ACCELERATION OF A TWO-GRID METHOD FOR EIGENVALUE PROBLEMS

作者：Hu, Xiaozhe^*; Cheng, Xiaoliang

来源：Mathematics of Computation, 2011, 80(275): 1287-1301.

DOI：10.1090/S0025-5718-2011-02458-0

• Eigenvalue problems
• finite elements
• partial differential equations
• integral equations
• two-grid method

This paper provides a new two-grid discretization method for solving partial differential equation or integral equation eigenvalue problems. In 2001, Xu and Zhou introduced a scheme that reduces the solution of an eigenvalue problem on a finite element grid to that of one single linear problem on the same grid together with a similar eigenvalue problem on a much coarser grid. By solving a slightly different linear problem on the fine grid, the new algorithm in this paper significantly improves the theoretical error estimate which allows a much coarser mesh to achieve the same asymptotic convergence rate. Numerical examples are also provided to demonstrate the efficiency of the new method.

• 出版日期2011-7
• 单位浙江大学