Work

Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems

Year: 2024

Type: article

Abstract: Common formulations of the eddy current problem involve either vector or scalar potentials, each with its own advantages and disadvantages. An impasse arises when using scalar potential-based formulations in the presence of conductors with non-trivial topology. A remedy is to augment the approximation spaces with generators of the first cohomology group. Most existing algorithms for this require a special, e.g., hierarchical, finite element basis construction. Using insights from de Rham complex approximation with splines, we show that additional conditions are here unnecessary. Spanning tree techniques can be adapted to operate on a hexahedral mesh resulting from isomorphisms between spline spaces of differential forms and de Rham complexes on an auxiliary control mesh.

Source: Advances in Computational Mathematics

DOI: 10.1007/s10444-024-10181-0

Authors: Bernard Kapidani, Melina Merkel, Sebastian Schöps, Rafael Vázquez

Institutions: École Polytechnique Fédérale de Lausanne, Technische Universität Darmstadt, Universidade de Santiago de Compostela

Language: English

Topic: Advanced Numerical Analysis Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090