Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell’s equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism, there has also been considerable progress in the mathematical understanding of the properties of Maxwell’s equations relevant to numerical analysis. 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 is 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 analysis involves a complete justification of the discrete de Rham diagram and discrete compactness of edge elements. The numerical methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book ends with a short introduction to inverse problems in electromagnetism.
%0 Book
%1 monk2008finite
%A Monk, Peter
%C Oxford
%D 2008
%I Clarendon
%K 35q60-pdes-in-connection-with-optics-and-electromagnetic-theory 65z05-applications-of-numerical-analysis-to-physics 78-01-optics-electromagnetic-theory-instructional-exposition 78a25-electromagnetic-theory-general 78a45-diffraction-scattering 78a46-inverse-problems-in-optics-and-electromagnetic-theory 78m10-optics-electromagnetism-finite-element-method
%R 10.1093/acprof:oso/9780198508885.001.0001
%T Finite element methods for Maxwell's equations
%U https://oxford.universitypressscholarship.com/view/10.1093/acprof:oso/9780198508885.001.0001/acprof-9780198508885
%X Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell’s equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism, there has also been considerable progress in the mathematical understanding of the properties of Maxwell’s equations relevant to numerical analysis. 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 is 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 analysis involves a complete justification of the discrete de Rham diagram and discrete compactness of edge elements. The numerical methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book ends with a short introduction to inverse problems in electromagnetism.
%@ 9780198508885 0198508883
@book{monk2008finite,
abstract = {Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell’s equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism, there has also been considerable progress in the mathematical understanding of the properties of Maxwell’s equations relevant to numerical analysis. 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 is 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 analysis involves a complete justification of the discrete de Rham diagram and discrete compactness of edge elements. The numerical methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book ends with a short introduction to inverse problems in electromagnetism.},
added-at = {2022-02-17T06:47:19.000+0100},
address = {Oxford},
author = {Monk, Peter},
biburl = {https://www.bibsonomy.org/bibtex/2272c62cd8f66b88731513236623c826d/gdmcbain},
doi = {10.1093/acprof:oso/9780198508885.001.0001},
interhash = {61f0c4cc9beae2532f9519b2d091b107},
intrahash = {272c62cd8f66b88731513236623c826d},
isbn = {9780198508885 0198508883},
keywords = {35q60-pdes-in-connection-with-optics-and-electromagnetic-theory 65z05-applications-of-numerical-analysis-to-physics 78-01-optics-electromagnetic-theory-instructional-exposition 78a25-electromagnetic-theory-general 78a45-diffraction-scattering 78a46-inverse-problems-in-optics-and-electromagnetic-theory 78m10-optics-electromagnetism-finite-element-method},
publisher = {Clarendon},
refid = {909930886},
timestamp = {2022-02-17T06:48:59.000+0100},
title = {Finite element methods for Maxwell's equations},
url = {https://oxford.universitypressscholarship.com/view/10.1093/acprof:oso/9780198508885.001.0001/acprof-9780198508885},
year = 2008
}