scholarly journals Existence of dynamical low-rank approximations to parabolic problems

2020 ◽  
pp. 1
Author(s):  
Markus Bachmayr ◽  
Henrik Eisenmann ◽  
Emil Kieri ◽  
André Uschmajew
Keyword(s):  
Low Rank ◽  
Parabolic Problems ◽  
Low Rank Approximations

scholarly journals Connectome smoothing via low-rank approximations

2019 ◽  
Vol 38 (6) ◽  
pp. 1446-1456 ◽  
Author(s):  
Runze Tang ◽  
Michael Ketcha ◽  
Alexandra Badea ◽  
Evan D. Calabrese ◽  
Daniel S. Margulies ◽  
...  
Keyword(s):  
Low Rank ◽  
Low Rank Approximations

scholarly journals Computing Low-Rank Approximations of Large-Scale Matrices with the Tensor Network Randomized SVD

2018 ◽  
Vol 39 (3) ◽  
pp. 1221-1244 ◽  
Author(s):  
Kim Batselier ◽  
Wenjian Yu ◽  
Luca Daniel ◽  
Ngai Wong
Keyword(s):  
Large Scale ◽  
Low Rank ◽  
Tensor Network ◽  
Low Rank Approximations

scholarly journals Low-Rank Space-Time Decoupled Isogeometric Analysis for Parabolic Problems with Varying Coefficients

2019 ◽  
Vol 19 (1) ◽  
pp. 123-136 ◽  
Author(s):  
Angelos Mantzaflaris ◽  
Felix Scholz ◽  
Ioannis Toulopoulos
Keyword(s):  
Isogeometric Analysis ◽  
Evolution Equations ◽  
Space Time ◽  
Point Of View ◽  
Low Rank ◽  
Parabolic Problems ◽  
Computational Point ◽  
Varying Coefficients ◽  
Analysis Scheme ◽  
Parabolic Evolution Equations

AbstractIn this paper we present a space-time isogeometric analysis scheme for the discretization of parabolic evolution equations with diffusion coefficients depending on both time and space variables. The problem is considered in a space-time cylinder in {\mathbb{R}^{d+1}}, with {d=2,3}, and is discretized using higher-order and highly-smooth spline spaces. This makes the matrix formation task very challenging from a computational point of view. We overcome this problem by introducing a low-rank decoupling of the operator into space and time components. Numerical experiments demonstrate the efficiency of this approach.

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