Badia et al 2019a - Revision history

Cecilia.soriano at 09:57, 21 February 2020

2020-02-21T09:57:56Z

Cecilia.soriano at 09:57, 21 February 2020

2020-02-21T09:57:37Z

Cecilia.soriano: Cecilia.soriano moved page Draft Soriano 705589772 to Badia et al 2019a

2020-02-21T09:55:05Z

Cecilia.soriano moved page Draft Soriano 705589772 to Badia et al 2019a

Cecilia.soriano: Created page with " == Abstract == A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices betwee..."

2020-02-21T09:55:03Z

Created page with " == Abstract == A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices betwee..."

New page

== 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/h)2, where C is a constant, and h and L are the characteristic sizes of the mesh and the subobjects, respectively. As L can be chosen almost freely, the condition number can theoretically be as small as 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 ==
<pdf>Media:Draft_Soriano_705589772-9822-document.pdf</pdf>

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 == 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>(1). We will discuss the pros and cons of the preconditioner and its application to heterogeneous problems. Numerical results on supercomputers are provided.
+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 ==
 <pdf>Media:Draft_Soriano_705589772-9822-document.pdf</pdf>

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