Computing with functions in the ball
A collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are numerically and adaptively resolved to essentially machine precision by using a three-dimensional analogue of the double F...
| Үндсэн зохиолчид: | , |
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| Формат: | Journal article |
| Хэл сонгох: | English |
| Хэвлэсэн: |
Society for Industrial and Applied Mathematics
2020
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| _version_ | 1826257909331263488 |
|---|---|
| author | Boullé, N Townsend, A |
| author_facet | Boullé, N Townsend, A |
| author_sort | Boullé, N |
| collection | OXFORD |
| description | A collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are numerically and adaptively resolved to essentially machine precision by using a three-dimensional analogue of the double Fourier sphere method to form “Ballfun" objects. Operations such as function evaluation, differentiation, integration, fast rotation by an Euler angle, and a Helmholtz solver are designed. Our algorithms are particularly efficient for vector calculus operations, and we describe how to compute the poloidal-toroidal and Helmholtz--Hodge decompositions of a vector field defined on the ball.
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| first_indexed | 2024-03-06T18:25:37Z |
| format | Journal article |
| id | oxford-uuid:07da1374-da48-43c5-bedc-ccc8c201255d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:25:37Z |
| publishDate | 2020 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:07da1374-da48-43c5-bedc-ccc8c201255d2022-03-26T09:09:50ZComputing with functions in the ballJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:07da1374-da48-43c5-bedc-ccc8c201255dEnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2020Boullé, NTownsend, AA collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are numerically and adaptively resolved to essentially machine precision by using a three-dimensional analogue of the double Fourier sphere method to form “Ballfun" objects. Operations such as function evaluation, differentiation, integration, fast rotation by an Euler angle, and a Helmholtz solver are designed. Our algorithms are particularly efficient for vector calculus operations, and we describe how to compute the poloidal-toroidal and Helmholtz--Hodge decompositions of a vector field defined on the ball. |
| spellingShingle | Boullé, N Townsend, A Computing with functions in the ball |
| title | Computing with functions in the ball |
| title_full | Computing with functions in the ball |
| title_fullStr | Computing with functions in the ball |
| title_full_unstemmed | Computing with functions in the ball |
| title_short | Computing with functions in the ball |
| title_sort | computing with functions in the ball |
| work_keys_str_mv | AT boullen computingwithfunctionsintheball AT townsenda computingwithfunctionsintheball |