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Short Course on Tensor Numerical Methods for Multidimensional PDEs

Date

Apr. 6 ~ Apr. 12, 2017

Lecturer

Venue

Room 601 & 602, Pao Yue-Kong Library, Minhang Campus, Shanghai Jiao Tong University

Application and Registration

No registration fee. Participants should cover their own lodging and meals.

Schedule

Date Time Title Venue
Apr. 6 14:00 ~ 15:00 Lecture 1. Approximation of bivariate functions by separation of variables. Matrix case. 601
  15:00 ~ 16:00 Lecture 2. Matrix SVD, EVD, Cholesky decompositions. FFT transform. Kronecker product. 601
  16:00 ~ 17:00 Lecture 3. Matrix factorizations, examples and exercises in Matlab (Cholesky, LU, QR, Kron). 601
Apr. 7 14:00 ~ 15:00 Lecture 4. Basic rank-structured tensor formats: canonical (CP), Tucker decompositions. 601
  15:00 ~ 16:00 Lecture 5. Approximation of multivariate functions by the canonical and Tucker tensors. 601
  16:00 ~ 17:00 Lecture 6. Algorithms for Tucker decomposition with Matlab examples. Canonical-to-Tucker algorithm. 601
Apr. 10 09:00 ~ 10:00 Lecture 7. Polynomial and Sinc approximation of multivariate functions. Separable approximation in analytic form via the Laplace transform. 601
  10:00 ~ 11:00 Lecture 8. Matrix product states (MPS, TT) decomposition. Quantized tensor approximation in log-complexity (QCan, QTT). Super-fast integration. 601
  11:00 ~ 12:00 Lecture 9. Exercises in Matlab on sinc- and QTT approximation of discretized functions. 601
Apr. 11 14:00 ~ 15:00 Lecture 10. Operators in many dimensions. Superfast Laplacian inverse, QTT-FFT and convolution. 602
  15:00 ~ 16:00 Lecture 11. Multi-parametric (stochastic) PDEs. Preconditioning in many dimensions. 602
  16:00 ~ 17:00 Lecture 12. Calculation of 3D integral operators in 1D complexity. Fast Hartree-Fock solver. Excitation energies by the Bethe-Salpeter equation. 602
Apr. 12 09:00 ~ 10:00 Lecture 13. Time-dependent (parabolic) problems in d + 1 formulation. Example of chemical master equation. 601
  10:00 ~ 11:00 Lecture 14. Equations with oscillating coecients. Asymptotic homogenization. The Hartree-Fock on lattice structured compounds. 601
  11:00 ~ 12:00 Lecture 15. Super-fast summation of electrostatic potentials on nite lattices with defects. Range separated tensor formats and application to general many-particle systems. 601

Reference

  1. Recommended literature for getting the preliminary impression (plus some knowledge in numerical linear algebra and Matlab programing):
    • B.N. Khoromskij. Introduction to tensor numerical methods in scientific computing. Lecture Notes, Preprint 06-2011, University of Zuerich, 2010.
    • B.N. Khoromskij. Tensors-structured Numerical Methods in Scientific Computing: Survey on Recent Advances. Chemometr. Intell. Lab. Syst. 110 (2012), 1-19.
    • Boris N. Khoromskij. Tensor Numerical Methods for High-dimensional PDEs: Basic Theory and Initial Applications. ESAIM: Proceedings and Surveys, January 2015, Vol. 48, p. 1-28. E-preprint arXiv:1408.4053, 2014.
    • V. Khoromskaia and B.N. Khoromskij. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies. Phys. Chem. Chem. Phys., 17:31491 - 31509, 2015 (open access).
    • T. G. Kolda and B. W. Bader. Tensor Decompositions and Applications. SIAM Rev. 51(3) (2009) 455–500.
  2. The slides for each of one-day lecture (3-hours lectures) will be distributed one day before the lecture day (say, slides for the first 3 lectures distribute on April 5th).
  3. Students will need Matlab for programming practices.

Contact Us

Yiqiong Yu

Directions to INS

http://ins.sjtu.edu.cn/for-vistors/arrive.html