Download A Projection Transformation Method for Nearly Singular by Ken Hayami PDF

By Ken Hayami

In 3 dimensional boundary aspect research, computation of integrals is a vital point because it governs the accuracy of the research and likewise since it frequently takes the foremost a part of the CPU time. The integrals which make certain the effect matrices, the interior box and its gradients comprise (nearly) singular kernels of order lIr a (0:= 1,2,3,4,.··) the place r is the gap among the resource aspect and the combination element at the boundary point. For planar components, analytical integration could be attainable 1,2,6. despite the fact that, it really is changing into more and more very important in sensible boundary point codes to exploit curved components, similar to the isoparametric components, to version basic curved surfaces. for the reason that analytical integration isn't really attainable for normal isoparametric curved parts, one has to depend on numerical integration. while the gap d among the resource aspect and the point over which the combination is played is adequately huge in comparison to the point measurement (d> 1), the traditional Gauss-Legendre quadrature formulation 1,3 works successfully. besides the fact that, while the resource is de facto at the point (d=O), the kernel 1I~ turns into singular and the effortless program of the Gauss-Legendre quadrature formulation breaks down. those integrals could be referred to as singular integrals. Singular integrals take place whilst calculating the diagonals of the effect matrices.

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Additional resources for A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals

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I c. 65) 41f I and the calculation of the singular integral H .. 66) = x. 67) (r,n) 41f r3 become unnecessary. This technique is equivalent to what is known as the use of rigid body motion in elastostatics. On the other hand, it is a good check to calculate Hii directly from Ci and Hij. For discontinuous elements 1, Ci = 1 / 2 for i = 1-N, and calculating the singular integrals Hii directly are reported to give more accurate results 15. 68) where u* = 1/(47l"r) and G ii = L k x = x. 71) which contribute to the non-diagonal element Hij and Gij.

When d> 1 , the integrals do not cause difficulties since they may be calculated accurately using the standard Gauss-Legendre formula 1,3 with relatively few integration points. ) It is for the singular (d=O), and nearly singular integrals (O

63) 27 H II.. = H .. + c. = 1 U, n - L H .. ) I c. 65) 41f I and the calculation of the singular integral H .. 66) = x. 67) (r,n) 41f r3 become unnecessary. This technique is equivalent to what is known as the use of rigid body motion in elastostatics. On the other hand, it is a good check to calculate Hii directly from Ci and Hij. For discontinuous elements 1, Ci = 1 / 2 for i = 1-N, and calculating the singular integrals Hii directly are reported to give more accurate results 15. 68) where u* = 1/(47l"r) and G ii = L k x = x.

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