A Meshless Local Petrov-Galerkin Method for Magnetic Diffusion in Non-magnetic Conductors
J.N. Johnson; and J.M. Owen

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 22, No. 3, pp. 165-188, 2007
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Keywords meshless method, local weak form, magnetic field, diffusion, resistivity, conductivity, conductor, moving least squares, anisotropic, Maxwell's equations, magnetohydrodynamics
Abstract In this paper, we propose a Meshless Local Petrov-Galerkin method for studying the diffusion of a magnetic field within a non-magnetic ($\mu = \mu _0$) 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.
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