1,408 research outputs found
Structure-preserving mesh coupling based on the Buffa-Christiansen complex
The state of the art for mesh coupling at nonconforming interfaces is
presented and reviewed. Mesh coupling is frequently applied to the modeling and
simulation of motion in electromagnetic actuators and machines. The paper
exploits Whitney elements to present the main ideas. Both interpolation- and
projection-based methods are considered. In addition to accuracy and
efficiency, we emphasize the question whether the schemes preserve the
structure of the de Rham complex, which underlies Maxwell's equations. As a new
contribution, a structure-preserving projection method is presented, in which
Lagrange multiplier spaces are chosen from the Buffa-Christiansen complex. Its
performance is compared with a straightforward interpolation based on Whitney
and de Rham maps, and with Galerkin projection.Comment: 17 pages, 7 figures. Some figures are omitted due to a restricted
copyright. Full paper to appear in Mathematics of Computatio
Combinatorial modulus and type of graphs
Let a be the 1-skeleton of a triangulated topological annulus. We
establish bounds on the combinatorial modulus of a refinement , formed by
attaching new vertices and edges to , that depend only on the refinement and
not on the structure of itself. This immediately applies to showing that a
disk triangulation graph may be refined without changing its combinatorial
type, provided the refinement is not too wild. We also explore the type problem
in terms of disk growth, proving a parabolicity condition based on a
superlinear growth rate, which we also prove optimal. We prove our results with
no degree restrictions in both the EEL and VEL settings and examine type
problems for more general complexes and dual graphs.Comment: 24 pages, 12 figure
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