A Simple Device to Improve the Accuracy of Evaluating Weakly Singular Boundary Element Integrals
Abstract
The question of the accurate numerical evaluation of weakly singular integrals arising in the boundary element method has attracted considerable recent attention. A popular method is to use a non-linear transformation with zero derivative at the singular point to adjust the position of the Gauss-Legendre quadrature points, resulting in a more accurate evaluation of the integral. This paper presents a simple algebraic device to overcome a numerical round-off problem which has limited previous implementations of non-linear transformations. Utilization of this device allows higher orders of transformation to be used, resulting ...
View more >The question of the accurate numerical evaluation of weakly singular integrals arising in the boundary element method has attracted considerable recent attention. A popular method is to use a non-linear transformation with zero derivative at the singular point to adjust the position of the Gauss-Legendre quadrature points, resulting in a more accurate evaluation of the integral. This paper presents a simple algebraic device to overcome a numerical round-off problem which has limited previous implementations of non-linear transformations. Utilization of this device allows higher orders of transformation to be used, resulting in lower relative errors in the numerical evaluation of the weakly singular integrals.
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View more >The question of the accurate numerical evaluation of weakly singular integrals arising in the boundary element method has attracted considerable recent attention. A popular method is to use a non-linear transformation with zero derivative at the singular point to adjust the position of the Gauss-Legendre quadrature points, resulting in a more accurate evaluation of the integral. This paper presents a simple algebraic device to overcome a numerical round-off problem which has limited previous implementations of non-linear transformations. Utilization of this device allows higher orders of transformation to be used, resulting in lower relative errors in the numerical evaluation of the weakly singular integrals.
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Journal Title
Communications in Numerical Methods in Engineering
Volume
18
Publisher URI
Copyright Statement
© 2002 John Wiley & Sons, Ltd. Self-archiving of the author-manuscript version is not yet supported by this publisher. Please refer to the journal link for access to the definitive, published version or contact the author for more information.
Subject
Mathematical sciences
Engineering