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Preconditioned iterative methods for space-time fractional advection-diffusion equations

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Zhi Zhao, Xiao-Qing Jin, Matthew M. Lin

Numerical Analysis · Submitted 17 Oct 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Numerical experiments are implemented to show the efficiency of our preconditioner, even with cases of variable coefficients.

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arXiv ID1510.05089 (version 1)
Pith IDBVUF2DT3, Pith's permanent record of this paper and its review
CitationMatthew M. Lin, Xiao-Qing Jin, Zhi Zhao. "Preconditioned iterative methods for space-time fractional advection-diffusion equations." arXiv:1510.05089 (2015). https://pith.science/paper/BVUF2DT3
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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.13 · mentions code or data availability 0.02.

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In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of space-time fractional advection-diffusion equations. To start with, an implicit method based on two-sided Gr\"unwald formulae is proposed with a discussion of the stability and consistency. Then, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient normal residual ({preconditioned} CGNR) method, with an easily constructed preconditioner, are developed. Importantly, because the resulting systems are Topelitz-like, the fast Fourier transform can be applied to significantly reduce the computational cost. Numerical experiments are implemented to show the efficiency of our preconditioner, even with cases of variable coefficients.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of space-time fractional advection-diffusion equations. contribution 0.89 0.37 0.06 asserted 0.51
s1 To start with, an implicit method based on two-sided Gr\"unwald formulae is proposed with a discussion of the stability and consistency. method 0.80 0.90 0.04 asserted 0.99
s2 Then, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient normal residual ({preconditioned} CGNR) method, with an easily constructed preconditioner, are developed. method 0.71 0.93 0.11 asserted 1.00
s3 Importantly, because the resulting systems are Topelitz-like, the fast Fourier transform can be applied to significantly reduce the computational cost. method 0.77 0.57 0.16 asserted 0.94
s4 Numerical experiments are implemented to show the efficiency of our preconditioner, even with cases of variable coefficients. result 0.95 0.96 0.53 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of space-time fractional advection-diffusion equations. To start with, an implicit method based on two-sided Gr\"unwald formulae is proposed with a discussion of the stability and consistency. Then, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient normal residual ({preconditioned} CGNR) method, with an easily constructed preconditioner, are developed. Importantly, because the resulting systems are Topelitz-like, the fast Fourier transform can be applied to significantly reduce the computational cost. Numerical experiments are implemented to show the efficiency of our preconditioner, even with cases of variable coefficients.

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