Source Nodes On Elliptic Pseudo-Boundaries In the Method of Fundamental Solutions for Laplace's Equation; Selection of Pseudo-Boundaries
Mathematics and Natural Sciences
In the method of fundamental solutions (MFS), source nodes on circles outside the solution domains S has been widely applied in numerical computation. In this paper, source nodes on an ellipse are proposed for solving Laplace’s equation using the MFS, and a robust error and stability analysis is established. Bounds on errors and condition numbers are derived for bounded simply-connected domains. Polynomial convergence rates can be achieved, but the exponential growth of the condition number is also obtained. In previous stability analysis of the MFS, circulant matrices have been always employed. This is the first time the stability analysis is explored for non-circular pseudo-boundaries, based on new techniques without using circulant matrices. The criteria for evaluating numerical techniques are provided, and some strategies for choosing pseudo-boundaries are suggested.
Journal of Computational and Applied Mathematics
(2020). Source Nodes On Elliptic Pseudo-Boundaries In the Method of Fundamental Solutions for Laplace's Equation; Selection of Pseudo-Boundaries. Journal of Computational and Applied Mathematics, 377.
Available at: https://aquila.usm.edu/fac_pubs/17845