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A BDDC algorithm with deluxe scaling for $ H(curl)$ in two dimensions with irregular subdomains


Author: Juan G. Calvo
Journal: Math. Comp. 85 (2016), 1085-1111
MSC (2010): Primary 65N55, 65N30; Secondary 65F10, 35Q60
DOI: https://doi.org/10.1090/mcom/3028
Published electronically: August 18, 2015
MathSciNet review: 3454359
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Abstract: A bound is obtained for the condition number of a BDDC algorithm for problems posed in $ H($$ \text {curl})$ in two dimensions, where the subdomains are only assumed to be uniform in the sense of Peter Jones. For the primal variable space, a continuity constraint for the tangential average over each interior subdomain edge is imposed. For the averaging operator, a new technique named deluxe scaling is used. Our optimal bound is independent of jumps in the coefficients across the interface between the subdomains and depends only on a few geometric parameters of the decomposition. Numerical results that verify the result are shown, including some with subdomains with fractal edges and others obtained by a mesh partitioner.


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Additional Information

Juan G. Calvo
Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
Email: calvo@cims.nyu.edu

DOI: https://doi.org/10.1090/mcom/3028
Keywords: Domain decomposition, BDDC preconditioner, irregular subdomain boundaries, H(curl), Maxwell's equations, discontinuous coefficients, preconditioners
Received by editor(s): May 27, 2014
Received by editor(s) in revised form: November 3, 2014
Published electronically: August 18, 2015
Additional Notes: This work was supported in part by the National Science Foundation Grant DMS-1216564 and in part by the U.S. Department of Energy under contracts DE-FG02-06ER25718.
Article copyright: © Copyright 2015 American Mathematical Society

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