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The purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell's equations involving metamaterials. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant attention from researchers across many disciplines. Thanks to enormous efforts on the part of engineers and physicists, metamaterials present great potential applications in antenna and radar design, sub-wavelength imaging, and invisibility cloak design. Hence the efficient simulation of electromagnetic phenomena in metamaterials has become a very important issue and is the subject of this book, in which various metamaterial modeling equations are introduced and justified mathematically. The development and practical implementation of edge finite element methods for metamaterial Maxwell's equations are the main focus of the book. The book finishes with some interesting simulations such as backward wave propagation and time-domain cloaking with metamaterials.
List of contents
Introduction to Metamaterials.- Introduction to Finite Element Methods.- Time-Domain Finite Element Methods for Metamaterials.- Discontinuous Galerkin Methods for Metamaterials.- Superconvergence Analysis for Metamaterials.- A Posteriori Error Estimation.- A Matlab Edge Element Code.- Perfectly Matched Layers.- Simulation of Metamaterials.- References.- Index.
Summary
The purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell’s equations involving metamaterials. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant attention from researchers across many disciplines. Thanks to enormous efforts on the part of engineers and physicists, metamaterials present great potential applications in antenna and radar design, sub-wavelength imaging, and invisibility cloak design. Hence the efficient simulation of electromagnetic phenomena in metamaterials has become a very important issue and is the subject of this book, in which various metamaterial modeling equations are introduced and justified mathematically. The development and practical implementation of edge finite element methods for metamaterial Maxwell’s equations are the main focus of the book. The book finishes with some interesting simulations such as backward wave propagation and time-domain cloaking with metamaterials.
Additional text
From the reviews:
“The book is rigorous, clearly presented, and written for researchers as well as graduate students in the fields of mathematics, computing, physics, engineering, material sciences, and optics. It helps the reader to get deeper insight and better understanding of actual mathematical and computational problems in the field of metamaterial simulations.” (Gunther Schmidt, zbMATH, Vol. 1304, 2015)
“The book is devoted to simulations of electromagnetic phenomena in metamaterials by using the finite element method (FEM). … The book is rigorous, clearly presented, and written for research mathematicians as well as graduate students in the fields of mathematics, physics, engineering, material sciences, and optics. Its pedagogical style allows the reader to get a better understanding of the mathematical analysis and metamaterial simulations.” (Barbara Zubik-Kowal, Mathematical Reviews, October, 2013)
Report
From the reviews:
"The book is rigorous, clearly presented, and written for researchers as well as graduate students in the fields of mathematics, computing, physics, engineering, material sciences, and optics. It helps the reader to get deeper insight and better understanding of actual mathematical and computational problems in the field of metamaterial simulations." (Gunther Schmidt, zbMATH, Vol. 1304, 2015)
"The book is devoted to simulations of electromagnetic phenomena in metamaterials by using the finite element method (FEM). ... The book is rigorous, clearly presented, and written for research mathematicians as well as graduate students in the fields of mathematics, physics, engineering, material sciences, and optics. Its pedagogical style allows the reader to get a better understanding of the mathematical analysis and metamaterial simulations." (Barbara Zubik-Kowal, Mathematical Reviews, October, 2013)
