Automating the solution of PDEs on the sphere and other manifolds in FEniCS 1.2
Differential equations posed over immersed manifolds are of particular importance in studying geophysical flows; for instance, ocean and atmosphere simulations crucially rely on the capability to solve equations over the sphere. This paper presents the extension of the FEniCS software compon...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2013-12-01
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| Series: | Geoscientific Model Development |
| Online Access: | http://www.geosci-model-dev.net/6/2099/2013/gmd-6-2099-2013.pdf |
| Summary: | Differential equations posed over immersed manifolds are of
particular importance in studying geophysical flows; for instance,
ocean and atmosphere simulations crucially rely on the capability to
solve equations over the sphere. This paper presents the extension
of the FEniCS software components to the automated solution of
finite element formulations of differential equations defined over
general, immersed manifolds. We describe the implementation and, in
particular detail, how the required extensions essentially reduce to
the extension of the FEniCS form compiler to cover this case. The
resulting implementation has all the properties of the FEniCS
pipeline and we demonstrate its flexibility by an extensive range of
numerical examples covering a number of geophysical benchmark
examples and test cases. The results are all in agreement with the
expected values. The description here relates to DOLFIN/FEniCS 1.2. |
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| ISSN: | 1991-959X 1991-9603 |