Preconditioners and Tensor Product Solvers for Optimal Control Problems from Chemotaxis

Sergey Dolgov, John W. Pearson

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Abstract

In this paper, we consider the fast numerical solution of an optimal control formulation of the Keller--Segel model for bacterial chemotaxis. Upon discretization, this problem requires the solution of huge-scale saddle point systems to guarantee accurate solutions. We consider the derivation of effective preconditioners for these matrix systems, which may be embedded within suitable iterative methods to accelerate their convergence. We also construct low-rank tensor-train techniques which enable us to present efficient and feasible algorithms for problems that are finely discretized in the space and time variables. Numerical results demonstrate that the number of preconditioned GMRES iterations depends mildly on the model parameters. Moreover, the low-rank solver makes the computing time and memory costs sublinear in the original problem size.
Original languageEnglish
Pages (from-to)B1228-B1253
JournalSIAM Journal on Scientific Computing
Volume41
Issue number6
Early online date12 Nov 2019
DOIs
Publication statusPublished - 2019

Keywords

  • math.NA
  • 35Q93, 65F08, 65F10, 65N22, 92C17

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