Implementing a Restricted Function Space Class in Firedrake
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917746122424320 |
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| author | Rothwell, Emma |
| author_facet | Rothwell, Emma |
| contents | The implementation process of a $\texttt{RestrictedFunctionSpace}$ class in Firedrake, a Python library which numerically solves partial differential equations through the use of the finite element method, is documented. This includes an introduction to the current $\texttt{FunctionSpace}$ class in Firedrake, and the key features that it has. With the current $\texttt{FunctionSpace}$ class, the limitations of the capabilities of the solvers in Firedrake when imposing Dirichlet boundary conditions are explored, as well as what the $\texttt{RestrictedFunctionSpace}$ class does differently to remove these issues. These will be considered in both a mathematical way, and in the code as an abstraction of the mathematical ideas presented. Finally, the benefits to the user of the $\texttt{RestrictedFunctionSpace}$ class are considered, and demonstrated through tests and comparisons. This leads to the conclusion that in particular, the eigensolver in Firedrake is improved through the use of the $\texttt{RestrictedFunctionSpace}$, through the removal of eigenvalues associated with the Dirichlet boundary conditions for a system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05217 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Implementing a Restricted Function Space Class in Firedrake Rothwell, Emma Mathematical Software Numerical Analysis The implementation process of a $\texttt{RestrictedFunctionSpace}$ class in Firedrake, a Python library which numerically solves partial differential equations through the use of the finite element method, is documented. This includes an introduction to the current $\texttt{FunctionSpace}$ class in Firedrake, and the key features that it has. With the current $\texttt{FunctionSpace}$ class, the limitations of the capabilities of the solvers in Firedrake when imposing Dirichlet boundary conditions are explored, as well as what the $\texttt{RestrictedFunctionSpace}$ class does differently to remove these issues. These will be considered in both a mathematical way, and in the code as an abstraction of the mathematical ideas presented. Finally, the benefits to the user of the $\texttt{RestrictedFunctionSpace}$ class are considered, and demonstrated through tests and comparisons. This leads to the conclusion that in particular, the eigensolver in Firedrake is improved through the use of the $\texttt{RestrictedFunctionSpace}$, through the removal of eigenvalues associated with the Dirichlet boundary conditions for a system. |
| title | Implementing a Restricted Function Space Class in Firedrake |
| topic | Mathematical Software Numerical Analysis |
| url | https://arxiv.org/abs/2408.05217 |