Two meshless methods based on local radial basis function and barycentric rational interpolation for solving 2D viscoelastic wave equation

Abstract

In this paper, 2D viscoelastic wave equation is solved numerically both on regular and irregular domains. For spatial approximation of viscoelastic wave equation two meshless methods based on local radial basis function and barycentric rational interpolation are proposed. Both of the spatial approximation methods do not need mesh, node connectivity or integration process on local subdomains so they are truly meshless. For local radial basis function method we used an existing algorithm in literature to choose an acceptable shape parameter. Time marching is performed with fourth order Runge Kutta method. L2 and L∞ error norms for some test problems are reckoned to indicate efficiency and performance of the proposed two methods. Also, stability of the methods is discussed. Acquired results confirm the applicability of the proposed methods for 2D viscoelastic wave equation. We have performed some comparisons between the proposed two methods in the sense of accuracy and computational cost. From the comparisons, we have observed that performance of the barycentric rational interpolation in the sense of accuracy is slightly better than the performance of local radial basis function however computational cost of the local radial basis function is less than the computational cost of barycentric rational interpolation.