Stefano Zampini

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A BDDC (Balancing Domain Decomposition by Constraints) preconditioner with a novel deluxe scaling, introduced by Dohrmann for problems with more than one variable coefficient, is extended to Isogeometric Analysis of scalar elliptic problems. This new scaling turns out to be much more powerful than BDDC with standard ρand stiffness scaling studied in a(More)
A BDDC domain decomposition preconditioner is defined by a coarse component, expressed in terms of primal constraints, a weighted average across the interface between the subdomains, and local components given in terms of solvers of local subdomain problems. BDDC methods for vector field problems discretized with Raviart-Thomas finite elements are(More)
Balancing domain decomposition by constraints (BDDC) algorithms are constructed and analyzed for the system of almost incompressible elasticity discretized with Gauss–Lobatto– Legendre spectral elements in three dimensions. Initially mixed spectral elements are employed to discretize the almost incompressible elasticity system, but a positive definite(More)
Isogeometric analysis has been introduced as an alternative to finite element methods in order to simplify the integration of CAD software and the discretization of variational problems of continuum mechanics. In contrast with the finite element case, the basis functions of isogeometric analysis are often not nodal. As a consequence, there are fat(More)
A class of preconditioners based on balancing domain decomposition by constraints methods is introduced in the Portable, Extensible Toolkit for Scientific Computation (PETSc). The algorithm and the underlying nonoverlapping domain decomposition framework are described with a specific focus on their current implementation in the library. Available user(More)
The cardiac Bidomain model consists in a reaction-diffusion system of PDEs for the intraand extra-cellular cardiac potentials coupled with a nonlinear system of ODEs accounting for the cellular model of ionic currents. Fully implicit methods in time have been considered in a few studies, see e.g. [16] and references therein. As in most of previous work (see(More)
BDDC algorithms are constructed and analyzed for the system of almost incompressible elasticity discretized with Gauss-Lobatto-Legendre spectral elements in three dimensions. Initially mixed spectral elements are employed to discretize the almost incompressible elasticity system, but a positive definite reformulation is obtained by eliminating all pressure(More)
Balancing Neumann–Neumann preconditioners are constructed, analyzed and numerically studied for the cardiac Bidomain model in three-dimensions. This reaction–diffusion system is discretized by low-order finite elements in space and implicit–explicit methods in time, yielding very ill-conditioned linear systems that must be solved at each time step. The(More)