An adaptive fast solver for the modified Helmholtz equation in two dimensions
Journal of Computational Physics
Short note: A kernel independent fast multipole algorithm for radial basis functions
Journal of Computational Physics
Compensated optimal grids for elliptic boundary-value problems
Journal of Computational Physics
The black-box fast multipole method
Journal of Computational Physics
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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.