Stochastic finite integration technique for magnetostatic problems

Both non-intrusive and intrusive stochastic approaches based on Polynomial Chaos Expansion are presented for the Finite Integration Technique over generic polyhedral grids for three-dimensional magnetostatic linear problems. Such algorithms outperform Monte Carlo methods (when the number of random parameters is small), both in terms of accuracy and efficiency. A novel algorithm for the intrusive approach is also provided, by which the intrusive approach becomes less computationally expensive than the non-intrusive approach. Validation is carried out by solving a magnetic circuit where the reluctivity is uncertain.