Splitting Extrapolation Algorithm for First Kind Boundary Integral Equations with Singularities by Mechanical Quadrature MethodsAdvances in Computational Mathematics
Editor(s)Greengard, Leslie and Shelley, Michael
AbstractThe accuracy of numerical solutions near singular points is crucial for numerical methods. In this paper we develop an efficient mechanical quadrature method (MQM) with high accuracy. The following advantages of MQM show that it is very promising and beneficial for practical applications: (1) the O(h3max) convergence rate; (2) the O(h5max) convergence rate after splitting extrapolation; (3) Cond = O(hâˆ'1min) ; (4) the explicit discrete matrix entries. In this paper, the above theoretical results are briefly addressed and then verified by numerical experiments. The solutions of MQM are more accurate than those of other methods. Note that for the discontinuous model in Li et al. (Eng Anal Bound Elem 29:59â€“75, 2005), the highly accurate solutions of MQM may even compete with those of the collocation Trefftz method.
Department(s)Mathematics and Statistics
Keywords and Phrases
- First-kind boundary integral equation,
- mechanical quadrature method,
- splitting extrapolation,
- a posteriori estimate,
- stability analysis
Document TypeArticle - Journal
Rights© 2012 Springer Verlag, All rights reserved.
Citation InformationJin Huang, Guang Zeng, Xiaoming He and Zi-Cai Li. "Splitting Extrapolation Algorithm for First Kind Boundary Integral Equations with Singularities by Mechanical Quadrature Methods" Advances in Computational Mathematics (2012)
Available at: http://works.bepress.com/xiaoming-he/42/