Discrete fractional Sobolev norms for domain decomposition preconditioning

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DOI	10.5286/raltr.2008031
Persistent URL	http://purl.org/net/epubs/work/50394
Record Status	Checked
Record Id	50394
Title	Discrete fractional Sobolev norms for domain decomposition preconditioning
Contributors	M Arioli (STFC Rutherford Appleton Lab.), D Loghin (Birmingham U.), D Kourunis (Joannina U. and Stanford U.)
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
Licence Information:
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