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RESEARCH PRODUCT

Existence of dynamical low-rank approximations to parabolic problems

Henrik EisenmannEmil KieriMarkus BachmayrAndré Uschmajew

subject

Algebra and Number TheoryPartial differential equationRank (linear algebra)Applied MathematicsNumerical Analysis (math.NA)010103 numerical & computational mathematics01 natural sciencesManifold010101 applied mathematics35K15 35R01 (Primary) 15A69 65L05 (Secondary)Computational MathematicsMathematics - Analysis of PDEsScheme (mathematics)FOS: MathematicsApplied mathematicsUniquenessMathematics - Numerical Analysisddc:5100101 mathematicsDiffusion (business)Analysis of PDEs (math.AP)Mathematics

description

The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is based on a variational time-stepping scheme on the low-rank manifold. Moreover, this scheme is shown to be closely related to practical methods for computing such low-rank evolutions.

yearjournalcountryeditionlanguage
2021-03-23
http://arxiv.org/abs/2002.12197