Investigation of Radial Basis Collocation Method for Incremental-Iterative Analysis

Abstract

We propose an incremental-iterative algorithm by using the strong form collocation method for solving geometric nonlinear problems. As nonlinear analyses concerning large deformation have been relied on the weak form-based methods such as the finite element methods and the reproducing kernel particle methods, the recently developed strong form collocation methods could be new research directions in that the mesh control and quadrature rule are abandoned in the collocation methods. In this work, the radial basis collocation method is adopted to perform the nonlinear analysis. The corresponding parameters affecting the deformation paths such as the increment of applied traction and shape parameter of the radial basis function are discussed. We also investigate the possibility of using the weighted collocation methods in the nonlinear analysis.

Direct Collocation with Reproducing Kernel Approximation for Two-Phase Coupling System in a Porous Enclosure

“…The commonly adopted global function is the radial basis function (RBF) defined by the Euclidean norm; nevertheless, the shape parameter of RBF cannot be determined uniquely by a given formula so far. As the resulting system is often ill-conditioned with a large condition number, numerical instability might be raised; for more information, see [8][9][10]. In contrast, the reproducing kernel (RK) shape function is a local function; although it maintains an algebraic convergence rate, the resulting system is more stable to yield promising results [11][12][13].…”