Local surrogate models with reduced dimensionality via overlapping domain decomposition and proper generalized decomposition

TL;DR

This paper introduces an efficient non-intrusive method combining domain decomposition and proper generalized decomposition to create low-dimensional surrogate models for linear elliptic parametric problems, enhancing computational efficiency.

Contribution

It presents a novel algorithm that integrates overlapping domain decomposition with PGD, enabling local surrogate models with reduced parametric dimensionality for elliptic problems.

Findings

Demonstrates efficiency through numerical results

Achieves minimal parametric dimensionality in local models

Provides a fully non-intrusive offline-online framework

Abstract

We propose an efficient algorithm that combines overlapping domain decomposition and proper generalized decomposition (PGD) to construct surrogate models of linear elliptic parametric problems. The technique is composed of an offline and an online phase that can be implemented in a fully non-intrusive way. The online phase relies on a substructured algebraic formulation of the alternating Schwarz method, while the offline phase exploits the linearity of the boundary value problem to characterize a PGD basis and generate local surrogate models, with minimal parametric dimensionality, in each subdomain. Numerical results show the efficiency of the proposed methodology.