Computations on preconditioning cubic spline collocation method of elliptic equations

被引:0
作者
Yong Hun Lee
机构
[1] Chonbuk National University,Department of Mathematics
[2] Chonju,undefined
关键词
65N30; 65N35; 65F05; 65F10; preconditioned matrix; cubic spline collocation; finite element method;
D O I
10.1007/BF02941966
中图分类号
学科分类号
摘要
In this work we investigate the finite element preconditioning method for theC1-cubic spline collocation discretizations for an elliptic operatorA defined byAu:=−Δu+a1ux+a2uy+a0u in the unit square with some boundary conditions. We compute the condition number and the numerical solution of the preconditioning system for the several example problems. Finally, we compare the this preconditioning system with the another preconditioning system.
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页码:279 / 294
页数:15
相关论文
共 13 条
  • [1] Cerutti J.(1974)Collocation Methods for Parabolic Partial Differential Equations in one dimensional space Numer. Math. 26 227-254
  • [2] Parter S. V.(1990)Finite-Element Preconditioning for Pseudospectral Solutions of Elliptic Problems SIAM J. Sci. Stat. Comput. 11 311-342
  • [3] Deville M. O.(1997)Finite difference preconditioning cubic spline collocation method of elliptic equations Numer. Math. 77 83-103
  • [4] Mund E. H.(1995)Preconditioning cubic spline collocation discretization of elliptic equations Numer. Math. 72 39-72
  • [5] Kim H. O.(1980)Spectral methods for problems in complex geometries J. Comp. Physics 37 70-92
  • [6] Kim S. D.(1986)GMRES: A generalized minimal residual algorithm for solving non-symmetric linear systems SIAM J. Sci. Stat. Comput. 7 856-869
  • [7] Lee Y. H.(1992)Bi-CGSTAB: A fast and smoothly converging variant of BiCG for the solution of nonsymmetric linear system SIAM J. Sci. Stat. Comput. 13 631-644
  • [8] Kim S. D.(undefined)undefined undefined undefined undefined-undefined
  • [9] Parter S. V.(undefined)undefined undefined undefined undefined-undefined
  • [10] Orszag S. A.(undefined)undefined undefined undefined undefined-undefined