  We introduce Gradient Particle Magnetohydrodynamics (GPM), a new Lagrangian
method for magnetohydrodynamics based on gradients corrected for the locally
disordered particle distribution. The development of a numerical code for MHD
simulation using the GPM algorithm is outlined. Validation tests simulating
linear and nonlinear sound waves, linear MHD waves, advection of magnetic
fields in a magnetized vortex, hydrodynamical shocks, and three-dimensional
collapse are presented, demonstrating the viability of an MHD code using GPM.
The characteristics of a GPM code are discussed and possible avenues for
further development and refinement are mentioned. We conclude with a view of
how GPM may complement other methods currently in development for the next
generation of computational astrophysics.
