The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation

In this paper, the application of the method of fundamental solutions to inverse problems associated with the two-dimensional biharmonic equation is investigated. The resulting system of linear algebraic equations is ill-conditioned and, therefore, its solution is regularized by employing the 0th-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.