Hierarchical Matrices [electronic resource] :A Means to Efficiently Solve Elliptic Boundary Value Problems / by Mario Bebendorf.
by Bebendorf, Mario [author.]; SpringerLink (Online service).
Material type:
BookSeries: Lecture Notes in Computational Science and Engineering: 63Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.Description: XVI, 296 p. online resource.ISBN: 9783540771470.Subject(s): Mathematics | Differential equations, partial | Computer science -- Mathematics | Numerical analysis | Mathematics | Computational Mathematics and Numerical Analysis | Numerical Analysis | Partial Differential EquationsDDC classification: 518 | 518 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| MAIN LIBRARY | QA71-90 (Browse shelf) | Available |
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| Minerals as Advanced Materials I | TK7876-7876.42 Radio Wave Propagation | TL1-483 Vehicular-2-X Communication | QA71-90 Hierarchical Matrices | QK1-989 Plant Microtubules | QA164-167.2 Horizons of Combinatorics | QA71-90 Mathematics – Key Technology for the Future |
Low-Rank Matrices and Matrix Partitioning -- Hierarchical Matrices -- Approximation of Discrete Integral Operators -- Application to Finite Element Discretizations.
Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way. Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients. Furthermore, it presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions.The theory is supported by many numerical experiments from real applications.
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