  Magnetic nulls are ubiquitous in space plasmas, and are of interest as sites
of localized energy dissipation or magnetic reconnection. As such, a number of
methods have been proposed for detecting nulls in both simulation data and in
situ spacecraft data from Earth's magnetosphere. The same methods can be
applied to detect stagnation points in flow fields. In this paper we describe a
systematic comparison of different methods for finding magnetic nulls. The
Poincare index method, the first-order Taylor expansion (FOTE) method, and the
trilinear method are considered. We define a magnetic field containing fourteen
magnetic nulls whose positions and types are known to arbitrary precision.
Furthermore, we applied the selected techniques in order to find and classify
those nulls. Two situations are considered: one in which the magnetic field is
discretized on a rectangular grid, and the second in which the magnetic field
is discretized along synthetic `spacecraft trajectories' within the domain. At
present, FOTE and trilinear are the most reliable methods for finding nulls in
the spacecraft data and in numerical simulations on Cartesian grids,
respectively. The Poincare index method is suitable for simulations on both
tetrahedral and hexahedral meshes. The proposed magnetic field configuration
can be used for grading and benchmarking the new and existing tools for finding
magnetic nulls and flow stagnation points.
