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Article Dans Une Revue Multiscale Science and Engineering Année : 2022

Double-Preconditioning Techniques for Fractional Partial Differential Equation Solvers

Résumé

This paper is devoted to the numerical computation of fractional linear systems. The proposed approach is based on an efficient computation of Cauchy integrals allowing to estimate the real power of a (sparse) matrix A. A first preconditioner M is used to reduce the length of the Cauchy integral contour enclosing the spectrum of M A, hence allowing for a large reduction of the number of quadrature nodes along the integral contour. Next, ILU-factorizations are used to efficiently solve the linear systems involved in the computation of approximate Cauchy integrals. Numerical examples related to stationary (deterministic or stochastic) fractional Poisson-like equations are finally proposed to illustrate the methodology.
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Dates et versions

hal-02340820 , version 1 (31-10-2019)

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Xavier Antoine, Emmanuel Lorin. Double-Preconditioning Techniques for Fractional Partial Differential Equation Solvers. Multiscale Science and Engineering, 2022, 4, pp.137-160. ⟨10.1007/s42493-022-00084-x⟩. ⟨hal-02340820⟩
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