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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 <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</math> | + | 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 , where is a constant, and and are the characteristic sizes of the mesh and the subobjects, respectively. As can be chosen almost freely, the condition number can theoretically be as small as . We will discuss the pros and cons of the preconditioner and its application to heterogeneous problems. Numerical results on supercomputers are provided.
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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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