An introduction to POD-Greedy-Galerkin reduced basis method

TL;DR

This paper introduces the POD-Greedy-Galerkin reduced basis method, a reduced order modeling technique that significantly decreases computational costs for parametric PDEs, enabling real-time simulations.

Contribution

It presents a comprehensive introduction to the POD-Greedy-Galerkin reduced basis method, highlighting its application to parametric PDEs and its advantages over traditional discretization methods.

Findings

Reduces computational cost for parametric PDEs

Enables real-time simulation capabilities

Provides reliable solutions with fewer resources

Abstract

Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or finite volume methods, the so-called full order models) are widely used to numerically solve these problems. However, when many physical and/or geometrical parameters are involved, the computational cost required by full order models becomes prohibitively expensive and this is not acceptable for real-time computations that are becoming more and more popular for rapid prototyping. Therefore, there is the need to introduce reduced order methods (also referred to as reduced basis methods) able to provide, as the input parameters change, fast and reliable solutions at a reduced computational cost.