@Article{cmes.2007.022.165, AUTHOR = {J.N. Johnson, J.M. Owen}, TITLE = {A Meshless Local Petrov-Galerkin Method for Magnetic Diffusion in Non-magnetic Conductors}, JOURNAL = {Computer Modeling in Engineering \& Sciences}, VOLUME = {22}, YEAR = {2007}, NUMBER = {3}, PAGES = {165--188}, URL = {http://www.techscience.com/CMES/v22n3/25056}, ISSN = {1526-1506}, ABSTRACT = {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.}, DOI = {10.3970/cmes.2007.022.165} }