The hierarchical basis multigrid method |
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Authors: | Randolph E Bank Todd F Dupont Harry Yserentant |
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Institution: | (1) Department of Mathematics, University of California at San Diego, 92093 La Jolla, CA, USA;(2) Department of Mathematics, University of Chicago, 60637 Chicago, IL, USA;(3) Fachbereich Mathematik, Universität Dortmund, D-4600 Dortmund 50, Federal Republic of Germany |
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Abstract: | Summary We derive and analyze the hierarchical basis-multigrid method for solving discretizations of self-adjoint, elliptic boundary value problems using piecewise linear triangular finite elements. The method is analyzed as a block symmetric Gauß-Seidel iteration with inner iterations, but it is strongly related to 2-level methods, to the standard multigridV-cycle, and to earlier Jacobi-like hierarchical basis methods. The method is very robust, and has a nearly optimal convergence rate and work estimate. It is especially well suited to difficult problems with rough solutions, discretized using highly nonuniform, adaptively refined meshes. |
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Keywords: | AMS(MOS): 65F10 65F35 65N20 65N30 CR:G1 8 |
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