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On the diffusion algorithm for density-equalizing maps with piecewise constant initial data

We mathematically analyze the diffusion-based algorithm to produce maps with a given Jacobian, introduced independently by M. T. Gastner and M. E. J. Newman (2004) and ourselves (2003), but in particular cases where the initial density has line or angle discontinuities in the plane. In this situation, the conclusion reinforces the conjecture that the algorithm is always well-posed, in accordance with its extensive numerical use in some areas of applied sciences (cartograms, sensor networks, computational grids, or image registration)

This work was partially supported by grants from the Spanish Government (MTM2008-06349-C03-01, MTM2011-27739-C04-01, and MTM2011-27739-C04-03) and the Catalan Government (2009SGR345)

© Mathematical Methods in the Applied Sciences, 2012, vol. 35, núm. 10, p. 1234-1240

Wiley

Author: Avinyó Andrés, Albert
Solà-Morales i Rubió, Joan de
València i Guitart, Marta
Date: 2012 July 15
Abstract: We mathematically analyze the diffusion-based algorithm to produce maps with a given Jacobian, introduced independently by M. T. Gastner and M. E. J. Newman (2004) and ourselves (2003), but in particular cases where the initial density has line or angle discontinuities in the plane. In this situation, the conclusion reinforces the conjecture that the algorithm is always well-posed, in accordance with its extensive numerical use in some areas of applied sciences (cartograms, sensor networks, computational grids, or image registration)
This work was partially supported by grants from the Spanish Government (MTM2008-06349-C03-01, MTM2011-27739-C04-01, and MTM2011-27739-C04-03) and the Catalan Government (2009SGR345)
Format: application/pdf
ISSN: 0170-4214 (versió paper)
1099-1476 (versió electrònica)
Document access: http://hdl.handle.net/10256/11266
Language: eng
Publisher: Wiley
Collection: MICINN/PN 2012-2015/MTM2011-27739-C04-03
AGAUR/2014-2016/2014 SGR-345
Reproducció digital del document publicat a: http://dx.doi.org/10.1002/mma.2526
Articles publicats (D-IMA)
Is part of: © Mathematical Methods in the Applied Sciences, 2012, vol. 35, núm. 10, p. 1234-1240
Rights: Tots els drets reservats
Subject: Funcional de densitat, Teoria del
Density functionals
Equacions funcionals
Functional equations
Title: On the diffusion algorithm for density-equalizing maps with piecewise constant initial data
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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