论文信息 - Adaptive Vector Integration as an Efficient Quadrature Scheme for p-Version Finite Element Matrices

Adaptive Vector Integration as an Efficient Quadrature Scheme for p-Version Finite Element Matrices

In this paper we present an adaptive version of vector quadrature having been first proposed by H.E. Hinnant. Focussing on the quadrature of finite-element matrices, arising from higher order discretizations, we outline a modified vector integration, which leads to a significant speed-up, even in case of strongly distorted elements. The method has been implemented in an existing p-version finite-element code and its efficiency is demonstrated by numerical examples.

[1] D. Griffin,et al. Finite-Element Analysis , 1975 .

[2] Ernst Rank,et al. On the accuracy of p-version elements for the Reissner-Mindlin plate problem , 1998 .

[3] J. Fish,et al. The p-version of finite element method for shell analysis , 1995 .

[4] Barna A. Szabó,et al. Hierarchic models for laminated plates and shells , 1999 .

[5] W. J. Gordon,et al. Construction of curvilinear co-ordinate systems and applications to mesh generation , 1973 .

[6] Ernst Rank,et al. An implementation of the hp‐version of the finite element method for Reissner‐Mindlin plate problems , 1990 .

[7] H. Broeker,et al. The efficiency of the p‐version finite element method in a distributed computing environment , 2001 .

[8] Ivo Babuška,et al. On the Rates of Convergence of the Finite Element Method , 1982 .

[9] C. Schwab. P- and hp- finite element methods : theory and applications in solid and fluid mechanics , 1998 .

[10] Howard E. Hinnant. A fast method of numerical quadrature for p-version finite element matrices , 1993 .

[11] B. Szabó. Mesh design for the p-version of the finite element method , 1986 .

[12] Jens Markus Melenk,et al. Fully discrete hp-finite elements: fast quadrature , 2001 .