Author(s)

Jorge Lopez

UJAT, Tabasco, México.

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.

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

Lopez, J. (2023) Helmholtz Decomposition of Vector Fields Using an Optimal Preconditioned Conjugate Gradient Algorithm. Journal of Applied Mathematics and Physics, 11, 1337-1348. doi: 10.4236/jamp.2023.115086.