Fast Solver for Potential and LFFFs

This is a fast solver for computing the potential and linear force-free
field (LFFF) above the full photosphere with the line-of-sight synoptic magnetogram as
input. The global potential field and the LFFF are dealt with in an unified way by solving a three-dimensional Helmholtz equation in spherical shell and a two-dimensional
Poisson equation on the photosphere. The solver is based on a combination of the
spectral method and the finite-difference scheme. In longitude direction the equation
is transformed into Fourier spectral space and the resulted 2D equations in r–θ plane
for the Fourier coefficients are solved by finite difference in a direct way. The solver
shows a distinguish virtue of extremely fast computing speed, e.g., the computation for
a magnetogram with resolution of 180(θ) × 360(φ) is completed by only less than two
seconds and even on a very high resolution 600 × 1200, the solution can be obtained
within about one minute on a single 2.66G CPU.