Download Boundary Elements: Implementation and Analysis of Advanced by Bernd H. Kleemann, Andreas Rathsfeld (auth.), Wolfgang PDF

By Bernd H. Kleemann, Andreas Rathsfeld (auth.), Wolfgang Hackbusch, Gabriel Wittum (eds.)

The GAMM Committee for "Efficient Numerical tools for Partial Differential Equations" organizes seminars and workshops on topics about the algorithmic therapy of partial differential equations. the themes are discretisation tools just like the finite point and the boundary aspect technique for varied kind of functions in struc­ tural and fluid mechanics. specific cognizance is dedicated to complicated resolution method". the most recent seminar during this sequence was once the twelfth Kiel-Seminar which happened on January 19-21, 1996 at Christian-Albrechts-University of Kiel and focussed at the subject Boundary components: Implementation and research of complex Algorithms. The seminar used to be attended by means of sixty five scientists from 10 international locations. 23 lectures got, together with survey lectures. within the final years, a extraordinary development within the numerical remedy of boundary de­ ment tools (BEM) has been acquired in Germany. this can be, particularly, a res~I1t of a Schwerpunktverfahren supported through the DFG. Many features of the BEM aren't ouly analysed but in addition applied. consequently, those court cases current a few papers on implementational facets along with the research of complicated techniques.

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Additional info for Boundary Elements: Implementation and Analysis of Advanced Algorithms: Proceedings of the Twelfth GAMM-Seminar Kiel, January 19–21, 1996

Example text

In the case of coincident elements all of the four integrations may be performed analytically, if constant or linear shape functions are used. The three inner integrations over polynomials are performed by the standard function "int" of MapleV. The resulting outer integral was decomposed into integrals Ik of the type (26) where qn is a polynomial of degee n and a, b, c are constants. First the general integral (26) was evaluated. Then the integrals h were obtained by simple insertion of the constants.

We begin with the case of identical panels K1 = K 2 . The representation (13) is approximated by GN1 M;~ [gd where gi ('TI, w) is an abbreviation of the integrand 3 of (13). The following theorem concerns the cubature error. l := IIi - GN1 M;~ [gi]l. Let 0 :::; s, t and p denote the polynomial degree of the trial space. t'Yl- 1 1Iullml IIvllm2 + h'Y2+l- s-t Ilullp_s Ilvllp- t) with a constant>. independent of the discretization parameters hand p and the orders mj of the operators Dj defined at the beginning of the previous section.

Hackbusch and S. Sauter. On nwnerical cubature of nearly singular surface integrals arising in BEM collocation. Computing, 52:139-159, 1994. [8] L. Hormander. The Analysis of Linear Partial Differential Operators, volwne I. Springer, Berlin, Heidelberg, New York, Tokyo, 1983. [9] T. , J. Tomas Pereira, and C. S. de Barcellos. On general fundamental solutions of some linear elliptic differential operators. Eng. Anal. with Bound. Elements (to appear), 1996. [10] C. Lage. A Parallel Implementation of 3-d BEM with Focus on Panel Clustering.

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