## 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 ${\displaystyle C(1+log({\frac {L}{h}}))^{2}}$, where ${\displaystyle C}$ is a constant, and ${\displaystyle h}$ and ${\displaystyle L}$ are the characteristic sizes of the mesh and the subobjects, respectively. As ${\displaystyle L}$ can be chosen almost freely, the condition number can theoretically be as small as ${\displaystyle O(1)}$. 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

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