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== Abstract == | == Abstract == | ||
| − | A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices between pairs of subedges) is presented. We are able to show that the condition number of the preconditioner is bounded by C 1 + log(L | + | A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices between pairs of subedges) is presented. We are able to show that the condition number of the preconditioner is bounded by <math>C(1 + log(\frac {L}{h}))^2</math>, where <math>C</math> is a constant, and <math>h</math> and <math>L</math> are the characteristic sizes of the mesh and the subobjects, respectively. As <math>L</math> can be chosen almost freely, the condition number can theoretically be as small as <math>O(1)</math>. We will discuss the pros and cons of the preconditioner and its application to heterogeneous problems. Numerical results on supercomputers are provided. |
== Full document == | == Full document == | ||
<pdf>Media:Draft_Soriano_705589772-9822-document.pdf</pdf> | <pdf>Media:Draft_Soriano_705589772-9822-document.pdf</pdf> | ||
Latest revision as of 10:57, 21 February 2020
Abstract
A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices between pairs of subedges) is presented. We are able to show that the condition number of the preconditioner is bounded by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): C(1 + log(\frac {L}{h}))^2 , where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): C
is a constant, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): h
and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): L
are the characteristic sizes of the mesh and the subobjects, respectively. As Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): L
can be chosen almost freely, the condition number can theoretically be as small as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): O(1)
. We will discuss the pros and cons of the preconditioner and its application to heterogeneous problems. Numerical results on supercomputers are provided.
Full document
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Published on 01/01/2019
DOI: 10.1016/j.aml.2018.07.033
Licence: CC BY-NC-SA license
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