Overview

This study proposes a numerical integration method for nearly singular integrals over general curved surfaces, arising in three dimensional boundary element analysis. Nearly singular integrals frequently occur in engineering problems involving thin structures of gaps and when calculating the field near the boundary. Numerical experiments show that the method is far more efficient compared to previous methods and is robust concerning the type of integral kernel and position of the source point. Theoretical error estimates for the method are derived using complex function theory. The method is also shown to be applicable to weakly singular and hypersingular integrals. Knowledge in basic calculus is assumed. The book is intended for engineers and researchers using the boundary element method who require accurate methods for numerical integration and also for numerical analysts interested in an application area for numerical integration.

Full Product Details

Author:   Ken Hayami
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1992
Volume:   73
Dimensions:   Width: 17.00cm , Height: 2.40cm , Length: 24.20cm
Weight:   0.794kg
ISBN:  

9783540550006

ISBN 10:   3540550003
Pages:   456
Publication Date:   30 March 1992
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

I Theory and Algorithms.- 1 Introduction.- 2 Boundary Element Formulation of 3-d Potential Problems.- 3 Nature of Integrals in 3-d Potential Problems.- 4 Survey of Quadrature Methods for 3-d Boundary Element Method.- 5 The Projection and Angular & Radial Transformation (Part) Method.- 6 Elementary Error Analysis.- 7 Error Analysis using Complex Function Theory.- II Applications and Numerical Results.- 8 Numerical Experiment Procedures and Element Types.- 9 Applications to Weakly Singular Integrals.- 10 Applications to Nearly Singular Integrals.- 11 Applications to Hypersingular Integrals.- 12 Conclusions.- References.

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