Wavelet Based Fast Solution of Boundary Integral Equations
Author: Helmut Harbrecht
Publisher:
Published: 2006
Total Pages:
ISBN-13:
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Author: Helmut Harbrecht
Publisher:
Published: 2006
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Helmut Harbrecht
Publisher:
Published: 2006
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Sergej Rjasanow
Publisher: Springer Science & Business Media
Published: 2007-04-17
Total Pages: 285
ISBN-13: 0387340424
DOWNLOAD EBOOKThis book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.
Author: Madan Mohan Panja
Publisher: CRC Press
Published: 2020-06-07
Total Pages: 466
ISBN-13: 0429534280
DOWNLOAD EBOOKMany mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It’s main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.
Author: Zhang Pingwen
Publisher:
Published: 1995
Total Pages: 16
ISBN-13:
DOWNLOAD EBOOKAuthor: Thanh Tran
Publisher:
Published: 1996
Total Pages: 16
ISBN-13:
DOWNLOAD EBOOKAuthor: Zhang Pingwen
Publisher:
Published: 1995
Total Pages: 15
ISBN-13:
DOWNLOAD EBOOKAuthor: Angela Kunoth
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 150
ISBN-13: 332280027X
DOWNLOAD EBOOKDiese Monographie spannt einen Bogen rund um die aktuelle Thematik Wavelets, um neueste Entwicklungen anhand aufeinander aufbauender Probleme darzustellen und das konzeptuelle Potenzial von Waveletmethoden für Partielle Differentialgleichungen zu demonstrieren.
Author: Sergej Rjasanow
Publisher: Springer
Published: 2008-11-01
Total Pages: 0
ISBN-13: 9780387513836
DOWNLOAD EBOOKThis book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.
Author: Ulf Kähler
Publisher: VDM Publishing
Published: 2008
Total Pages: 0
ISBN-13: 9783836465595
DOWNLOAD EBOOKThe numerical treatment of integral equations is an important problem in science and industry. Regardless of whether the integral equation is a straight model of a physical state, like the radiosity or the heat radiation equation, or whether it is derived from partial differential equations, a memory and computing time efficient solving algorithm is essential for all practical applications. The present book is dedicated to the fast solution of boundary integral equations on unstructured meshes by the Galerkin scheme and its application to the special situation of the radiosity equation. Throughout the pages a new fast method based on the wavelet compression and the ideas of the hierarchical matrices will be constructed. To allow for comfortable comprehension, the author describes in detail all used methods and algorithms including the wavelet method as well as the H -matrices. Although this book is primarily written for applied mathematicians, its detailed descriptions also provide a good introduction to the field of fast boundary element methods for computer scientists and engineers."