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- catalog abstract ""The aim of this book is to provide an up-to-date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis in on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book. The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism."--Jacket.".
- catalog contributor b12906335.
- catalog created "2003.".
- catalog date "2003".
- catalog date "2003.".
- catalog dateCopyrighted "2003.".
- catalog description ""The aim of this book is to provide an up-to-date and sound theoretical foundation for finite element methods in computational electromagnetism.".
- catalog description "Includes bibliographical references (p. 428-445) and index.".
- catalog description "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.".
- catalog description "The emphasis in on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book.".
- catalog description "The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism."--Jacket.".
- catalog extent "xiv, 450 p. :".
- catalog identifier "0198508883".
- catalog isPartOf "Numerical mathematics and scientific computation".
- catalog isPartOf "Oxford science publications".
- catalog issued "2003".
- catalog issued "2003.".
- catalog language "eng".
- catalog publisher "Oxford : Clarendon Press ; New York : Oxford University Press,".
- catalog subject "621.30151535 21".
- catalog subject "Electromagnetism Mathematical models.".
- catalog subject "Finite element method.".
- catalog subject "Maxwell equations.".
- catalog subject "QC760 .M56 2003".
- catalog tableOfContents "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.".
- catalog title "Finite element methods for Maxwell's equations / Peter Monk.".
- catalog type "text".