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DOI 10.5286/raltr.2008031
Persistent URL http://purl.org/net/epubs/work/50394
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Record Id 50394
Title Discrete fractional Sobolev norms for domain decomposition preconditioning
Abstract We present a new approach for preconditioning the interface Schur complement arising in domain decomposition of second-order scalar elliptic problems. The preconditioners are discrete interpolation norms recently introduced in [3]. In particular, we employ discrete representations of norms for the Sobolev space of index 1/2 to approximate the Steklov-Poincar´e operators arising from non-overlapping one-level domain decomposition methods. We use the coercivity and continuity of the Schur complement with respect to the preconditioning norm to derive mesh-independent bounds on the convergence of iterative solvers. We also address the case of non-constant coefficients by considering the interpolation of weighted spaces and the corresponding discrete norms.
Organisation CSE , CSE-NAG , STFC
Keywords Domain Decomposition , SSTD 2008-2009 , Interpolation spaces
Funding Information
Related Research Object(s): 49210210
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2008-031. STFC, 2008. aklRALTR-2008-31.pdf 2008