Reduced order modelling of nonlinear cross-diffusion systems

作者：

Highlights：

• Nonlinear cross-diffusion system is transformed into a linear-quadratic ODE system.

• Offline computation of the full order solutions, the reduced basis and online computation of the reduced solutions are separated.

• Applying the POD in two time intervals, the reduced solutions are computed efficiently.

• The reduced solutions allow fast prediction of the patterns.

摘要

•Nonlinear cross-diffusion system is transformed into a linear-quadratic ODE system.•Offline computation of the full order solutions, the reduced basis and online computation of the reduced solutions are separated.•Applying the POD in two time intervals, the reduced solutions are computed efficiently.•The reduced solutions allow fast prediction of the patterns.

论文关键词：Pattern formation,Finite differences,Entropy,Proper orthogonal decomposition,Principal interval decomposition,Tensor algebra

论文评审过程：Received 9 June 2020, Revised 24 January 2021, Accepted 26 January 2021, Available online 22 February 2021, Version of Record 22 February 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126058