Finite element methods for Maxwell's equations

Finite element methods for Maxwell's equations / Peter Monk.

This reference provides an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains.

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Bibliographic Details
Main Author: Monk, Peter, 1956- (Author)
Format: eBook
Language:English
Published: Oxford ; New York : Clarendon Press, 2003.
Series:Numerical mathematics and scientific computation.
Subjects:
Electromagnetism > Mathematical models.
Finite element method.
Maxwell equations.
TECHNOLOGY & ENGINEERING > Electrical.
Electromagnetism > Mathematical models
Finite element method
Maxwell equations
Eletromagnetismo.
Método dos elementos finitos (aplicações)
Online Access:Click for online access
Table of Contents:
  • Mathematical models of electromagnetism
  • Maxwell's equations
  • Constitutive equations for linear media
  • Interface and boundary conditions
  • Scattering problems and the radiation condition
  • Boundary value problems
  • Time-harmonic problem in a cavity
  • Cavity resonator
  • Scattering from a bounded object
  • Scattering from a buried object
  • Functional analysis and abstract error estimates
  • Basic functional analysis and the Fredholm alternative
  • Hilbert space
  • Linear operators and duality
  • Variational problems
  • Compactness and the Fredholm alternative
  • Hilbert-Schmidt theory of eigenvalues
  • Abstract finite element convergence theory
  • Cea's lemma
  • Discrete mixed problems
  • Convergence of collectively compact operators
  • Eigenvalue estimates
  • Sobolev spaces, vector function spaces and regularity
  • Standard Sobolev spaces
  • Trace spaces
  • Regularity results for elliptic equations
  • Differential operators on a surface
  • Vector functions with well-defined curl or divergence
  • Integral identities
  • Properties of H(div; [Omega])
  • Properties of H(curl; [Omega])
  • Scalar and vector potentials
  • The Helmholtz decomposition
  • A function space for the impedance problem
  • Curl or divergence conserving transformations
  • Variational theory for the cavity problem
  • Assumptions on the coefficients and data
  • The space X and the nullspace of the curl
  • Helmholtz decomposition
  • Compactness properties of X[subscript 0]
  • The variational problem as an operator equation
  • Uniqueness of the solution.

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