H(curl) Spectral Elements: Solvers and Domain Decomposition Methods : Spectral Elements for Problems in H1 and H(Curl): Discretizations, Fast Solvers, and Domain Decomposition Preconditioners

Bernhard Hientzsch

ISBN 10: 3639173651 / ISBN 13: 9783639173659

Editore: VDM Verlag Dr. Müller, 2009

Riguardo questo articolo

nach der Bestellung gedruckt Neuware - Printed after ordering - For problems with piecewise smooth solutions, spectral element methods (SEM) hold great promise, combining the fast exponential convergence of spectral methods with the flexibility of finite elements. Once the problems are discretized with SEM, fast direct solvers are needed for the resulting systems. When the systems become too large, iterative solvers and good preconditioners are needed. Up to now, SEM have been mostly applied to elliptic problems (e.g., Poisson equations) and to fluid dynamics. This book applies SEM to problems derived from Maxwell equations, which present new issues and challenges. We derive and describe the problems, discretize them, develop several fast solvers for them, construct domain decomposition preconditioners for them, test the solvers and preconditioners on examples, and prove that the preconditioners are optimal, introducing many ideas, methods, and results along the way. The book presents an accessible introduction to SEM, domain decomposition methods, and fast solvers, applied to computational electromagnetics. It should be useful and interesting for both beginners and specialists.

Codice articolo 9783639173659

Dati bibliografici

• Titolo: H(curl) Spectral Elements: Solvers and Domain Decomposition Methods : Spectral Elements for Problems in H1 and H(Curl): Discretizations, Fast Solvers, and Domain Decomposition Preconditioners
• Editore: VDM Verlag Dr. Müller
• Data di pubblicazione: 2009
• Lingua: Inglese
• ISBN 10: 3639173651
• ISBN 13: 9783639173659
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 22 L x 15 A x 1 P centimetri 22 centimetri di larghezza per 15 centimetri di altezza per 1 centimetri di profondità
• Peso: 284 grammi

Descrizione articolo

Riassunto

For problems with piecewise smooth solutions, spectral element methods (SEM) hold great promise, combining the fast exponential convergence of spectral methods with the flexibility of finite elements. Once the problems are discretized with SEM, fast direct solvers are needed for the resulting systems. When the systems become too large, iterative solvers and good preconditioners are needed. Up to now, SEM have been mostly applied to elliptic problems (e.g., Poisson equations) and to fluid dynamics. This book applies SEM to problems derived from Maxwell equations, which present new issues and challenges. We derive and describe the problems, discretize them, develop several fast solvers for them, construct domain decomposition preconditioners for them, test the solvers and preconditioners on examples, and prove that the preconditioners are optimal, introducing many ideas, methods, and results along the way. The book presents an accessible introduction to SEM, domain decomposition methods, and fast solvers, applied to computational electromagnetics. It should be useful and interesting for both beginners and specialists.

Informazioni sull?autore

Ph.D. (Mathematics) from the Courant Institute of Mathematical Sciences at New York University, M.S. (Mathematics, Minor: Computer Science) from University of Cologne (Germany). 10 years research and application experience in spectral element methods for various applications. Presented work at talks and conferences.