A new MOX Report entitled “A mixed-dimensional model for the electrostatic problem on coupled domains” by Crippa, B., Scotti, A.; Villa, A has appeared in the MOX Report Collection. Check it out here: https://www.mate.polimi.it/biblioteca/add/qmox/74-2024.pdf Abstract: We derive a mixed-dimensional 3D-1D formulation of the electrostatic equation in two domains with different dielectric constants to compute, with an affordable computational cost, the electric field and potential in the relevant case of thin inclusions in a larger 3D domain. The numerical solution is obtained by Mixed Finite Elements for the 3D problem and Finite Elements on the 1D domain. We analyze some test cases with simple geometries to validate the proposed approach against analytical solutions, and perform comparisons with the fully resolved 3D problem. We treat the case where ramifications are present in the one-dimensional domain and show some results on the geometry of an electrical treeing, a ramified structure that propagates in insulators causing their failure.
You may also like
A new MOX Report entitled “PTPI-DL-ROMs: Pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs” by Brivio, S.; Fresca, S.; […]
A new MOX Report entitled “A NLP-based semi-automatic identification system for delays in follow-up examinations: an Italian case study on clinical referrals” […]
A new MOX Report entitled “A scalable well-balanced numerical scheme for a depth-integrated lava flow model” by Gatti, F.; de Falco, C.; […]
A new MOX Report entitled “Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression” by Cicci, L.; […]