A reduced basis super-localized orthogonal decomposition for reaction-convection-diffusion problems
Journal article, 2024

This paper presents a method for the numerical treatment of reaction-convection-diffusion problems with parameter-dependent coefficients that are arbitrary rough and possibly varying at a very fine scale. The presented technique combines the reduced basis (RB) framework with the recently proposed super-localized orthogonal decomposition (SLOD). More specifically, the RB is used for accelerating the typically costly SLOD basis computation, while the SLOD is employed for an efficient compression of the problem's solution operator requiring coarse solves only. The combined advantages of both methods allow one to tackle the challenges arising from parametric heterogeneous coefficients. Given a value of the parameter vector, the method outputs a corresponding compressed solution operator which can be used to efficiently treat multiple, possibly non-affine, right-hand sides at the same time, requiring only one coarse solve per right-hand side.

Model order reduction

Reaction-convection-diffusion problems

Multiscale method

Reduced basis

Numerical homogenization

Parameter-dependent PDE

Author

Francesca Bonizzoni

Polytechnic University of Milan

Moritz Hauck

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Daniel Peterseim

University of Augsburg

Journal of Computational Physics

0021-9991 (ISSN) 1090-2716 (eISSN)

Vol. 499 112698

Subject Categories

Computer Science

DOI

10.1016/j.jcp.2023.112698

More information

Latest update

3/14/2024