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 -