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5 papers · 2 filters
Automated generation and symbolic manipulation of tensor product finite elements
Andrew T. T. McRae, Gheorghe-Teodor Bercea, Lawrence Mitchell +2
We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilater…
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…
On the pathwise approximation of stochastic differential equations
Tony Shardlow, Phillip Taylor
We consider one-step methods for integrating stochastic differential equations and prove pathwise convergence using ideas from rough path theory. In contrast to alternative theorie…
Efficient Multigrid Preconditioners for Atmospheric Flow Simulations at High Aspect Ratio
Andreas Dedner, Eike Hermann Müller, Robert Scheichl
Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical we…
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…