TY  - EJOU
AU  - Johnson, J.N.  
AU  - Owen, J.M.  

TI  - A Meshless Local Petrov-Galerkin Method for Magnetic Diffusion in Non-magnetic Conductors
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2007
VL  - 22
IS  - 3
SN  - 1526-1506

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

DO  - 10.3970/cmes.2007.022.165