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Numerical Solution of Elliptic Differential Equations by Reduction to the Interface Softcover Repri Edition
Contributor(s): Khoromskij, Boris N. (Author), Wittum, Gabriel (Author)
ISBN: 3540204067     ISBN-13: 9783540204060
Publisher: Springer
OUR PRICE:   $104.49  
Product Type: Paperback
Published: March 2004
Qty:
Annotation:

This is the first book that deals systematically with the numerical solution of elliptic partial differential equations by their reduction to the interface via the Schur complement.
Inheriting the beneficial features of finite element, boundary element and domain decomposition methods, our approach permits solving iteratively the Schur complement equation with linear-logarithmic cost in the number of the interface degrees of freedom.
The book presents the detailed analysis of the efficient data-sparse approximation techniques to the nonlocal Poincar??-Steklov interface operators associated with the Laplace, biharmonic, Stokes and Lam?? equations. Another attractive topic are the robust preconditioning methods for elliptic equations with highly jumping, anisotropic coefficients. A special feature of the book is a unified presentation of the traditional
iterative substructuring and multilevel methods combined with modern matrix compression techniques applied to the Schur complement on the interface.


Additional Information
BISAC Categories:
- Mathematics | Differential Equations - General
- Mathematics | Number Systems
- Mathematics | Applied
Dewey: 515.353
LCCN: 2004042926
Series: Lecture Notes in Computational Science and Engineering
Physical Information: 0.66" H x 6.14" W x 9.21" (0.98 lbs) 293 pages
 
Descriptions, Reviews, Etc.
Publisher Description:
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.