By H. Antes, K. Volk (auth.), Wolfgang Hackbusch (eds.)
Read Online or Download Numerical Techniques for Boundary Element Methods: Proceedings of the Seventh GAMM-Seminar Kiel, January 25–27, 1991 PDF
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Extra resources for Numerical Techniques for Boundary Element Methods: Proceedings of the Seventh GAMM-Seminar Kiel, January 25–27, 1991
The treatment for L 2 is similar. We first integrate analytically, and then perform the limiting process using the expansions for am(e). · + Nc(71) b;(y)} 2 e 2 t (1- et'm sgn(c5))] + Nc(71) b;(y)}-! Bm e 2 m=1 F~2 + Nc(71)b;(y)}- m=1 fJm ('(;~~;c5) + D]. )] (fJm) 2 (35) This formula is equivalent to expression (26) in  (3D case). In particular sgn(c5hm corresponds to 1(8), since 1(8) = -1(8 + 1r). Bm and /m account for the distorsion of the originally symmetric neighbourhood as introduced by the geometric discretization of the boundary (Figures 2 and 3).
To show the effect of already optimized programs on CPU-time reduction some of them were taken from a vectorized programlibrary (VECLffi). Table 2 shows the different solution schemes which were chosen for methods A, B and C. Table 2: Solution schemes for linear equations denotation used for method Sl S2 S3 S4 A,B A,B c c solution scheme Schmidt-orthonormalization QR-Householder (using VECLffi) Cholesky decomposition (using symmetric storage mode) Cholesky decomposition (full stored matrix, VECLID) CPU-TIME ANALYSIS The computation time for the combined boundary element time stepping technique (see Fig.
Notice that, only in the very special case of v, being part of a circle centered at y, the line integral in (1) will match the CPV definition which requires e, to be symmetric around y. o+ r J(r-e,)+•• [V;(y,x)u(x)- W;(y,x)q(x)]dsz} = 0, (2) where W; = oUioy; and V; = oTioy;. For 2D potential problems, we have 1 27rTr,;' W;(y,x) V;(y,x) :r - 2 2 [2r,;~: -n;(x)], (3) where r,; = or I ox; = -or I oy;. The kernel W; shows a strong singularity of order r- 1 while the kernel V; is hypersingular of order r- 2 , as r -+ 0.