# Coulomb interactions on planar structures: Inverting the square root of the Laplacian

Zydrunas Gimbutas, Leslie Greengard, Michael Minion

Research output: Contribution to journalArticle

### 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.

Original language English (US) 2093-2108 16 SIAM Journal on Scientific Computing 22 6 https://doi.org/10.1137/S1064827599361199 Published - 2001

### Fingerprint

Coulomb Interaction
Electrical engineering
Fluid dynamics
Coulomb interactions
Vorticity
Square root
Geophysical Fluid Dynamics
Fast multipole Method
Electrical Engineering
Thin films
Thin Films
Computational Cost
Costs
Two Dimensions
Linearly
Charge
Mesh
Evaluation

### Keywords

• Integral equation methods
• Planar circuits
• Quasi-geostrophic fluid dynamics
• Thin films

### ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

### Cite this

Coulomb interactions on planar structures : Inverting the square root of the Laplacian. / Gimbutas, Zydrunas; Greengard, Leslie; Minion, Michael.

In: SIAM Journal on Scientific Computing, Vol. 22, No. 6, 2001, p. 2093-2108.

Research output: Contribution to journalArticle

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