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

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.