Accuracy analysis of a spectral Poisson solver
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| Title: | Accuracy analysis of a spectral Poisson solver |
|---|---|
| Authors: | Rambaldi, S.1 rambaldi@bo.infn.it, Turchetti, G.1, Benedetti, C.1, Mattioli, F.2, Franchi, A.3 |
| Source: | Nuclear Instruments & Methods in Physics Research Section A. Jun2006, Vol. 561 Issue 2, p223-229. 7p. |
| Subjects: | Boundary value problems, Ellipsoids, Computational complexity, Poisson's equation |
| Abstract: | Abstract: We solve Poisson''s equation in space dimensions by using a spectral method based on Fourier decomposition. The choice of the basis implies that Dirichlet boundary conditions on a box are satisfied. A Green''s function-based procedure allows us to impose Dirichlet conditions on any smooth closed boundary, by doubling the computational complexity. The error introduced by the spectral truncation and the discretization of the charge distribution is evaluated by comparison with the exact solution, known in the case of elliptical symmetry. To this end boundary conditions on an equipotential ellipse (ellipsoid) are imposed on the numerical solution. Scaling laws for the error dependence on the number K of Fourier components for each space dimension and the number N of point charges used to simulate the charge distribution are presented and tested. A procedure to increase the accuracy of the method in the beam core region is briefly outlined. [Copyright &y& Elsevier] |
| Copyright of Nuclear Instruments & Methods in Physics Research Section A is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 20923543 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.nima.2006.01.019 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 223 Subjects: – SubjectFull: Boundary value problems Type: general – SubjectFull: Ellipsoids Type: general – SubjectFull: Computational complexity Type: general – SubjectFull: Poisson's equation Type: general Titles: – TitleFull: Accuracy analysis of a spectral Poisson solver Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Rambaldi, S. – PersonEntity: Name: NameFull: Turchetti, G. – PersonEntity: Name: NameFull: Benedetti, C. – PersonEntity: Name: NameFull: Mattioli, F. – PersonEntity: Name: NameFull: Franchi, A. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2006 Type: published Y: 2006 Identifiers: – Type: issn-print Value: 01689002 Numbering: – Type: volume Value: 561 – Type: issue Value: 2 Titles: – TitleFull: Nuclear Instruments & Methods in Physics Research Section A Type: main |
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