The application of the \(hp\)-finite element method to electromagnetic problems
type: Item
instance of: scholarly article
title: The application of the \(hp\)-finite element method to electromagnetic problems
zbMATH Open document ID: 1195.78059
DOI: 10.1007/BF02736177
author: J. Blot
published in: Archives of Computational Methods in Engineering
publication date: 2009-07-06T00:00:00Z
review text: This is a review paper on the application of hp-finite element method to electromagnetic problems. The authors reviewed the works and the main development of finite element methods for electromagnetic scattering problems and electromagnetic eigenvalue problems. This paper addressed many issues in the numerical solution of time-harmonic scattering problems and eigenvalue problems. The main topics discussed in this paper include the following items. 1. The authors reviewed several PDE models of Maxwell's equations with different boundary conditions and weak formulations. 2. The authors reviewed the H(curl)-conforming edge element methods and their historical development. Considerable references to edge elment methods, which particularly include the works due to Whitney, Nédélec, Bossavit, Mur and De Hoop, Hiptmair, Demkowicz, Ainsworth, Ledge, and so on, are mentioned in the development of numerical Maxwell's equations. 3. The hp-edge element approximations: The paper presents the explicit forms of hierarchical basis functions of both \(H^1\)-conforming high-order nodal element spaces and H(curl)-conforming high-order edge element spaces in 2D and 3D. The main efforts are devoted to the computational aspect of finite element methods. The authors discussed the affine transformation and the covariant mappings from the reference element to physical elements, numerical integrations in implementations, and the technique of static condensation which removes in the element-level the interior unknowns of high-order elements from the global stiffness matrix. 4. Computation of time-harmonic scattering problems: The authors reviewed the recent works on deriving the discrete dispersion relationship and on reducing the dispersion by hp-finite element methods and modified finite element methods. Moreover, a brief review of the application of the perfectly matched layer method to electromagnetic scattering problems is presented for the computation of the far-field pattern. The ``goa…
Mathematics Subject Classification ID: 78M10
zbMATH DE Number: 5575518
Wikidata QID: Q113327886
describes a project that uses: TRIFOU
MaRDI profile type: Publication
cites work: Q5558293
cites work: Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number
cites work: Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
cites work: Dispersive properties of high–order Nédélec/edge element approximation of the time–harmonic Maxwell equations
cites work: Computation of Maxwell eigenvalues on curvilinear domains using hp-version Nédélec elements
cites work: Hierachic \(hp\)-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes
cites work: Conditioning of Hierarchic p-Version Nédélec Elements on Meshes of Curvilinear Quadrilaterals and Hexahedra
cites work: Hierarchic finite element bases on unstructured tetrahedral meshes
cites work: A posteriori error estimation in finite element analysis
cites work: hp-Approximation Theory forBDFMandRTFinite Elements on Quadrilaterals
cites work: Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers
cites work: A comparison of solvers for large eigenvalue problems occuring in the design of resonant cavities
cites work: Multigrid in H(div) and H(curl)
cites work: Approximation properties of the \(h\)-\(p\) version of the finite element method
cites work: A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
cites work: Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
cites work: Radiation boundary conditions for wave-like equations
cites work: A perfectly matched layer for the absorption of electromagnetic waves
cites work: A numerical integration scheme for special finite elements for the Helmholtz equation
cites work: A note on the de Rham complex and a discrete compactness property
cites work: DISCRETE COMPACTNESS FOR p AND hp 2D EDGE FINITE ELEMENTS
cites work: Computational Models of Electromagnetic Resonators: Analysis of Edge Element Approximation
cites work: Q4235028
cites work: A two-dimensional infinite element for Maxwell's equations
cites work: Q4378197
cites work: Q2761234
cites work: Weighted regularization of Maxwell equations in polyhedral domains. A rehabilitation of Nodal finite elements
cites work: Q4462353
cites work: Evidence of exponential convergence in the computation of Maxwell eigenvalues
cites work: An \(hp\)-adaptive finite element method for electromagnetics. I: Data structure and constrained approximation
cites work: Q4450074
cites work: Maxwell eigenvalues and discrete compactness in two dimensions
cites work: de Rham diagram for \(hp\) finite element spaces
cites work: Recent progress on application of hp‐adaptive BE/FE methods to elastic scattering
cites work: Modeling of electromagnetic absorption/scattering problems using \(hp\)-adaptive finite elements
cites work: Q4951622
cites work: Q4024095
cites work: Whitney elements on pyramids
cites work: Parallel multigrid 3D Maxwell solvers
cites work: High–order nodal discontinuous Galerkin methods for the Maxwell eigenvalue problem
cites work: Nodal high-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations
cites work: Q4659231
cites work: Coupling of Finite Elements and Boundary Elements in Electromagnetic Scattering
cites work: Multigrid Method for Maxwell's Equations
cites work: Finite elements in computational electromagnetism
cites work: Computation of resonant modes for axisymmetric Maxwell cavities usinghp-version edge finite elements
cites work: Interior penalty method for the indefinite time-harmonic Maxwell equations
cites work: Q4844981
cites work: Q4490850
cites work: Mixed and penalty formulations for finite element analysis of an eigenvalue problem in electromagnetism
cites work: Solution of Maxwell equation in axisymmetric geometry by Fourier series decomposition and by use of \(H\)(rot) conforming finite element
cites work: SHORT WAVE MODELLING USING SPECIAL FINITE ELEMENTS
cites work: Modelling of short wave diffraction problems using approximating systems of plane waves
cites work: Arbitrary order edge elements for electromagnetic scattering simulations using hybrid meshes and a PML
cites work: Frequency and time domain electromagnetic scattering simulations employing higher order edge elements
cites work: Plane wave \(\mathcal H(\text{curl};\Omega)\) conforming finite elements for Maxwell's equations
cites work: ROBUST NUMERICAL METHODS FOR TRANSONIC FLOWS
cites work: Parameterised electromagnetic scattering solutions for a range of incident wave angles
cites work: A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem
cites work: Phase-accuracy comparisons and improved far-field estimates for 3-D edge elements on tetrahedral meshes
cites work: THE NEAR FIELD TO FAR FIELD TRANSFORMATION
cites work: Finite Element Methods for Maxwell's Equations
cites work: A Dispersion Analysis of Finite Element Methods for Maxwell’s Equations
cites work: Q4845226
cites work: The Adaptive Computation of Far-Field Patterns by A Posteriori Error Estimation of Linear Functionals
cites work: Parallel processing for the simulation of problems involving scattering of electromagnetic waves

