Abstract
We have implemented a numerical code (ReLPM, Real Leja Points Method) for polynomial interpolation of the matrix exponential propagators exp (\({\it \Delta}\) tA) v and ϕ(\({\it \Delta}\) 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 equations.
Work supported by the MIUR PRIN 2003 project “Dynamical systems on matrix manifolds: numerical methods and applications” (co-ordinator L. Lopez, University of Bari), by the ex-60% funds of the University of Padova, and by the GNCS-INdAM.
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Keywords
- Spatial Discretization
- Polynomial Interpolation
- Krylov Subspace
- Superlinear Convergence
- Homogeneous Dirichlet Boundary Condition
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Bergamaschi, L., Caliari, M., Martínez, A., Vianello, M. (2006). Comparing Leja and Krylov Approximations of Large Scale Matrix Exponentials. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758549_93
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DOI: https://doi.org/10.1007/11758549_93
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