Imperial College London
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DrSheehanOlver

Faculty of Natural Sciences, Department of Mathematics

Reader in Applied Mathematics and Mathematical Physics
 
 
 
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Location

 

Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Gutleb:2023:10.1007/s00365-022-09606-0,
author = {Gutleb, TS and Carrillo, JA and Olver, S},
doi = {10.1007/s00365-022-09606-0},
journal = {Constructive Approximation},
pages = {75--120},
title = {Computation of power law equilibrium measures on balls of arbitrary dimension},
url = {http://dx.doi.org/10.1007/s00365-022-09606-0},
volume = {58},
year = {2023}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We present a numerical approach for computing attractive-repulsive power law equilibrium measures in arbitrary dimension. We prove new recurrence relationships for radial Jacobi polynomials on d-dimensional ball domains, providing a substantial generalization of the work started in Gutleb et al. (Math Comput 9:2247–2281, 2022) for the one-dimensional case based on recurrence relationships of Riesz potentials on arbitrary dimensional balls. Among the attractive features of the numerical method are good efficiency due to recursively generated banded and approximately banded Riesz potential operators and computational complexity independent of the dimension d, in stark constrast to the widely used particle swarm simulation approaches for these problems which scale catastrophically with the dimension. We present several numerical experiments to showcase the accuracy and applicability of the method and discuss how our method compares with alternative numerical approaches and conjectured analytical solutions which exist for certain special cases. Finally, we discuss how our method can be used to explore the analytically poorly understood gap formation boundary to spherical shell support.
AU  - Gutleb,TS
AU  - Carrillo,JA
AU  - Olver,S
DO  - 10.1007/s00365-022-09606-0
EP  - 120
PY  - 2023///
SN  - 0176-4276
SP  - 75
TI  - Computation of power law equilibrium measures on balls of arbitrary dimension
T2  - Constructive Approximation
UR  - http://dx.doi.org/10.1007/s00365-022-09606-0
UR  - http://arxiv.org/abs/2109.00843v1
UR  - https://link.springer.com/article/10.1007/s00365-022-09606-0
UR  - http://hdl.handle.net/10044/1/101089
VL  - 58
ER  -
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