Multilevel preconditioning and low‐rank tensor iteration for space–time simultaneous discretizations of parabolic PDEs

By Roman Andreev, Christine Tobler. 2015

48 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. V. Dolgov
2. Sergey V. Dolgov
3. Dmitry V. Savostyanov
4. Peter Benner
5. Martin Stoll
6. Akwum Onwunta
7. Boris N. Khoromskij
8. Ivan V. Oseledets

In Computational Mechanics

1. Sergey V. Dolgov
2. V. Dolgov
3. Dmitry V. Savostyanov
4. Peter Benner
5. Martin Stoll
6. Akwum Onwunta
7. Boris N. Khoromskij

In Computational Theory and Mathematics

1. V. Dolgov
2. Sergey V. Dolgov
3. Dmitry V. Savostyanov
4. Peter Benner
5. Martin Stoll
6. Akwum Onwunta
7. Ivan V. Oseledets
8. Boris N. Khoromskij

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “…include the use of approximate inverses for high-dimensional Laplace operators [151, 165, 172, 210], low-rank manipulation of the PDE coefficients [60], low-rank tensor approximation of multilevel preconditioners [8], and low-rank tensor diagonal preconditioners for wavelet discretizations [11].”
• ALTERNATING MINIMAL ENERGY METHODS FOR LINEAR SYSTEMS IN HIGHER DIMENSIONS∗ (2014, methodology): “, algorithms for the solution of linear systems [51, 21, 47, 38, 34, 31, 39, 2, 8, 4, 3], partial eigenproblems [41, 40, 24, 20], and Fourier transform [11].”
• Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, unknown): “, algorithms for the solution of linear systems [51, 21, 47, 38, 34, 31, 39, 2, 8, 4, 3], partial eigenproblems [41, 40, 24, 20], and Fourier transform [11].”
• Low-rank solvers for unsteady Stokes–Brinkman optimal control problem with random data (2016, methodology): “These properties allow to adopt classical 9 iterative methods such as MINRES or GMRES in an inexact fashion, keeping all Krylov vectors in the TT 10 format and performing the TT-SVD re-compression [33, 4, 1, 10].”