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Hierarchical Matrices : A Means to Efficiently Solve Elliptic Boundary Value Problems /

By: Bebendorf, Mario [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Computational Science and Engineering: 63Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.Description: XVI, 296 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540771470.Subject(s): Mathematics | Partial differential equations | Computer mathematics | Numerical analysis | Mathematics | Computational Mathematics and Numerical Analysis | Numerical Analysis | Partial Differential EquationsDDC classification: 518 Online resources: Click here to access online
Contents:
Low-Rank Matrices and Matrix Partitioning -- Hierarchical Matrices -- Approximation of Discrete Integral Operators -- Application to Finite Element Discretizations.
In: Springer eBooksSummary: 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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Item type Current location Call number Status Date due Barcode Item holds
E books E books PK Kelkar Library, IIT Kanpur
Available EBK10409
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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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