  The potential field (PF) solution of the solar corona is a vital modeling
tool for a wide range of applications, including minimum energy estimates,
coronal magnetic field modeling, and empirical solar wind solutions. Given its
popularity, it is important to understand how choices made in computing a PF
may influence key properties of the solution. Here we study PF solutions for
the global coronal magnetic field on 2012 June 13, computed with our
high-performance finite difference code POT3D. Solutions are analyzed for their
global properties and locally around NOAA AR 11504, using the net open flux,
open field boundaries, total magnetic energy, and magnetic structure as
metrics. We explore how PF solutions depend on 1) the data source, type, and
processing of the inner boundary conditions, 2) the choice of the outer
boundary condition height and type, and 3) the numerical resolution and spatial
scale of information at the lower boundary. We discuss the various qualitative
and quantitative differences that naturally arise by using different maps as
input, and illustrate how coronal morphology and open flux depend most strongly
on the outer boundary condition. We also show how large-scale morphologies and
the open magnetic flux are remarkably insensitive to model resolution, while
the surface mapping and embedded magnetic complexity vary considerably. This
establishes important context for past, current, and future applications of the
PF for coronal and solar wind modeling.
