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

We apply the proper generalized decomposition (PGD) to a static electrothermal model subject to uncertainties. The quadratic electrothermal coupling term is non-standard and requires the introduction of a trilinear form. We use an existing finite integration technique (FIT)-based solver to demonstrate the opportunities of integrating the PGD in existing codes. The obtained reduced model approximates the temperature distribution in a voltage-excited microelectronic chip package that exhibits 12 wires of uncertain length.