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extrapolation

By Chuanmiao Chen, Hongling Hu, Ziqing Xie and Shangyou ZhangChuanmiao Chen, Hongling Hu, Ziqing Xie and Shangyou Zhang

Abstract

The multigrid method solves the finite element equations in optimal order, i.e., solving a linear system of O(N) equations in O(N) arithmetic operations. Based on low level solutions, we can use finite element extrapolation to obtain the high-level finite element solution on some coarse-level element boundary, at an higher accuracy O(h 4 i). Thus, we can solve higher level (hj, j < ∼ 2i) finite element problems locally on each such coarse-level element. That is, we can skip the finite element problem on middle levels, hi+1, hi+2,..., hj−1. Roughly speaking, such a jumping multigrid method solves an order O(N) = O(2 2di) linear system of equations by a memory of O ( √ N) = O(2 di), and by a parallel computation of O ( √ N), where d is the space dimension. elliptic equation, finite element, extrapolation, uniform grid, super-Keywords. convergence

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.227.4705
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