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


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
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