Efficient Cohomology Computation for Electromagnetic Modeling

@article{otko2010EfficientCC,
  title={Efficient Cohomology Computation for Electromagnetic Modeling},
  author={Pawe D otko and Ruben Specogna},
  journal={Cmes-computer Modeling in Engineering \& Sciences},
  year={2010},
  volume={60},
  pages={247-278}
}
  • Pawe D otko, R. Specogna
  • Published 1 April 2010
  • Computer Science
  • Cmes-computer Modeling in Engineering & Sciences
The systematic potential design is of high importance in computational electromagnetics. For example, it is well known that when the efficient eddycurrent formulations based on a magnetic scalar potential are employed in problems which involve conductive regions with holes, the so-called thick cuts are needed to make the boundary value problem well defined. Therefore, a considerable effort has been invested over the past twenty-five years to develop fast and general algorithms to compute thick… 
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TLDR
This paper introduces an upgrade in the Dłotko–Specogna (DS) algorithm that speeds up the execution for very complicated geometries, and provides a detailed comparison of computational resources needed for the topological pre-processing by the toolbox and the tool to compute a standard cohomology basis available in the mesh generator GMSH.
Fast Computation of Cuts With Reduced Support by Solving Maximum Circulation Problems
TLDR
A technique to efficiently compute optimal cuts required to solve 3-D eddy current problems by magnetic scalar potential formulations is presented, based on a novel graph-theoretic algorithm to solve a maximum circulation network flow problem in unweighted graphs that typically runs in linear time.
Physics inspired algorithms for (co)homology computation
TLDR
This paper presents a physics inspired algorithm for first cohomology group computations on three-dimensional complexes that solves one of the most long-lasting problems in low-frequency computational electromagnetics.
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