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A Meshless Local Petrov-Galerkin Method for Magnetic Diffusion in Non-magnetic Conductors

J.N. Johnson1, J.M. Owen2
UC Davis/LLNL, Livermore, CA, USA.
LLNL, Livermore, CA, USA.

Computer Modeling in Engineering & Sciences 2007, 22(3), 165-188.


In this paper, we propose a Meshless Local Petrov-Galerkin method for studying the diffusion of a magnetic field within a non-magnetic (μ = μ0) conducting medium with non-homogeneous and anisotropic electrical resistivity. We derive a local weak form for the magnetic diffusion equation and discuss the effects of different trial/test functions and nodal spacings on its solution. We then demonstrate that the method produces convergent results for several relevant one-dimensional test problems for which solutions are known. This method has the potential to be combined with other mesh-free methods such as Smoothed Particle Hydrodynamics (SPH) to solve problems in resistive magnetohydrodynamics, which has several applications in astrophysics, plasma physics, and engineering.


meshless method, local weak form, magnetic field, diffusion, resistivity, conductivity, conductor, moving least squares, anisotropic, Maxwell's equations, magnetohydrodynamics

Cite This Article

Johnson, J., Owen, J. (2007). A Meshless Local Petrov-Galerkin Method for Magnetic Diffusion in Non-magnetic Conductors. CMES-Computer Modeling in Engineering & Sciences, 22(3), 165–188.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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