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.

The International Symposium on Computational & Applied PDEs was held at Zhangjiajie National Park of China from July 1-7, 2001. The main goal of this conference is to bring together computational, applied and pure mathematicians on different aspects of partial differential equations to exchange ideas and to promote collaboration. Indeed, it attracted a number of leading scientists in computational PDEs including Doug Arnold (Minnesota), Jim Bramble (Texas A & M), Achi Brandt (Weizmann), Franco Brezzi (Pavia), Tony Chan (UCLA), Shiyi Chen (John Hopkins), Qun Lin (Chinese Academy of Sciences), Mitch Luskin (Minnesota), Tom Manteuffel (Colorado), Peter Markowich (Vienna), Mary Wheeler (Texas Austin) and Jinchao Xu (Penn State); in applied and theoretical PDEs including Weinan E (Princeton), Shi Jin (Wisconsin), Daqian Li (Fudan) and Gang Tian (MIT). It also drew an international audience of size 100 from Austria, China, Germany, Hong Kong, Iseael, Italy, Singapore and the United States. The conference was organized by Yunqing Huang of Xiangtan University, Jinchao Xu of Penn State University, and Tony Chan of UCLA through ICAM (Institute for Computational and Applied Mathematics) of Xiangtan university which was founded in January 1997 and directed by Jinchao Xu. The scientific committee of this conference consisted of Randy Bank of UCSD, Tony Chan of UCLA, K. C.

These are the proceedings of the 19th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic equations that arise in various problems in mathematics, computational science, engineering and industry. They are designed for massively parallel computers and take the memory hierarchy of such systems into account. This is essential for approaching peak floating point performance. There is an increasingly well-developed theory which is having a direct impact on the development and improvement of these algorithms.

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.

These are the proceedings of the 19th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic equations that arise in various problems in mathematics, computational science, engineering and industry. They are designed for massively parallel computers and take the memory hierarchy of such systems into account. This is essential for approaching peak floating point performance. There is an increasingly well-developed theory which is having a direct impact on the development and improvement of these algorithms.

The International Symposium on Computational & Applied PDEs was held at Zhangjiajie National Park of China from July 1-7, 2001. The main goal of this conference is to bring together computational, applied and pure mathematicians on different aspects of partial differential equations to exchange ideas and to promote collaboration. Indeed, it attracted a number of leading scientists in computational PDEs including Doug Arnold (Minnesota), Jim Bramble (Texas A & M), Achi Brandt (Weizmann), Franco Brezzi (Pavia), Tony Chan (UCLA), Shiyi Chen (John Hopkins), Qun Lin (Chinese Academy of Sciences), Mitch Luskin (Minnesota), Tom Manteuffel (Colorado), Peter Markowich (Vienna), Mary Wheeler (Texas Austin) and Jinchao Xu (Penn State); in applied and theoretical PDEs including Weinan E (Princeton), Shi Jin (Wisconsin), Daqian Li (Fudan) and Gang Tian (MIT). It also drew an international audience of size 100 from Austria, China, Germany, Hong Kong, Iseael, Italy, Singapore and the United States. The conference was organized by Yunqing Huang of Xiangtan University, Jinchao Xu of Penn State University, and Tony Chan of UCLA through ICAM (Institute for Computational and Applied Mathematics) of Xiangtan university which was founded in January 1997 and directed by Jinchao Xu. The scientific committee of this conference consisted of Randy Bank of UCSD, Tony Chan of UCLA, K. C.