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Multigrid Methods: Axiomatic Convergence Theory for Linear and Weakly Nonlinear Problems by Abner J. Salgado, Steven M. Wise, Calvin Wong

Multigrid Methods: Axiomatic Convergence Theory for Linear and Weakly Nonlinear Problems

by Abner J. Salgado , Steven M. Wise , Calvin Wong
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Book cover type: Paperback
  • ISBN13: 9783111354194
  • Binding: Paperback
  • Subject: N/A
  • Publisher: de Gruyter
  • Publisher Imprint: de Gruyter
  • Publication Date:
  • Pages: 486
  • Original Price: USD 93.99
  • Language: English
  • Edition: N/A
  • Item Weight: 772 grams
  • BISAC Subject(s): Differential Equations / Partial

This book introduces the theory of multigrid methods for the fast numerical solution of linear and weakly nonlinear elliptic PDE. We use the finite element method to discretize the PDE problems, as this is the most natural choice, and the reader will get a thorough treatment of finite elements. No previous exposure to numerical discretization methods is assumed. All that is required of the reader is some knowledge of matrix theory. Coding the multigrid method is difficult. This book will help the reader build basic multigrid codes using easy-to-read sample Matlab codes. We use a matrix-based approach in the first part of the book, both as a way of presenting the theory in a natural way, and as a means for translating the theory into practical codes. The operators in the text and codes have the same names, which makes reading the sample codes simple, even if the reader has never coded. We deviate from the matrix-based approach only in the presentation of the nonlinear theory in the second part, which represents an area of current research. The book takes the reader from the basics and simple implementation issues all the way to the front lines of research.

Abner J. Salgado is a professor of mathematics at the University of Tennessee, Knoxville. His main area of research is the numerical analysis of nonlinear partial differential equations, and related questions. He has authored more that 60 publications and is the co-author of the graduate-level textbook "Classical Numerical Analysis," published by Cambridge University Press.

Steven Wise is a professor of mathematics at the University of Tennessee, Knoxville. He conducts research in the areas of partial differential equations, numerical analysis, and scientific computing, with applications in problems from thermodynamics, fluid mechanics, biophysics, and materials science. He is the author of over 120 journal articles and two books, including a graduate-level numerical analysis textbook with Abner Salgado.

Calvin (Ming Hei) Wong is a Ph.D. candidate in mathematics at the University of Tennessee, Knoxville. His ongoing research is focusing on Diffuse Domain Methods and machine-learning approaches in computational applied math.

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