Title of article :
A matrix triangularization algorithm for the polynomial point interpolation method Original Research Article
Author/Authors :
G.R. Liu، نويسنده , , Y.T. Gu، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2003
Abstract :
A novel matrix triangularization algorithm (MTA) is proposed to overcome the singularity problem in the point interpolation method (PIM) using the polynomial basis, and to ensure stable and reliable construction of PIM shape functions. The present algorithm is validated using several examples, and implemented in the local point interpolation method (LPIM) that is a truly meshfree method based on a local weak form. Numerical examples demonstrate that LPIM using the present MTA are very easy to implement, and very robust for solving problems of computational mechanics. It is shown that PIM with the present MTA is very effective in constructing shape functions. Most importantly, PIM shape functions possess Kronecker delta function properties. Parameters that influence the performance of them are studied in detail. The convergence and efficiency of them are thoroughly investigated.
Keywords :
Meshless method , Meshfree method , Polynomial interpolation , Interpolation function , Computational mechanics
Journal title :
Computer Methods in Applied Mechanics and Engineering
Journal title :
Computer Methods in Applied Mechanics and Engineering