Search

We present a simple and effective Chebyshev polynomial scheme (CPS) combined with the method of fundamental solutions (MFS) and the equilibrated collocation Trefftz method for the numerical solutions of inhomogeneous elliptic partial differential equations (PDEs). In this paper, CPS is applied in a two-step approach. First, Chebyshev polynomials are used to approximate a particular solution of a PDE. Chebyshev nodes which are the roots of Chebyshev polynomials are used in the polynomial interpolation due to its spectral convergence. Then the resulting homogeneous equation is solved by boundary type methods including the MFS and the equilibrated collocation Trefftz method. Numerical results for problems on various irregular domains show that our proposed scheme is highly accurate and efficient. [ABSTRACT FROM AUTHOR]

As a truly boundary-type meshless method, the hybrid boundary node method (HdBNM) does not require ‘boundary element mesh’, either for the purpose of interpolation of the solution variables or for the integration of ‘energy’. In this paper, the HdBNM is coupled with the finite element method (FEM) for predicting the mechanical behaviors of reinforced concrete. The steel bars are considered as body forces in the concrete. A bond model is presented to simulate the bond-slip between the concrete and steels using fictitious spring elements. The computational scale and cost for meshing can be further reduced. Numerical examples, in 2D and 3D cases, demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]