  We present an algorithm for simulating the equations of ideal
magnetohydrodynamics and other systems of differential equations on an
unstructured set of points represented by sample particles. The particles move
with the fluid, so the time step is not limited by the Eulerian
Courant-Friedrichs-Lewy condition. Full spatial adaptivity is required to
ensure the particles fill the computational volume, and gives the algorithm
substantial flexibility and power. A target resolution is specified for each
point in space, with particles being added and deleted as needed to meet this
target. We have parallelized the code by adapting the framework provided by
GADGET-2. A set of standard test problems, including 1e-6 amplitude linear MHD
waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities is presented.
Finally we demonstrate good agreement with analytic predictions of linear
growth rates for magnetorotational instability in a cylindrical geometry. This
paper documents the Phurbas algorithm as implemented in Phurbas version 1.1.
