Efficient Cohomology Computation for Electromagnetic Modeling

  title={Efficient Cohomology Computation for Electromagnetic Modeling},
  author={Pawe D otko and Ruben Specogna},
  journal={Cmes-computer Modeling in Engineering \& Sciences},
  • 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… 
Cohomology in 3 DMagneto-Quasistatics Modeling
Electromagnetic modeling provides an interesting context to present a link between physical phenomena and homology and cohomology theories. Over the past twenty-five years, a considerable effort has
Cohomology in 3D Magneto-Quasistatics Modeling
Several definitions of cuts are surveyed, defined as generators of the first cohomology group over integers of a finite CW-complex, which has the virtue of providing an automatic, general and efficient algorithm for the computation of cuts.
A novel technique for cohomology computations in engineering practice
Lazy Cohomology Generators: A Breakthrough in (Co)homology Computations for CEM
This paper exploits the novel concept of lazy cohomology generators and a fast and general algorithm to compute them and introduces the use of minimal boundary generators to ease human-based basis selection and to obtain representatives of generators with compact support.
Topoprocessor: An Efficient Computational Topology Toolbox for h-Oriented Eddy Current Formulations
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
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
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.


On making cuts for magnetic scalar potentials in multiply connected regions
The problem of making cuts is of importance to scalar potential formulations of three‐dimensional eddy current problems. Its heuristic solution has been known for a century [J. C. Maxwell, A Treatise
An algorithm to make cuts for magnetic scalar potentials in tetrahedral meshes based on the finite element method
It is shown that a finite element discretization can make the problem reduce to that of harmonic functions subject to peculiar interelement constraints and the effective degrees of freedom in the element assembly are identified with topological constraints.
Toward an algorithm to make cuts for magnetic scalar potentials in finite element meshes
Sufficiency conditions for the intersection of different cuts show that when several cuts are required it may not be possible to avoid intersections, which clarifies the question of what data must necessarily be given in order for an algorithm to work.
A new set of basis functions for the discrete geometric approach
Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques [for EM field analysis]
In this paper, some structures which underlie the numerical treatment of second-order boundary value problems are studied using magnetostatics as an example. The authors show that the construction of
Cutting multiply connected domains
The calculation of electromagnetic fields in three dimensions using discrete finite element methods and potential formulations requires that the topological connectivity of sub-domains of the total
Automatic implementation of Cuts in Multiply Connected Magnetic Scalar Regions for 3D Eddy Current Models
Modelling non-conductors with the magnetic scalar potential is a very popular ap- proach to 3D eddy current problems. However, cuts are required if the magnetic scalar region is multiply connected.
Voltage and Current Sources for Massive Conductors Suitable With the $A{\hbox{-}}\chi$ Geometric Eddy-Current Formulation
The aim of the paper is to present an automatic and general technique, suitable with the A-χ geometric eddy-current formulation, to impose sources over massive conductors of any shape. For this
Electromagnetic Theory and Computation: A Topological Approach
Although topology was recognized by Gauss and Maxwell to play a pivotal role in the formulation of electromagnetic boundary value problems, it is a largely unexploited tool for field computation. The