Titel: A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals (Lecture Notes in Engineering, 73)
Verlag: Springer
Erscheinungsjahr: 1992
Sprache: Englisch
ISBN-10: 3540550003
ISBN-13: 9783540550006
Einband: Softcover
Zustand: New

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Inhaltsangabe

This book proposes an accurate and efficient numerical inte- gration method for nearly singular integrals over general curved surfaces, arising in threedimensional boundary ele- ment analysis. Nearly singular integrals frequently occur in engineering problems involving thin structures or gaps and when calculating the field near the boundary. Numerical ex- periments show that the method is far more efficient compa- red to previous methods and is robust concerning the type of integral kernel and position of the source point. Theoreti- cal error estimates for the method is 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 engine- ers and researchers using the boundary element method who require accurate methods for numerical integration and also for numerical analysts interested in a rich application area for numerical integration.

Rese�a del editor

In three dimensional boundary element analysis, computation of integrals is an important aspect since it governs the accuracy of the analysis and also because it usually takes the major part of the CPU time. The integrals which determine the influence matrices, the internal field and its gradients contain (nearly) singular kernels of order lIr a (0:= 1,2,3,4,.��) where r is the distance between the source point and the integration point on the boundary element. For planar elements, analytical integration may be possible 1,2,6. However, it is becoming increasingly important in practical boundary element codes to use curved elements, such as the isoparametric elements, to model general curved surfaces. Since analytical integration is not possible for general isoparametric curved elements, one has to rely on numerical integration. When the distance d between the source point and the element over which the integration is performed is sufficiently large compared to the element size (d> 1), the standard Gauss-Legendre quadrature formula 1,3 works efficiently. However, when the source is actually on the element (d=O), the kernel 1I~ becomes singular and the straight forward application of the Gauss-Legendre quadrature formula breaks down. These integrals will be called singular integrals. Singular integrals occur when calculating the diagonals of the influence matrices.

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