ISSN:
1573-7691
Keywords:
Elliptic
;
spectral element
;
p-type finite element
;
iterative methods
;
multigrid
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract A variational spectral element multigrid algorithm is proposed, and results are presented for a one-dimensional Poisson equation on a finite interval. The key features of the proposed algorithm are as follows: the nested spaces and associated hierarchical bases are intra-element, resulting in simple data structures and rapid tensor-product sum-factorization evaluations; smoothing is effected by readily constructed and efficiently inverted (diagonal) Jacobi preconditioners; the technique is readily parallelized within the context of a medium-grained paradigm; and the (work-deflated) multigrid convergence rate $$\bar \rho $$ is bounded from above well below unity, and is only a weak function of the number of spectral elementsK, the (large) order of the polynomial approximation,N, and the number of multigrid levels,J. Preliminary tests indicate that these convergence properties persist in higher space dimensions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01061297
