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Numerical Solution of Elliptic Differential Equations by Reduction to the Interface

Numerical Solution of Elliptic Differential Equations by Reduction to the Interface

Numerical Solution of Elliptic Differential Equations by Reduction to the
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Numerical Solution of Elliptic Differential Equations by Reduction to the Interface Paperback - 2004

by Khoromskij, Boris N.; Wittum, Gabriel

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Springer, 2004. Paperback. Very Good. Former library book; May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More, Spend Less.Dust jacket quality is not guaranteed.
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Details

  • Title Numerical Solution of Elliptic Differential Equations by Reduction to the Interface
  • Author Khoromskij, Boris N.; Wittum, Gabriel
  • Binding Paperback
  • Edition Softcover reprin
  • Condition Used - Very good
  • Pages 293
  • Volumes 1
  • Language ENG
  • Publisher Springer
  • Publication date 2004
  • Features Bibliography
  • Bookseller's Inventory # G3540204067I4N10
  • ISBN 9783540204060 / 3540204067
  • Weight 0.98 lbs (0.44 kg)
  • Dimensions 9.21 x 6.14 x 0.66 in (23.39 x 15.60 x 1.68 cm)
  • Category Mathematics
  • Library of Congress subjects Differential equations, Elliptic - Numerical
  • Library of Congress Catalogue Number 2004042926
  • Dewey Decimal Code 515.353
  • Quantity available 1

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From the publisher

During the last decade essential progress has been achieved in the analysis and implementation of multilevel/rnultigrid and domain decomposition methods to explore a variety of real world applications. An important trend in mod- ern numerical simulations is the quick improvement of computer technology that leads to the well known paradigm (see, e. g., [78,179]): high-performance computers make it indispensable to use numerical methods of almost linear complexity in the problem size N, to maintain an adequate scaling between the computing time and improved computer facilities as N increases. In the h-version of the finite element method (FEM), the multigrid iteration real- izes an O(N) solver for elliptic differential equations in a domain n c IRd d with N = O(h- ), where h is the mesh parameter. In the boundary ele- ment method (BEM), the traditional panel clustering, fast multi-pole and wavelet based methods as well as the modern hierarchical matrix techniques are known to provide the data-sparse approximations to the arising fully populated stiffness matrices with almost linear cost O(Nr log?Nr), where 1 d Nr = O(h - ) is the number of degrees of freedom associated with the boundary. The aim of this book is to introduce a wider audience to the use of a new class of efficient numerical methods of almost linear complexity for solving elliptic partial differential equations (PDEs) based on their reduction to the interface.

First line

In this chapter, the main tools of the FEM for elliptic equations will be considered.

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