Material discontinuity problems solved by a meshless method based on variably scaled discontinuous radial functions

The paper presents a meshless method based on global interpolation with radial base functions and shows its application in solving interface problems. Such problems arise when two or more different materials are used to construct the element under consideration. Across the interface between the materials, a discontinuity of material parameters arises. To solve the problem, the radial basis function-based collocation method is applied. To properly reflect the discontinuity, the base functions are modified. In this paper, the method is applied to solve problems described by elliptic equations. Using these examples, the accuracy, stability and convergence of the method are examined.