The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

An efficient implementation of an adaptive finite element method on distributed memory
systems requires an efficient linear solver. Most solver methods, which show scalability to a …

Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the
most successful domain decomposition solvers for partial differential equations. The …

A class of preconditioners based on balancing domain decomposition by constraints
methods is introduced in the Portable, Extensible Toolkit for Scientific Computation (PETSc) …

In this theoretical study, we explore how to automate the selection of weights and primal
constraints in BDDC methods for general SPD problems. In particular, we address the three …

The cardiac Bidomain model consists in a reaction–diffusion system of partial differential
equations which is often discretized by low-order finite elements in space and implicit …

A nonoverlapping domain decomposition algorithm is proposed to solve the linear system
arising from mixed finite element approximation of incompressible Stokes equations. A …

We consider the numerical solution of unsteady Stokes equations in patient-specific arterial-
like domains in 3D. A Stokes-like solver is a necessary component in a more sophisticated …

The FETI-DP (dual-primal finite element tearing and interconnecting) algorithms, proposed
by the authors in [SIAM J. Numer. Anal., 51 (2013), pp. 1235--1253] and [Internat. J. Numer …

SUMMARY A unified framework of dual‐primal finite element tearing and interconnecting
(FETI‐DP) algorithms is proposed for solving the system of linear equations arising from the …