Meshless analysis of elliptic interface boundary value problems

In the present paper, Multiquadric radial basis function (MQ RBF) and its integrated form are used to construct collocation methods for numerical solution of two-dimensional elliptic problems with curved or closed interface. The main purpose of this work is to perform a comparative analysis of both the methods via accuracy and condition number of the coefficient matrix for elliptic interface problems. In the classical RBF collocation method, the shape parameter is selected by using cross validation approach [1]. In the case of Integrated MQ RBF, a reasonable accuracy is obtained for a wide range of values of the shape parameter. Some of the benchmark problems such as linearized Poisson-Boltzmann problem [2], Poisson interface problem [3], Pennes Bioheat Equation [4] (with no exact solution, containing two phases), are considered to validate accuracy and efficiency of the RBFs collocation methods.