Imperial College London

ProfessorColinCotter

Faculty of Natural SciencesDepartment of Mathematics

Professor of Computational Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 3468colin.cotter

 
 
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Location

 

755Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{McRae:2018:10.1137/16M1109515,
author = {McRae, ATT and Cotter, CJ and Budd, CJ},
doi = {10.1137/16M1109515},
journal = {SIAM Journal on Scientific Computing},
pages = {A1121--A1148},
title = {Optimal-transport-based mesh adaptivity on the plane and sphere using finite elements},
url = {http://dx.doi.org/10.1137/16M1109515},
volume = {40},
year = {2018}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - In moving mesh methods, the underlying mesh is dynamically adapted withoutchanging the connectivity of the mesh. We specifically consider the generationof meshes which are adapted to a scalar monitor function throughequidistribution. Together with an optimal transport condition, this leads to aMonge-Amp\`ere equation for a scalar mesh potential. We adapt an existingfinite element scheme for the standard Monge-Amp\`ere equation to this meshgeneration problem; this is a mixed finite element scheme, in which an extradiscrete variable is introduced to represent the Hessian matrix of secondderivatives. The problem we consider has additional nonlinearities over thebasic Monge-Amp\`ere equation due to the implicit dependence of the monitorfunction on the resulting mesh. We also derive the equivalentMonge-Amp\`ere-like equation for generating meshes on the sphere. The finiteelement scheme is extended to the sphere, and we provide numerical examples.All numerical experiments are performed using the open-source finite elementframework Firedrake.
AU - McRae,ATT
AU - Cotter,CJ
AU - Budd,CJ
DO - 10.1137/16M1109515
EP - 1148
PY - 2018///
SP - 1121
TI - Optimal-transport-based mesh adaptivity on the plane and sphere using finite elements
T2 - SIAM Journal on Scientific Computing
UR - http://dx.doi.org/10.1137/16M1109515
UR - http://arxiv.org/abs/1612.08077v3
UR - http://hdl.handle.net/10044/1/56480
VL - 40
ER -