Leslie Greengard, Zydrunas Gimbutas and
Michael L. Minion,
SIAM Journal on Scientific Computating, 2001
Abstract:
We present an adaptive fast multipole method for inverting the square root
of the Laplacian in two dimensions. Solving this problem is the dominant
computational cost in many applications arising in
electrical engineering, geophysical fluid dynamics, and the study of thin
films. It corresponds to the
evaluation of the field induced by a planar distribution of charge or
vorticity. Our algorithm is direct and assumes only that the source
distribution is discretized using an adaptive quad-tree. The amount of
work grows linearly with the number of mesh points.