Título: | CONSISTENT BOUNDARY ELEMENT IMPLEMENTATION OF A FAST MULTIPOLE TECHNIQUE FOR THREEDIMENSIONAL POTENTIAL PROBLEMS | ||||||||||||
Autor: |
HILTON MARQUES SOUZA SANTANA |
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Colaborador(es): |
NEY AUGUSTO DUMONT - Orientador HELVIO DE FARIAS COSTA PEIXOTO - Coorientador |
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Catalogação: | 28/JUN/2022 | Língua(s): | PORTUGUESE - BRAZIL |
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Tipo: | TEXT | Subtipo: | THESIS | ||||||||||
Notas: |
[pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio. [en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio. |
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Referência(s): |
[pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=59794&idi=1 [en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=59794&idi=2 |
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DOI: | https://doi.org/10.17771/PUCRio.acad.59794 | ||||||||||||
Resumo: | |||||||||||||
The fast multipole is a powerful algorithm for modelling on a simple desktop
computer problems with many millions of degrees of freedom. Its combination with
the collocation boundary element method, which is based on fundamental solutions
with global support, leads to a scheme whose efficiency or sometimes just simulation
feasibility cannot be matched by any other numerical tool. The basic goal of this
research work is the consolidation of computer algorithms previously developed at
PUC-Rio in language C++ for the analysis of threedimensional potential problems. An
analytic, thus machine-precision, evaluation scheme of integrals for the case of close
distances between boundary elements and source points is implemented for the specific
case of three-node triangle elements. For larger distances an adaptative quadrature
scheme is applied for the sake of saving computational effort. For very large distances
a reverse fast multipole scheme previously implemented by M.Sc. and Ph.D. works is
implemented – also making use of machine-precision boundary integral evaluations.
This has ultimately led to a complete revisiting of the recent fast multipole
developments carried out at PUC-Rio. The implemented code is validated by means of
a few elucidative numerical examples.
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