Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics



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BibTex format

author = {Degond, PAA and Ferreira, MA and Motsch, S},
doi = {10.1016/},
journal = {Journal of Computational Physics},
pages = {47--65},
title = {Damped Arrow-Hurwicz algorithm for sphere packing},
url = {},
volume = {332},
year = {2016}

RIS format (EndNote, RefMan)

AB - We consider algorithms that, from an arbitrarily sampling ofNspheres(possibly overlapping), nd a close packed con guration without overlapping.These problems can be formulated as minimization problems with non-convexconstraints. For such packing problems, we observe that the classical iterativeArrow-Hurwicz algorithm does not converge. We derive a novel algorithmfrom a multi-step variant of the Arrow-Hurwicz scheme with damping. Wecompare this algorithm with classical algorithms belonging to the class oflinearly constrained Lagrangian methods and show that it performs better.We provide an analysis of the convergence of these algorithms in the simplecase of two spheres in one spatial dimension. Finally, we investigate thebehaviour of our algorithm when the number of spheres is large in two andthree spatial dimensions.
AU - Degond,PAA
AU - Ferreira,MA
AU - Motsch,S
DO - 10.1016/
EP - 65
PY - 2016///
SN - 1090-2716
SP - 47
TI - Damped Arrow-Hurwicz algorithm for sphere packing
T2 - Journal of Computational Physics
UR -
UR -
VL - 332
ER -