Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Low-order polynomial approximation of propagators for the time-dependent Schro¨dinger equation
Journal of Computational Physics
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
An interpolatory approximation of the matrix exponential based on Faber polynomials
Journal of Computational and Applied Mathematics
Exponential time differencing for stiff systems
Journal of Computational Physics
Interpolating discrete advection-diffusion propagators at Leja sequences
Journal of Computational and Applied Mathematics
Generalized integrating factor methods for stiff PDEs
Journal of Computational Physics
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
The LEM exponential integrator for advection-diffusion-reaction equations
Journal of Computational and Applied Mathematics
A second-order Magnus-type integrator for nonautonomous parabolic problems
Journal of Computational and Applied Mathematics
A parallel exponential integrator for large-scale discretizations of advection-diffusion models
PVM/MPI'05 Proceedings of the 12th European PVM/MPI users' group conference on Recent Advances in Parallel Virtual Machine and Message Passing Interface
Comparing leja and krylov approximations of large scale matrix exponentials
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
An exponential integrator for advection-dominated reactive transport in heterogeneous porous media
Journal of Computational Physics
Parallel inexact constraint preconditioners for saddle point problems
Euro-Par'11 Proceedings of the 17th international conference on Parallel processing - Volume Part II
Banded target matrices and recursive FSAI for parallel preconditioning
Numerical Algorithms
Journal of Computational Physics
Hi-index | 7.30 |
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.