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

Calvo, Juan

doi:10.1090/mcom/3028

A BDDC algorithm with deluxe scaling for $H(\text {curl})$ in two dimensions with irregular subdomains
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Math. Comp. 85 (2016), 1085-1111 Request permission

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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