Department of Mathematics
The Effective-Condition-Number(ECN) is a sensitivity measure for a linear system; it differs from the traditional condition-number in the sense that the ECN is also right-hand side vector dependent. The first part of this work, in [EABE33(5)pp.637-643], revealed the close connection between the ECN and the accuracy of the Method of Fundamental Solutions (MFS) for each given problem. In this paer, we show how the ECN can help achieve the problem-dependent quasi-optimal settings for MFS calculations - that is, determining the position and density of the source points. A series of examples on Dirichlet and boundary conditions shows the reliability of the proposed scheme; whenever the MFS fails, the corresponding value of the ECN strongly indicates to the user to switch to other numerical methods.
Engineering Analysis with Boundary Elements
First Page (page number)
Last Page (page number)
Wong, Kwun Ying, and L. Ling. "Optimality of the method of fundamental solutions." Engineering Analysis with Boundary Elements 35.1 (2011): 42-46.