Vector finite elements for electromagnetic field computation

Cendes, Z.J.

doi:10.1109/20.104970

Cited by 133 publications

(47 citation statements)

References 24 publications

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“…The discretization of the boundary-integral operators also uses Galerkin's variant of the method of moments, except that the unknown surface currents are expanded in vector edge-elements that are defined on a surface mesh [13][14]. These elements preserve continuity of normal components of the currents across edges of the mesh, thereby guaranteeing that the unknown currents belong to H(div), the space of square-integrable functions, whose divergences are also square-integrable.…”

Section: Discretization Of the Boundary-integral Operatorsmentioning

confidence: 99%

Boundary-Integral Equations in Eddy-Current Calculations

Murphy

Sabbagh

1995

Review of Progress in Quantitative Nondestructive Evaluation

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Volume-integral equations have proven to be very successful in the computation of eddy-current probe-flaw responses for NDE problems having a number of simple geometries. This approach to NDE computations has proven superior to the finite-element approach in both accuracy and computer resources required, and is the basis of our proprietary code VIC-3Dl. The volume-integral approach, however, is not as well adapted to accommodating the complex geometries sometimes required in practical applications. An example is the separation of edge and corner effects from the response of a flaw. We will discuss an extension of the volume-integral approach that incorporates boundary-integral equations to provide a description of complicated surface geometries. BACKGROUND

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Section: Discretization Of the Boundary-integral Operatorsmentioning

confidence: 99%

Boundary-Integral Equations in Eddy-Current Calculations

Murphy

Sabbagh

1995

Review of Progress in Quantitative Nondestructive Evaluation

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“…33 [43,44] . To define the 14 element functions, we use simplex (or barycentric) coordinates, defined over the triangular element via the affine transformation [45,46],…”

Section: Vector Basis Functions For M=1 Modesmentioning

confidence: 99%

Ultra-Low Threshold Vertical-Cavity Surface-Emitting Lasers for USAF Applications

Nelson¹

2005

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information SPONSORING/MONITORING AGENCY REPORT NUMBER(S) AFRL-SN-WP-TR-2005-1039 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTESReport contains color. ABSTRACTThis report summarizes research on the development of ultra-low threshold vertical-cavity surface-emitting lasers. AbstractThis report summarizes research on the development of ultra-low threshold vertical-cavity surface-emitting lasers.

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“…modes that are not solenoidal. This was first analyzed by Bossavit [35] and Cendes [36], and was historically the primary impetus for using edge-based H(curl) -conforming basis functions in electromagnetics.…”

Section: Frequency Domain Resonant Cavitymentioning

confidence: 99%

Development and Application of Compatible Discretizations of Maxwell’s Equations

White

Koning

Rieben

Compatible Spatial Discretizations

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Abstract.We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we have designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve .

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Vector finite elements for electromagnetic field computation

Cited by 133 publications

References 24 publications

Boundary-Integral Equations in Eddy-Current Calculations

Boundary-Integral Equations in Eddy-Current Calculations

Ultra-Low Threshold Vertical-Cavity Surface-Emitting Lasers for USAF Applications

Development and Application of Compatible Discretizations of Maxwell’s Equations

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