Maria-Cecilia Rivara
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Index Terms
- Design and data structure of fully adaptive, multigrid, finite-element software
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Reviews
R. Bruce Simpson
The major feature of this paper for the reviewer was the discussion of a data structure for representing a nested series of general triangular grids generated by essentially arbitrary (conforming) refinement strategies; that is an alternative to the refinement tree list structures (cf., Babuska and Rheinboldt (see, e.g., [1]), and Bank and Sherman [2]). The author indicates how this data structure is used to support the multigrid iterative method for solving finite element equations on the series of grids and discusses, briefly, conforming mesh refinement strategies. The proposed data structure is based on storing the vertex to vertex incidence relations of the mesh, rather than the triangles directly. As the author points out this will be familiar to readers of sparse matrix literature from the compact row-wise representation of a finite element matrix for a single mesh. The author indicates how this basic list structure can be extended to accommodate refinement, and the multigrid method, in a way which appears to be more storage efficient than refinement tree schemes. Computational studies for two boundary value problems, using an implementation of the schemes for adaptive refinement, uniform refinements, and multigrid solutions, are included. The accuracy versus number of unknowns results reported are interesting, but more germane to the subject matter of the paper would have been a report on efficiency performance of the data structure plus multigrid solver. Nevertheless, this rates with the reviewer as an important paper for anyone interested in dynamic software for PDEs.
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