Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker-Planck Equation

@article{Dolgov2012FastSO,
  title={Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker-Planck Equation},
  author={S. V. Dolgov and Boris N. Khoromskij and Ivan V. Oseledets},
  journal={SIAM J. Scientific Computing},
  year={2012},
  volume={34}
}
In this paper we propose two schemes of using the so-called quantized tensor train (QTT)-approximation for the solution of multidimensional parabolic problems. First, we present a simple one-step implicit time integration scheme using a solver in the QTT-format of the alternating linear scheme (ALS) type. As the second approach, we use the global space-time formulation, resulting in a large block linear system, encapsulating all time steps, and solve it at once in the QTT-format. We prove the… CONTINUE READING

Citations

Publications citing this paper.
Showing 1-10 of 23 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 47 references

Constructive Representation of Functions in Tensor Formats

  • I. V. Oseledets
  • preprint 2010- 04, INM RAS, Moscow
  • 2010
Highly Influential
4 Excerpts

Superfast Fourier transform using QTT approximation

  • S. V. Dolgov, B. N. Khoromskij, D. V. Savostyanov
  • J. Fourier Anal. Appl., 18
  • 2012
1 Excerpt

Similar Papers

Loading similar papers…