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C.F. Rodrigues, M.L. Bittencourt, "Numerical Efficiency of Minimum Energy Bases for the High Order Finite Element Method", in , (Editors), "Proceedings of the Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 210, 2013. doi:10.4203/ccp.102.210

Keywords: minimum energy basis, simultaneous diagonalization, high-order finite element method.

Summary

Generally, the high order finite element method (p-FEM) is associated with the use of numerical models and efficient algorithms. This is evident since in the p-FEM, the convergence of the solution is obtained using a fixed mesh and varying the order of the interpolating functions. A direct consequence when increasing the polynomial order is the sudden increase of the matrix rank.

This paper discusses a formulation for constructing the minimum energy basis in a high order approach, applied to Helmholtz problems. We consider the simultaneous diagonalization of the matrices internal modes, together with the minimum energy orthogonalization of boundary modes. The obtained basis are verified through numerical tests using the conjugate gradient method, with distorted and undistorted element meshes.

The basis efficiency is analysed in terms of the number of iterations to convergence and the matrix conditioning associated to the approximation problem in 2D and 3D domains.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 102 PROCEEDINGS OF THE FOURTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: Paper 210 Numerical Efficiency of Minimum Energy Bases for the High Order Finite Element Method C.F. Rodrigues and M.L. Bittencourt Department of Mechanical Design, Faculty of Mechanical Engineering University of Campinas, Brazil doi:10.4203/ccp.102.210 purchase the full-text of this paper Full Bibliographic Reference for this paper C.F. Rodrigues, M.L. Bittencourt, "Numerical Efficiency of Minimum Energy Bases for the High Order Finite Element Method", in , (Editors), "Proceedings of the Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 210, 2013. doi:10.4203/ccp.102.210 Keywords: minimum energy basis, simultaneous diagonalization, high-order finite element method. Summary Generally, the high order finite element method (p-FEM) is associated with the use of numerical models and efficient algorithms. This is evident since in the p-FEM, the convergence of the solution is obtained using a fixed mesh and varying the order of the interpolating functions. A direct consequence when increasing the polynomial order is the sudden increase of the matrix rank. This paper discusses a formulation for constructing the minimum energy basis in a high order approach, applied to Helmholtz problems. We consider the simultaneous diagonalization of the matrices internal modes, together with the minimum energy orthogonalization of boundary modes. The obtained basis are verified through numerical tests using the conjugate gradient method, with distorted and undistorted element meshes. The basis efficiency is analysed in terms of the number of iterations to convergence and the matrix conditioning associated to the approximation problem in 2D and 3D domains. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £65 +P&P)
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