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

Autor
Avinyó, A.; Sola-morales, J.; Valencia, M.
Tipus d'activitat
Article en revista
Revista
Mathematical methods in the applied sciences
Data de publicació
2012-07-15
Volum
35
Número
10
Pàgina inicial
1234
Pàgina final
1240
DOI
https://doi.org/10.1002/mma.2526 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/16684 Obrir en finestra nova
Resum
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, comp...
Citació
Avinyó, A.; De Solà-Morales, J.; València, M. On the diffusion algorithm for density-equalizing maps with piecewise constant initial data. "Mathematical methods in the applied sciences", 15 Juliol 2012, vol. 35, núm. 10, p. 1234-1240.
Paraules clau
Advection Process, Analytic Solution, Cartograms, Density-equalizing Map, Diffusion-based Algorithm, Singular Initial Data
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

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