A bi‐cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods
Open Access
- 1 May 1989
- journal article
- research article
- Published by Wiley in International Journal for Numerical Methods in Engineering
- Vol. 28 (5) , 987-999
- https://doi.org/10.1002/nme.1620280502
Abstract
The numerical strategies employed in the evaluation of singular integrals existing in the Cauchy principal value (CPV) sense are, undoubtedly, one of the key aspects which remarkably affect the performance and accuracy of the boundary element method (BEM).Thus, a new procedure, based upon a bi‐cubic co‐ordinate transformation and oriented towards the numerical evaluation of both the CPV integrals and some others which contain different types of singularity is developed.Both the ideas and some details involved in the proposed formulae are presented, obtaining rather simple and‐attractive expressions for the numerical quadrature which are also easily embodied into existing BEM codes.Some illustrative examples which assess the stability and accuracy of the new formulae are included.Keywords
This publication has 13 references indexed in Scilit:
- Direct computation of Cauchy principal value integrals in advanced boundary elementsInternational Journal for Numerical Methods in Engineering, 1987
- p‐adaptive boundary elements for three‐dimensional potential problemsCommunications in Applied Numerical Methods, 1987
- Self-Adaptive P-Hierarchical Boundary Elements in ElastostaticsPublished by Springer Nature ,1987
- Solution of elasticity problems by a self-adaptive mesh refinement technique for boundary element computationInternational Journal for Numerical Methods in Engineering, 1986
- p‐adaptive boundary elementsInternational Journal for Numerical Methods in Engineering, 1986
- Hierarchical boundary elementsComputers & Structures, 1985
- Efficient evaluation of integrals of order 1/r 1/r2, 1/r3 using Gauss quadratureEngineering Analysis, 1985
- A Boundary Element Formulation of Problems in Linear Isotropic Elasticity with Body ForcesPublished by Springer Nature ,1981
- The numerical evaluation of principal value integrals by finite-part integrationNumerische Mathematik, 1975
- An algorithm for the numerical evaluation of certain Cauchy principal value integralsNumerische Mathematik, 1972