English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we develop and analyse domain decomposition methods for linearsystems of equations arising from conforming finite element discretisations ofpositive Maxwell-type equations, namely for $\mathbf{H}(\mathbf{curl})$problems. It is well known that convergence of domain decomposition methodsrely heavily on the efficiency of the coarse space used in the second level. Wedesign adaptive coarse spaces that complement a near-kernel space made from thegradient of scalar functions. The new class of preconditioner is inspired bythe idea of subspace decomposition, but based on spectral coarse spaces, and isspecially designed for curl-conforming discretisations of Maxwell's equationsin heterogeneous media on general domains which may have holes. Our approachhas wider applicability and theoretical justification than the well-knownHiptmair-Xu auxiliary space preconditioner, with results extending to thevariable coefficient case and non-convex domains at the expense of a largercoarse space.

A robust and adaptive GenEO-type domain decomposition preconditioner for  $\mathbf{H}(\mathbf{curl})$ problems in general non-convex three-dimensional  geometries