A Jumping Multigrid Method via Finite Element Extrapolation
نویسندگان
چکیده
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 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. Loosely speaking, this jumping multigrid method solves a linear system of O(N) equations by a memory of O( √ N), and by a parallel computation of O( √ N).
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