The use of the L-curve in the regularization of discrete ill-posed problems
SIAM Journal on Scientific Computing
Fundamental solutions for differential operators and applications
Fundamental solutions for differential operators and applications
Stable determination of boundaries from Cauchy data
SIAM Journal on Mathematical Analysis
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Stable and Convergent Unsymmetric Meshless Collocation Methods
SIAM Journal on Numerical Analysis
Numerical simulations of 2D fractional subdiffusion problems
Journal of Computational Physics
Inverse shape and surface heat transfer coefficient identification
Journal of Computational and Applied Mathematics
A multilayer method of fundamental solutions for Stokes flow problems
Journal of Computational Physics
| Hi-index | 31.45 |
In this paper, the method of fundamental solutions (MFS) is employed for determining an unknown portion of the boundary from the Cauchy data specified on parts of the boundary. We propose a new numerical method with adaptive placement of source points in the MFS to solve the inverse boundary determination problem. Since the MFS source points placement here is not trivial due to the unknown boundary, we employ an adaptive technique to choose a sub-optimal arrangement of source points on various fictitious boundaries. Afterwards, the standard Tikhonov regularization method is used to solve ill-conditional matrix equation, while the regularization parameter is chosen by the L-curve criterion. The numerical studies of both open and closed fictitious boundaries are considered. It is shown that the proposed method is effective and stable even for data with relatively high noise levels.