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1. Numerical solutions of elliptic partial differential equations using Chebyshev polynomials.

Author

Khatri Ghimire, B., Tian, H.Y., and Lamichhane, A.R.

Subjects
*NUMERICAL analysis, *CHEBYSHEV polynomials, *ELLIPTIC differential equations, *APPROXIMATION theory, *INTERPOLATION, *STOCHASTIC convergence, *BOUNDARY value problems
Abstract

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]

Published
2016
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2. An edge/face-based smoothed radial point interpolation method for static analysis of structures.

Author

Feng, S.Z., Cui, X.Y., Chen, F., Liu, S.Z., and Meng, D.Y.

Subjects
*STATISTICAL smoothing, *INTERPOLATION, *ALGEBRAIC field theory, *DISCRETIZATION methods, *BOUNDARY value problems, *APPROXIMATION theory
Abstract

This paper formulates an edge/face-based smoothed radial point interpolation method (ES/FS-RPIM) for the 2D and 3D static analysis of structures. In present method, the problem domain is discretized using triangular or tetrahedron cells and the edge-based or face-based smoothing domains are then constructed based on these background meshes. Field functions are approximated using RPIM shape functions which have Kronecker delta function property. An efficient T2L-scheme is employed for the RPIM shape function construction. The system equations are derived using the generalized smoothed Galerkin (GS-Galerkin) weak form and essential boundary conditions can be imposed directly as in the finite element method (FEM). Several numerical examples with different material models are investigated to verify the proposed method in terms of accuracy, stability, efficiency and convergence. [ABSTRACT FROM AUTHOR]

Published
2016
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