# Proper Generalized Decomposition of Parameterized Electrothermal Problems Discretized by the Finite Integration Technique

## TL;DR

This paper applies proper generalized decomposition to a parameterized electrothermal model discretized by finite integration, creating a reduced model that handles high-dimensional uncertainties and coupling complexities.

## Contribution

It introduces a novel application of PGD to electrothermal problems with quadratic coupling, including a trilinear form, and demonstrates integration with existing finite integration technique solvers.

## Key findings

- Reduced model effectively manages high-dimensional uncertainties.
- Successfully incorporates quadratic electrothermal coupling with a trilinear form.
- Highlights challenges and opportunities in integrating PGD with existing solvers.

## Abstract

The proper generalized decomposition is applied to a static electrothermal model subject to uncertainties. A reduced model that circumvents the curse of dimensionality is obtained. The quadratic electrothermal coupling term is non-standard and requires the introduction of a trilinear form. An existing finite integration technique based solver is used to demonstrate the opportunities and difficulties in integrating the proper generalized decomposition in existing codes.