A mixed-dimensional model for the electrostatic problem on coupled domains
Year: 2025
Type: article
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.
Source: Journal of Computational Physics
Authors: Beatrice Crippa, Anna Scotti, Andrea Villa
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,980
OpenAlex ID: W4409534291