H2-wavelet Galerkin BEM and Its Application to the Radiosity Equation
H2-wavelet Galerkin BEM and Its Application to the Radiosity Equation

Author: Ulf Kähler

Publisher: VDM Publishing

Published: 2008

Total Pages: 0

ISBN-13: 9783836465595

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The 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."

Hierarchical Matrices: Algorithms and Analysis
Hierarchical Matrices: Algorithms and Analysis

Author: Wolfgang Hackbusch

Publisher: Springer

Published: 2015-12-21

Total Pages: 532

ISBN-13: 3662473240

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This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.

Numerical Linear Algebra and Applications
Numerical Linear Algebra and Applications

Author: Biswa Nath Datta

Publisher: SIAM

Published: 2010-01-01

Total Pages: 546

ISBN-13: 0898717655

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Full of features and applications, this acclaimed textbook for upper undergraduate level and graduate level students includes all the major topics of computational linear algebra, including solution of a system of linear equations, least-squares solutions of linear systems, computation of eigenvalues, eigenvectors, and singular value problems. Drawing from numerous disciplines of science and engineering, the author covers a variety of motivating applications. When a physical problem is posed, the scientific and engineering significance of the solution is clearly stated. Each chapter contains a summary of the important concepts developed in that chapter, suggestions for further reading, and numerous exercises, both theoretical and MATLAB and MATCOM based. The author also provides a list of key words for quick reference. The MATLAB toolkit available online, 'MATCOM', contains implementations of the major algorithms in the book and will enable students to study different algorithms for the same problem, comparing efficiency, stability, and accuracy.

Programming — ALGOL
Programming — ALGOL

Author: D. J. Malcolme-Lawes

Publisher: Elsevier

Published: 2014-05-09

Total Pages: 119

ISBN-13: 1483180425

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Programming — ALGOL describes the basics of computer programming using Algol. Commands that could be added to Algol and could increase its scope are described, including multiplication and division and the use of brackets. The idea of labeling or naming a command is also explained, along with a command allowing two alternative results. Most of the important features of Algol syntax are discussed, and examples of compound statements (that is, sets of commands enclosed by a begin ... end command) are given. Comprised of 11 chapters, this book begins with an introduction to the digital computer and how it works using a list of instructions known as a program. The "punched-tape" method of feeding information into a computer is described together with the flexowriter. The next chapter provides an overview of Algol by studying a very simple program and comparing it with the same sequence of instructions written in normal English. The third chapter is about building a program, first by increasing the complexity of the actual computation and then economizing on memory stores. Subsequent chapters focus on how computer programs can be built up of simple commands; labeling or naming a command; facilities in the Algol language which allow the addition of a second alternative command to an if ... then statement; and the use of a flow diagram to translate a problem into Algol. The final chapter examines the method of running a program on a computer. This monograph will be of interest to computer programmers.

Wavelets, Multilevel Methods, and Elliptic PDEs
Wavelets, Multilevel Methods, and Elliptic PDEs

Author: M. Ainsworth

Publisher: Oxford University Press

Published: 1997

Total Pages: 320

ISBN-13: 9780198501909

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This book contains the Proceedings of the seventh EPSRC Numerical Analysis Summer School, held in 1996. Five major topics in numerical analysis are treated by world experts at a level which should be suitable for first year graduate students and experienced researchers alike, assuming onlythe knowledge acquired from a first degree in mathematics or in a scientific discipline with significant mathematical content. Often researchers need to obtain an up-to-date picture of work in an area with a substantial literature, either to avoid reproducing work which is already done, or to applyto their own research in a different subject. This book avoids the need to trawl through the literature by presenting important recent results together with references to all the main papers. Each contributor reviews the state of the art in his area, presenting new and often hitherto unpublishedmaterial.

Multiple Time Scales
Multiple Time Scales

Author: Jeremiah U. Brackbill

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 457

ISBN-13: 1483257568

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Multiple Time Scales presents various numerical methods for solving multiple-time-scale problems. The selection first elaborates on considerations on solving problems with multiple scales; problems with different time scales; and nonlinear normal-mode initialization of numerical weather prediction models. Discussions focus on analysis of observations, nonlinear analysis, systems of ordinary differential equations, and numerical methods for problems with multiple scales. The text then examines the diffusion-synthetic acceleration of transport iterations, with application to a radiation hydrodynamics problem and implicit methods in combustion and chemical kinetics modeling. The publication ponders on molecular dynamics and Monte Carlo simulations of rare events; direct implicit plasma simulation; orbit averaging and subcycling in particle simulation of plasmas; and hybrid and collisional implicit plasma simulation models. Topics include basic moment method, electron subcycling, gyroaveraged particle simulation, and the electromagnetic direct implicit method. The selection is a valuable reference for researchers interested in pursuing further research on the use of numerical methods in solving multiple-time-scale problems.