41 citations · 95 across the 7 of their papers we have counts for
5 papers · 1 filter
The scaling and skewness of optimally transported meshes on the sphere
Chris J. Budd, Andrew T. T. McRae, Colin J. Cotter
In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of intere…
Optimal-transport-based mesh adaptivity on the plane and sphere using finite elements
Andrew T. T. McRae, Colin J. Cotter, Chris J. Budd
In moving mesh methods, the underlying mesh is dynamically adapted without changing the connectivity of the mesh. We specifically consider the generation of meshes which are adapte…
Mesh Adaptation on the Sphere using Optimal Transport and the Numerical Solution of a Monge-Ampère type Equation
Hilary Weller, Philip Browne, Chris Budd +1
An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistribut…
The Geometry of r-adaptive meshes generated using Optimal Transport Methods
C. J. Budd, R. D. Russell, E. Walsh
The principles of mesh equidistribution and alignment play a fundamental role in the design of adaptive methods, and a metric tensor M and mesh metric are useful theoretical tools…
The Alignment Properties of Monge-Ampere based Mesh Redistribution Methods: I Linear Features
C. J. Budd, R. D. Russell, E. Walsh
Many adaptive mesh methods explicitly or implicitly use equidistribution and alignment. These principles can be considered central to mesh adaption. A Metric Tensor is the tool by…