A projection transformation method for nearly singular surface boundary element integrals
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.
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NATURE OF INTEGRALS
SURVEY OF QUADRATURE METHODS
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A Projection Transformation Method for Nearly Singular Surface Boundary ...
Limited preview - 2012
00 CN CN angular integration points angular variable transformation Boundary Element Method cancelling radial variable Cauchy principal value CN CN CN CN i-H CN rH compared constant planar elements curved element dimensional potential problems double exponential transformation du*/dxs dS efficiently ellipse Gauss Gauss-Legendre formula Gauss-Legendre quadrature formula gives Hence i-H CN i-H i-H i-H rH integral kernels integral of equation interpolation functions log-L2 transformation log-Li nearly singular integrals number of angular number of integration number of radial numerical integration methods numerical results point xs polar coordinates projection xs quadrilateral element radial integration points radial transformation radial variable transformation relative error rH CN rH i-H robust saddle point shown in Fig singularity cancelling radial source point source projection spherical Stirling's formula Table theoretical error estimates three dimensional potential transformation of equation variable transformation R(p weakly X X X