Summary
The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary simple abstract form. It is shown that their properties can be obtained from only a very small set of algebraic assumptions. The presentation is purely algebraic and it does not use any particular definition of method components, such as substructures and coarse degrees of freedom. It is then shown that P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC preconditioned operators are of the same algebraic form, and the standard condition number bound carries over to arbitrary abstract operators of this form. The equality of eigenvalues of BDDC and FETI-DP also holds in the minimalist abstract setting. The abstract framework is explained on a standard substructuring example.
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J. Mandel and B. Sousedík were supported by the National Science Foundation under grants CNS-0325314, CNS-0719641, and DMS-0713876.
B. Sousedík was supported by the program of the Information society of the Academy of Sciences of the Czech Republic 1ET400760509 and by the Grant Agency of the Czech Republic GA CR 106/05/2731.
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Mandel, J., Sousedík, B. BDDC and FETI-DP under minimalist assumptions. Computing 81, 269–280 (2007). https://doi.org/10.1007/s00607-007-0254-y
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DOI: https://doi.org/10.1007/s00607-007-0254-y