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Using PGD to Solve Nonseparable Fractional Derivative Elliptic Problems

  • Shimin LinEmail author
  • Mejdi Azaiez
  • Chuanju Xu
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119)

Abstract

A family of tensor-based methods called Proper Generalized Decomposition (PGD) methods have been recently introduced for the a priori construction of the solution of several partial differential equations. This strategy was tested with success to demonstrate the capability of representing the solution with a significant reduction of the calculation and storage cost. In this paper, we suggest to test the efficiency of a such approach in solving general nonseparable fractional derivative elliptic problem. We will illustrate by several numerical experiments the efficiency of PGD, especially when the mesh or the coefficients vary with high contrast ratio. Although the PGD scheme considered in this paper is based on spectral method, it is extendable to other methods such as finite element method.

Notes

Acknowledgements

This work was supported by IDEX-Bordeaux research programm and CAMPUS FRANCE PHC CAI YUANPEI Research program.

Chuanju Xu is supported by NSF of China (Grant numbers 11471274, 11421110001, 51661135011, and 91630204.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamenChina
  2. 2.Bordeaux INP, I2M (UMR CNRS 5295)PessacFrance

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