diagonal nature of the global system of linear equations.…”

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confidence: 99%

A Nodal Continuous-Discontinuous Galerkin Time-Domain Method for Maxwell's Equations

Angulo

Alvarez

Teixeira

et al. 2015

IEEE Trans. Microwave Theory Techn.

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A new nodal hybrid continuous-discontinuous Galerkin time-domain (CDGTD) method for the solution of Maxwell's curl equations is proposed and analyzed. This hybridization is made by clustering small collections of elements with a continuous Galerkin (CG) formalism. These clusters exchange information with their exterior through a discontinuous Galerkin (DG) numerical flux. This scheme shows reduced numerical dispersion error with respect to classical DG formulations for certain orders and numbers of clustered elements. The spectral radius of the clustered semi-discretized operator is smaller than its DG counterpart allowing for larger time steps in explicit time integrators. Additionally, the continuity across the element boundaries allows us a reduction of the number of degrees of freedom of up to about 80% for a low-order three-dimensional implementation. Index Terms-Continuous-discontinuous Galerkin time-domain (CDGTD), continuous Galerkin (CG) method, discontinuous Galerkin (DG) method, discontinuous Galerkin time-domain (DGTD), Maxwell's equations.

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A high order hybrid finite element method applied to the solution of electromagnetic wave scattering problems in the time domain

Cited by 32 publications

References 37 publications

On the Convergence of Finite Element Scattering Simulations

On the Convergence of Finite Element Scattering Simulations

Very high order discontinuous Galerkin method in elliptic problems

A Nodal Continuous-Discontinuous Galerkin Time-Domain Method for Maxwell's Equations

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