Article citationsMore>>

Polthier, K. and Preu, E. (2003) Identifying Vector Fields Singularities Using a Discrete Hodge Decomposition. In: Hege, H.C. and Polthier, K., Eds., Visualization and Mathematics III, Springer, Heidelberg, 113-134.
https://doi.org/10.1007/978-3-662-05105-4_6

has been cited by the following article:

• TITLE: Helmholtz Decomposition of Vector Fields Using an Optimal Preconditioned Conjugate Gradient Algorithm

  AUTHORS: Jorge Lopez

  KEYWORDS: Helmholtz Decomposition, Self-Adjoint Operator, Optimal Preconditioning, Finite Element

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.5, May 25, 2023

  ABSTRACT: In this article, we study numerically a Helmholtz decomposition methodology, based on a formulation of the mathematical model as a saddle-point problem. We use a preconditioned conjugate gradient algorithm, applied to an associated operator equation of elliptic type, to solve the problem. To solve the elliptic partial differential equations, we use a second order mixed finite element approximation for discretization. We show, using 2-D synthetic vector fields, that this approach, yields very accurate solutions at a low computational cost compared to traditional methods with the same order of approximation.