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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)

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)

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)

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)

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)

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)

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)

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)