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| Stability analysis of boundary knot method |
| Received:February 10, 2012 Revised:May 10, 2012 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201302012 |
| KeyWord:Boundary knot method ill-conditioned matrix effective condition number regularization Helmholtz equation |
| Author | Institution |
| 姜欣荣 |
河海大学 工程力学系,工程与科学数值模拟软件中心,南京 |
| 陈文 |
河海大学 工程力学系,工程与科学数值模拟软件中心,南京 |
| 林继 |
河海大学 工程力学系,工程与科学数值模拟软件中心,南京 |
| 王福章 |
河海大学 工程力学系,工程与科学数值模拟软件中心,南京 |
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| Abstract: |
| The boundary knot method (BKM) uses the non-singular general solution,which satisfies the governing equation,as its basis functions for the semi-analytical numerical solution of partial differential equation on boundary collocation discretization and is a truly meshfree collocation method with merits of high accuracy,rapid convergence,easy-to-program.But with the increasing number of boundary knots,the method often results in an ill-conditioned interpolation matrix equation.In this study,we employ the effective condition number (ECN) approach to estimate the computational stability and accuracy of the BKM solution of Helmholtz problems.And then this paper employs the three regularization techniques to damp the ill-posedness of the BKM interpolation matrix in conjunction with the Gaussian elimination method for the solution of discretization algebraic equations.Numerical experiments illustrate the relationship among the ECN,accuracy and regularization techniques with respect to the BKM solution of Helmholtz problems. |
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