The method of fundamental solutions for the numerical solution of the biharmonic equation
Journal of Computational Physics
A particular solution Trefftz method for non-linear Poisson problems in heat and mass transfer
Journal of Computational Physics
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
A meshless method for solving an inverse spacewise-dependent heat source problem
Journal of Computational Physics
Modified Tikhonov regularization method for the Cauchy problem of the Helmholtz equation
Journal of Computational and Applied Mathematics
The Fourier regularization for solving the Cauchy problem for the Helmholtz equation
Applied Numerical Mathematics
Mathematics and Computers in Simulation
On a quasi-reversibility regularization method for a Cauchy problem of the Helmholtz equation
Journal of Computational and Applied Mathematics
A regularization method for a Cauchy problem of the Helmholtz equation
Journal of Computational and Applied Mathematics
A meshless method for solving the cauchy problem in three-dimensional elastostatics
Computers & Mathematics with Applications
An adaptive greedy technique for inverse boundary determination problem
Journal of Computational Physics
Advances in Computational Mathematics
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Improved singular boundary method for elasticity problems
Computers and Structures
Hi-index | 0.01 |
In this paper, the application of the method of fundamental solutions to the Cauchy problem associated with two-dimensional Helmholtz-type equations is investigated. The resulting system of linear algebraic equations is ill-conditioned and therefore its solution is regularized by employing the first-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method. Numerical results are presented for both smooth and piecewise smooth geometries. The convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain, and decreasing the amount of noise added into the input data, respectively, are analysed.