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Evaluation of the Residual Vector in Global Element Calculations

Lookup NU author(s): Professor Chris Phillips


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The defining equations for the global element method [5], applied to the solution of (linear or nonlinear) elliptic partial differential equations, are most efficiently solved using an iterative scheme. It has been shown previously [6] that for a calculation in two dimensions, the operation count of such a scheme is Image (MN4) where M is the number of elements and N the size of the expansion used to approximate the solution in each element. This operation count results partly from the need to multiply an MN2 vector by an MN2 × MN2 matrix to form the residual vector at each iteration. We demonstrate here how the residual can be computed with the improved operation count of Image (MN2 ln N): an additional advantage of the new scheme is that the full diagonal blocks of the coefficient matrix need not be assembled.

Publication metadata

Author(s): Phillips C, Mohamed JL, Delves LM

Publication type: Article

Publication status: Published

Journal: Journal of Computational and Applied Mathematics

Year: 1987

Volume: 18

Issue: 3

Pages: 331-346

ISSN (print): 0377-0427

Publisher: Elsevier BV


DOI: 10.1016/0377-0427(87)90006-9


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