EXACT DE RHAM SEQUENCES OF FINITE
ELEMENT SPACES ON AGGLOMERATED ELEMENTS
PANAYOT S. VASSILEVSKI
Abstract. In this talk we introduce new finite element spaces
that can be constructed for agglomerates of standard elements
in 3–d. The agglomerates are assumed to have certain regular
structure in the sense that they share faces with closed boundaries
composed of 1-d edges. The spaces are subspaces of a originally
given de Rham sequence of respective H 1 -conforming, H(curl)–
conforming, H(div)–conforming and piecewise constant spaces.
The procedure can be recursively applied so that a sequence of
nested de Rham complexes can be constructed. As an applica-
tion, we use the sequence of nested counterparts of the respective
piecewise linears, the lowest order Nédélec, and the lowest order
Raviart–Thomas spaces, to construct V–cycle multigrid as precon-
ditioners in the conjugate gradient method. The latter AMGe (el-
ement agglomeration algebraic multigrid) methods appear to per-
form very similarly to the geometric MG in the case of uniformly
refined meshes.
This talk is based on a joint work with Joseph E. Pasciak, Texas
A&M University.
Center for Applied Scientific Computing, UC Lawrence Livermore
National Laboratory, P.O. Box 808, L-560, Livermore, CA 94551, U.S.A.
E-mail address: panayot@llnl.gov
This work was performed under the auspices of the U. S. Department of Energy
by University of California Lawrence Livermore National Laboratory under contract
W-7405-Eng-48.
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