Angeles Martinez

A massively parallel exponential integrator for advection-diffusion models

This work considers the Real Leja Points Method (ReLPM), [M. Caliari, M. Vianello, L. Bergamaschi, Interpolating discrete advection-diffusion propagators at spectral Leja sequences, J. Comput. Appl. Math. 172 (2004) 79-99], 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(@DtA)v and @f(@DtA)v, @f(z)=(exp(z)-1)/z. A scalability analysis of the most important computational kernel inside the code, the parallel sparse matrix-vector product, has been performed, as well as an experimental study of the communication overhead. As a result of this study an optimized parallel sparse matrix-vector product routine has been implemented. The resulting code shows good scaling behavior even when using more than one thousand processors. The numerical results presented on a number of very large test cases gives experimental evidence that ReLPM is a reliable and efficient tool for the simulation of complex hydrodynamic processes on parallel architectures.

Parallel acceleration of krylov solvers by factorized approximate inverse preconditioners

This paper describes and tests a parallel implementation of a factorized approximate inverse preconditioner (FSAI) to accelerate iterative linear system solvers. Such a preconditioner reveals an efficient accelerator of both Conjugate gradient and BiCGstab iterative methods in the parallel solution of large linear systems arising from the discretization of the advection-diffusion equation. The resulting message passing code allows the solution of large problems leading to a very cost-effective algorithm for the solution of large and sparse linear systems.

Multisplitting Preconditioners Based on Incomplete CholeskiFactorizations

Let

Low-rank update of preconditioners for the inexact Newton method with SPD Jacobian

Ax=b

Comparing leja and krylov approximations of large scale matrix exponentials

be a linear system where

Parallel preconditioned conjugate gradient optimization of the Rayleigh quotient for the solution of sparse eigenproblems

A

Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning

is a symmetric positive definite matrix. Preconditioners for the conjugate gradient method based on multisplittings obtained by incomplete Choleski factorizations of

Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems

A

FSAI-based parallel Mixed Constraint Preconditioners for saddle point problems arising in geomechanics

are studied. The validity of these preconditioners when

A parallel exponential integrator for large-scale discretizations of advection-diffusion models

A