Higher Order Numerical Solution Techniques in Electromagnetics

Graglia,; Peterson, Gilbert L.

doi:10.1049/sbew507e

Cited by 11 publications

(50 citation statements)

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“…The vector r denotes a point in the child space. In turn, the cells are parametrized by four dummy parent-variables {ξ β , ξ β±1 , ξ β+2 } whose subscripts are counted modulo 4, with [1]…”

Section: Parent Variables and Singular Functions On Tip Cellsmentioning

confidence: 99%

“…The electromagnetic modeling of complex three dimensional structures requires numerical techniques. In recent years, higher order representations have been developed to improve accuracy and efficiency of these approaches [1]. Higher order representations on smooth parts of an object can be effective, but the presence of wedges, sharp edges and tips can negate the improvement in efficiency due to the unbounded nature of current and charge densities in these locations.…”

Section: Introductionmentioning

confidence: 99%

“…Higher order representations on smooth parts of an object can be effective, but the presence of wedges, sharp edges and tips can negate the improvement in efficiency due to the unbounded nature of current and charge densities in these locations. Several types of special basis functions have been developed for the purpose of representing singular currents and charge densities near edges [1], [2], [3]. To date, less attention has been directed at the effect of tips [4], such as the tips of a square conducting plate [5].…”

Section: Introductionmentioning

confidence: 99%

“…The exponents in (1)(2)(3) are the sum of an integer m (even or odd) that depends on the outer summation index n plus an irrational number (indicated by the Greek letter ν o,q or ν e,q ) that depends on the inner summation index q. These exponents do not depend on the frequency and grow slowly with q and more rapidly with n [4].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Hierarchical Divergence Conforming Bases for Tip Singularities in Quadrilateral Cells

Graglia

Peterson

Petrini

2020

IEEE Trans. Antennas Propagat.

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Electromagnetic scattering from targets such as thin conducting plates induce singular currents and charges at sharp edges and sharp tips. In this paper, a hierarchical family of divergence-conforming singular basis functions are presented for modeling the singularities associated with current and charge density at tips. These new basis functions are used to increment existing edge-singular bases so that on cells that contain a singular tip where two singular edges join together, the final base combines a hierarchical polynomial representation with linearly independent singular terms that incorporate general exponents that may be adjusted for the specific wedge angle of interest and for the specific angle at the tip. Several variations on the tip functions are proposed.

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Section: Parent Variables and Singular Functions On Tip Cellsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hierarchical Divergence Conforming Bases for Tip Singularities in Quadrilateral Cells

Graglia

Peterson

Petrini

2020

IEEE Trans. Antennas Propagat.

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“…As a result, considerable research effort has been invested in understanding the nuances and ramifications of discretizing these equations. This includes various efforts to understand low frequency breakdown [6]- [8], develop well conditioned formulations [9], introduce higher order basis sets [10] and investigate accuracy and convergence [11], develop hierarchical basis [12], and so on. However, by and large, the problem has remained the same: how does one develop integral formulations that are well behaved across frequencies of interest especially when high discretization density is required to capture geometric features.…”

Section: Introductionmentioning

confidence: 99%

Generalized Debye Sources-Based EFIE Solver on Subdivision Surfaces

Jiang

et al. 2017

IEEE Trans. Antennas Propagat.

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Abstract-The electric field integral equation is a well known workhorse for obtaining fields scattered by a perfect electric conducting (PEC) object. As a result, the nuances and challenges of solving this equation have been examined for a while. Two recent papers motivate the effort presented in this paper. Unlike traditional work that uses equivalent currents defined on surfaces, recent research proposes a technique that results in well conditioned systems by employing generalized Debye sources (GDS) as unknowns. In a complementary effort, some of us developed a method that exploits the same representation for both the geometry (subdivision surface representations) and functions defined on the geometry, also known as isogeometric analysis (IGA). The challenge in generalizing GDS method to a discretized geometry is the complexity of the intermediate operators. However, thanks to our earlier work on subdivision surfaces, the additional smoothness of geometric representation permits discretizing these intermediate operations. In this paper, we employ both ideas to present a well conditioned GDS-EFIE. Here, the intermediate surface Laplacian is well discretized by using subdivision basis. Likewise, using subdivision basis to represent the sources, results in an efficient and accurate IGA framework. Numerous results are presented to demonstrate the efficacy of the approach.

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Assessing Curl-Conforming Bases for Pyramid Cells

Graglia,

Petrini

2024

IEEE J. Multiscale Multiphys. Comput. Tech.

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Successful three-dimensional finite element codes for Maxwell's equations must include and deal with all four types of geometrical shapes: tetrahedra, bricks, prisms, and quadrangular-based pyramids. However, pyramidal elements have so far been used very rarely because the basis functions associated with them have complicated expression, are complex in derivation, and have never been comprehensively validated. We recently published a simpler procedure for constructing higher-order vector bases for pyramid elements, so here we fill a gap by discussing a whole set of test case results that not only validate our new curl-conforming bases for pyramids, but which enable validation of other codes that use pyramidal elements for finite element method applications. The solutions of the various test cases are obtained using either higher order elements or multipyramidal meshes or both. Furthermore, the results are always compared with the solutions obtained with classical tetrahedral meshes using higher order bases. This allows us to verify that purely pyramidal meshes and elements give numerical results of comparable accuracy to those obtained with multitetrahedral meshes that use elements of the same order, essentially requiring the same number of degrees of freedom. The various results provided here also show that higher order vector bases always guarantee a superior convergence of the numerical results as the number of degrees of freedom increases.

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Higher Order Numerical Solution Techniques in Electromagnetics

Cited by 11 publications

References 0 publications

Hierarchical Divergence Conforming Bases for Tip Singularities in Quadrilateral Cells

Hierarchical Divergence Conforming Bases for Tip Singularities in Quadrilateral Cells

Generalized Debye Sources-Based EFIE Solver on Subdivision Surfaces

Assessing Curl-Conforming Bases for Pyramid Cells

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