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: The simulation of electromagnetic scattering in piecewise homogeneous media using unstructured grids

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: An unstructured grid algorithm for the solution of Maxwell's equations in the time domain

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: A time domain unstructured grid approach to the simulation of electromagnetic scattering in piecewise homogeneous media

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Mixed finite elements in \(\mathbb{R}^3\)

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: A new family of mixed finite elements in \({\mathbb{R}}^ 3\)

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems: The Helmholtz and Burgers equations

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Adaptive remeshing for compressible flow computations

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: An hp‐adaptive finite element method for electromagnetics—part II: A 3D implementation

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: An hp‐adaptive finite element method for scattering problems in computational electromagnetics

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Q4383843

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: A posteriori finite element error bounds for non-linear outputs of the Helmholtz equation

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Q3714651

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Q4426013

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Q5535928

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Q4000182

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: \(hp\)-adaptive finite elements in electromagnetics

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Q4509258

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Q4952288

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: An investigation of numerical dispersion in the vector finite element method using quadrilateral elements

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Efficient three‐dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Q3253193

The application of the \(hp\)-finite element method to electromagnetic problems (cites work)
cites work: Q3875490

The application of the \(hp\)-finite element method to electromagnetic problems (full work available at URL)
full work available at URL: https://doi.org/10.1007/bf02736177

The application of the \(hp\)-finite element method to electromagnetic problems (OpenAlex ID)
OpenAlex ID: W2026125788