A novel technique for cohomology computations in engineering practice

  title={A novel technique for cohomology computations in engineering practice},
  author={Pawel Dlotko and Ruben Specogna},
  journal={Computer Methods in Applied Mechanics and Engineering},
  • P. Dlotko, R. Specogna
  • Published 2013
  • Mathematics, Computer Science
  • Computer Methods in Applied Mechanics and Engineering
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.
Optimal Cohomology Generators for 2-D Eddy-Current Problems in Linear Time
  • R. Specogna
  • Mathematics
    IEEE Transactions on Magnetics
  • 2013
An automatic and efficient algorithm to find cohomology generators suitable for 2-D eddy-current problems formulated by means of complementary formulations that produces optimal representatives of generators.
Lean Cohomology Computation for Electromagnetic Modeling
Modifications to the Dłotko–Specogna algorithm are introduced to compute a regular basis of the first cohomology group in practically the same time as the generation of a lazy Cohomology basis.
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.
Construction of a Finite Element Basis of the First de Rham Cohomology Group and Numerical Solution of 3D Magnetostatic Problems
An efficient algorithm for the finite element approximation of harmonic fields and the numerical solution of three-dimensional magnetostatic problems is devised and a finite element basis of the first de Rham cohomology group of the computational domain is constructed.
Compatible discrete operator schemes on polyhedral meshes for elliptic and Stokes equations
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Robust full-wave Maxwell solver in time-domain using magnetic vector potential with edge elements
Magnetic vector potential (MVP) formulations are widely used in low-frequency eddy-current computation. For full-wave Maxwell problems with coupled resistive, inductive and capacitive effects,
Sheaf Theory as a Foundation for Heterogeneous Data Fusion


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Computational Topology - an Introduction
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Homology in Electromagnetic Boundary Value Problems
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