A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes


Autoria(s): Yang, Qianqian; Turner, Ian; Moroney, Timothy J.; Liu, Fawang
Contribuinte(s)

Gu, YuanTong

Data(s)

2012

Resumo

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

Formato

application/pdf

Identificador

http://eprints.qut.edu.au/58432/

Relação

http://eprints.qut.edu.au/58432/1/paper_2012_08_15_new.pdf

http://www.iccm-2012.org/

Yang, Qianqian, Turner, Ian, Moroney, Timothy J., & Liu, Fawang (2012) A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes. In Gu, YuanTong (Ed.) 4th International Conference on Computational Methods (ICCM2012), 25-28 November 2012, Crowne Plaza, Gold Coast, QLD.

Direitos

Copyright 2012 [please consult the author]

Fonte

Faculty of Science and Technology; School of Mathematical Sciences; Science & Engineering Faculty

Palavras-Chave #010302 Numerical Solution of Differential and Integral Equations #Fractional Laplacian #matrix transfer technique #matrix function #Lanczos method #Krylov subspace #preconditioner #deflation #fractional Fisher’s equation
Tipo

Conference Paper