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Advances in Computational Mathematics

, Volume 36, Issue 1, pp 79–97 | Cite as

Splitting extrapolation algorithm for first kind boundary integral equations with singularities by mechanical quadrature methods

  • Jin Huang
  • Guang Zeng
  • Xiaoming HeEmail author
  • Zi-Cai Li
Article

Abstract

The 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 \( O(h_{\rm {max}}^{3})\) convergence rate; (2) the \(O(h_{\rm {max}}^{5})\) convergence rate after splitting extrapolation; (3) Cond = \(O(h_{\rm {min}}^{-1})\); (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 29:59–75, 2005), the highly accurate solutions of MQM may even compete with those of the collocation Trefftz method.

Keywords

First-kind boundary integral equation Mechanical quadrature method Splitting extrapolation A posteriori estimate Singularity Stability analysis 

Mathematics Subject Classifications (2010)

45B05 45E99 65B05 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • Jin Huang
    • 1
  • Guang Zeng
    • 1
  • Xiaoming He
    • 2
    • 3
    Email author
  • Zi-Cai Li
    • 4
    • 5
  1. 1.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.Department of Scientific ComputingFlorida State UniversityTallahasseeUSA
  3. 3.Department of Mathematics and StatisticsMissouri University of Science and TechnologyRollaUSA
  4. 4.Department of Applied MathematicsNational Sun Yat-sen UniversityKaohsiungTaiwan
  5. 5.Department of Computer Science and EngineeringNational Sun Yat-sen UniversityKaohsiungTaiwan

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