@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 (<i>μ = μ<sub>0</sub></i>) 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}
}