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- Luca Bergamaschi, Angeles Martinez
- VECPAR
- 2004

- Angeles Martinez, Luca Bergamaschi, Marco Caliari, Marco Vianello
- J. Computational Applied Mathematics
- 2009

for the exponential integration of large-scale sparse systems of ODEs, generated by Finite Element or Finite Difference discretizations of 3-D advection-diffusion models. We present an efficient parallel implementation of ReLPM for polynomial interpolation of the matrix exponential propagators exp(tA)v and ϕ(tA)v, ϕ(z) = (exp(z) − 1)/z. A scalability… (More)

- Luca Bergamaschi, Rafael Bru, Angeles Martinez
- Mathematical and Computer Modelling
- 2011

In this note preconditioners for the Conjugate Gradient method are studied to solve the Newton system with a symmetric positive definite Jacobian. In particular, we define a sequence of preconditioners built by means of BFGS rank-two updates. Reasonable conditions are derived which guarantee that the preconditioned matrices are not far from the identity in… (More)

- Luca Bergamaschi, Marco Caliari, Angeles Martinez, Marco Vianello
- International Conference on Computational Science
- 2006

We have implemented a numerical code (ReLPM, Real Leja Points Method) for polynomial interpolation of the matrix exponential propagators exp (∆tA) v and ϕ(∆tA) v, ϕ(z) = (exp (z) − 1)/z. The ReLPM code is tested and compared with Krylov-based routines, on large scale sparse matrices arising from the spatial discretization of 2D and 3D advection-diffusion… (More)

- Luca Bergamaschi, Angeles Martinez
- Euro-Par
- 2011

In this paper we propose a parallel implementation of the FSAI preconditioner to accelerate the PCG method in the solution of symmetric positive definite linear systems of very large size. This pre-conditioner is used as building block for the construction of an indefinite Inexact Constraint Preconditioner (ICP) for saddle point-type linear systems arising… (More)

- Luca Bergamaschi, Rafael Bru, Angeles Martinez, Mario Putti
- Advances in Engineering Software
- 2012

In this work, preconditioners for the iterative solution by Krylov methods of the linear systems arising at each Newton iteration are studied. The preconditioner is defined by means of a Broyden-type rank-one update of a given initial preconditioner, at each nonlinear iteration, as described in [5] where convergence properties of the scheme are… (More)

- Luca Bergamaschi, Angeles Martinez, Giorgio Pini
- J. Applied Mathematics
- 2012

The present paper describes a parallel preconditioned algorithm for the solution of partial eigenvalue problems for large sparse symmetric matrices, on parallel computers. Namely, we consider the Deflation-Accelerated Conjugate Gradient (DACG) algorithm accelerated by factorized sparse approximate inverse (FSAI) type preconditioners. We present an enhanced… (More)

- Luca Bergamaschi, Rafael Bru, Angeles Martinez, José Mas, Mario Putti
- Mathematical and Computer Modelling
- 2013

Preconditioners for the Conjugate Gradient method are studied to solve the Newton system with symmetric positive definite (SPD) Jacobian. Following the theoretical work in [1] we start from a given approximation of the inverse of the initial Jacobian, and we construct a sequence of preconditioners by means of a low rank update, for the linearized systems… (More)

- Luca Bergamaschi, Marco Caliari, Angeles Martinez, Marco Vianello
- PVM/MPI
- 2005

We propose a parallel implementation of the ReLPM (Real Leja Points Method) for the exponential integration of large sparse systems of ODEs, generated by Finite Element discretizations of 3D advection-diffusion models. The performance of our parallel exponential integrator is compared with that of a parallelized Crank-Nicolson (CN) integrator, where the… (More)

- Luca Bergamaschi, Angeles Martinez, Giorgio Pini
- PARCO
- 2003