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Volume 2, Issue 4
A Jumping Multigrid Method Via Finite Element Extrapolation.

C. Wen & T.-Z. Huang

Int. J. Numer. Anal. Mod. B,2 (2011), pp. 281-297

Published online: 2011-02

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  • 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 (h_j, j\lesssim2i) finite element problems locally on each such coarse-level element. That is, we can skip the finite element problem on middle levels, h_{i+1}, h{_i+2},..., h_{j-1}. Loosely speaking, this jumping multigrid method solves a linear system of O(N) equations by a memory of O(p\sqrt{N}), and by a parallel computation of O(p\sqrt{N}).
  • Keywords

elliptic equation finite element extrapolation uniform grid superconvergence

  • AMS Subject Headings

65M60 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-2-281, author = {C. Wen and T.-Z. Huang}, title = {A Jumping Multigrid Method Via Finite Element Extrapolation.}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2011}, volume = {2}, number = {4}, pages = {281--297}, 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 (h_j, j\lesssim2i) finite element problems locally on each such coarse-level element. That is, we can skip the finite element problem on middle levels, h_{i+1}, h{_i+2},..., h_{j-1}. Loosely speaking, this jumping multigrid method solves a linear system of O(N) equations by a memory of O(p\sqrt{N}), and by a parallel computation of O(p\sqrt{N}).}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/313.html} }
TY - JOUR T1 - A Jumping Multigrid Method Via Finite Element Extrapolation. AU - C. Wen & T.-Z. Huang JO - International Journal of Numerical Analysis Modeling Series B VL - 4 SP - 281 EP - 297 PY - 2011 DA - 2011/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/313.html KW - elliptic equation KW - finite element KW - extrapolation KW - uniform grid KW - superconvergence AB - 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 (h_j, j\lesssim2i) finite element problems locally on each such coarse-level element. That is, we can skip the finite element problem on middle levels, h_{i+1}, h{_i+2},..., h_{j-1}. Loosely speaking, this jumping multigrid method solves a linear system of O(N) equations by a memory of O(p\sqrt{N}), and by a parallel computation of O(p\sqrt{N}).
C. Wen and T.-Z. Huang. (2011). A Jumping Multigrid Method Via Finite Element Extrapolation.. International Journal of Numerical Analysis Modeling Series B. 2 (4). 281-297. doi:
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