An Arbitrary-Order Discontinuous Skeletal Method for Solving Electrostatics on General Polyhedral Meshes

• Published in: IEEE transactions on magnetics Vol. 53; no. 6; pp. 1 - 4
• Main Authors: Di Pietro, Daniele A., Kapidani, Bernard, Specogna, Ruben, Trevisan, Francesco
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Algebra; Boundary conditions; Computer architecture; Condensation; Convergence; Discontinuity; Electrostatics; Equivalence; Face; Finite element analysis; high order; Magnetism; Mathematical analysis; Mathematics; Microprocessors; Numerical Analysis; Operators; Poisson problem; polyhedral meshes; Surveying; Hybrid High-Order; Poisson problem; Mixed High-Order; Electrostatics; Polyhedral meshes
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2017.2666546

We present a numerical method named mixed high order (MHO) to obtain high order of convergence for electrostatic problems solved on general polyhedral meshes. The method, based on high-order local reconstructions of differential operators from face and cell degrees of freedom, exhibits a moderate computational cost thanks to hybridization and static condensation that eliminate cell unknowns. After surveying the method, we assess its effectiveness for 3-D problems by comparing, for the first time in literature, its performances with classical conforming finite elements. Moreover, we emphasize the algebraic equivalence of MHO in the lowest order with the analog formulation obtained with the discrete geometric approach or the finite-integration technique.