TY - GEN
T1 - A family of energy minimizing coarse spaces for overlapping schwarz preconditioners
AU - Dohrmann, Clark R.
AU - Klawonn, Axel
AU - Widlund, Olof B.
PY - 2008
Y1 - 2008
N2 - A simple and effective approach is presented to construct coarse spaces for overlapping Schwarz preconditioners. The approach is based on energy minimizing extensions of coarse trace spaces, and can be viewed as a generalization of earlier work by Dryja, Smith, and Widlund. The use of these coarse spaces in overlapping Schwarz preconditioners leads to condition numbers bounded by C(1 + H/δ)(1 + log(H/h)) for certain problems when coefficient jumps are aligned with subdomain boundaries. For problems without coefficient jumps, it is possible to remove the log(H/h) factor in this bound by a suitable enrichment of the coarse space. Comparisons are made with the coarse spaces of two other substructuring preconditioners. Numerical examples are also presented for a variety of problems.
AB - A simple and effective approach is presented to construct coarse spaces for overlapping Schwarz preconditioners. The approach is based on energy minimizing extensions of coarse trace spaces, and can be viewed as a generalization of earlier work by Dryja, Smith, and Widlund. The use of these coarse spaces in overlapping Schwarz preconditioners leads to condition numbers bounded by C(1 + H/δ)(1 + log(H/h)) for certain problems when coefficient jumps are aligned with subdomain boundaries. For problems without coefficient jumps, it is possible to remove the log(H/h) factor in this bound by a suitable enrichment of the coarse space. Comparisons are made with the coarse spaces of two other substructuring preconditioners. Numerical examples are also presented for a variety of problems.
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U2 - 10.1007/978-3-540-75199-1_28
DO - 10.1007/978-3-540-75199-1_28
M3 - Conference contribution
AN - SCOPUS:70349607199
SN - 9783540751984
T3 - Lecture Notes in Computational Science and Engineering
SP - 247
EP - 254
BT - Domain Decomposition Methods in Science and Engineering XVII
T2 - 17th International Conference on Domain Decomposition Methods
Y2 - 3 July 2006 through 7 July 2006
ER -