Reduced order modeling for spectral element methods: current developments in Nektar++ and further perspectives

TL;DR

This paper discusses the development of reduced order modeling techniques for spectral element methods within the Nektar++ library, enabling faster parameter studies through POD-based intrusive methods with offline-online decomposition.

Contribution

It introduces the implementation of POD-based ROM for both continuous and discontinuous Galerkin spectral element methods in Nektar++, enhancing computational efficiency.

Findings

ROM enables fast evaluations for parameter studies

Implementation supports both continuous and discontinuous Galerkin methods

Open-source software ITHACA-SEM includes these ROM capabilities

Abstract

In this paper, we present recent efforts to develop reduced order modeling (ROM) capabilities for spectral element methods (SEM). Namely, we detail the implementation of ROM for both continuous Galerkin and discontinuous Galerkin methods in the spectral/hp element library Nektar++. The ROM approaches adopted are intrusive methods based on the proper orthogonal decomposition (POD). They admit an offline-online decomposition, such that fast evaluations for parameter studies and many-queries are possible. An affine parameter dependency is exploited such that the reduced order model can be evaluated independent of the large-scale discretization size. The implementation in the context of SEM can be found in the open-source model reduction software ITHACA-SEM.