| Texto completo | |
| Autor(es): |
Reddy, Gujji Murali Mohan
[1]
;
Seitenfuss, Alan B.
[2]
;
Medeiros, Debora de Oliveira
[2]
;
Meacci, Luca
[2]
;
Assuncao, Milton
[2]
;
Vynnycky, Michael
[3, 4]
Número total de Autores: 6
|
| Afiliação do(s) autor(es): | [1] Birla Inst Technol & Sci, Dept Math, Hyderabad Campus, Hyderabad 500078, Telangana - India
[2] Univ Sao Paulo Sao Carlos, Inst Math & Comp Sci, Dept Appl Math & Stat, POB 668, BR-13560970 Sao Carlos, SP - Brazil
[3] Univ Limerick, Dept Math & Stat, Limerick V94 T9PX - Ireland
[4] KTH Royal Inst Technol, Dept Mat Sci & Technol, Div Proc, Brinellvagen 23, S-10044 Stockholm - Sweden
Número total de Afiliações: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | ALGORITHMS; v. 13, n. 10 OCT 2020. |
| Citações Web of Science: | 0 |
| Resumo | |
Although two-dimensional (2D) parabolic integro-differential equations (PIDEs) arise in many physical contexts, there is no generally available software that is able to solve them numerically. To remedy this situation, in this article, we provide a compact implementation for solving 2D PIDEs using the finite element method (FEM) on unstructured grids. Piecewise linear finite element spaces on triangles are used for the space discretization, whereas the time discretization is based on the backward-Euler and the Crank-Nicolson methods. The quadrature rules for discretizing the Volterra integral term are chosen so as to be consistent with the time-stepping schemes; a more efficient version of the implementation that uses a vectorization technique in the assembly process is also presented. The compactness of the approach is demonstrated using the software Matrix Laboratory (MATLAB). The efficiency is demonstrated via a numerical example on an L-shaped domain, for which a comparison is possible against the commercially available finite element software COMSOL Multiphysics. Moreover, further consideration indicates that COMSOL Multiphysics cannot be directly applied to 2D PIDEs containing more complex kernels in the Volterra integral term, whereas our method can. Consequently, the subroutines we present constitute a valuable open and validated resource for solving more general 2D PIDEs. (AU) | |
| Processo FAPESP: | 16/19648-9 - Solução numérica do problema de Stefan inverso pelo método das soluções fundamentais |
| Beneficiário: | Gujji Murali Mohan Reddy |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |
| Processo FAPESP: | 18/07643-8 - Matemática industrial e técnicas assintóticas |
| Beneficiário: | José Alberto Cuminato |
| Modalidade de apoio: | Auxílio à Pesquisa - Pesquisador Visitante - Internacional |
| Processo FAPESP: | 17/11428-2 - Métodos numéricos para escoamentos não-newtonianos com superfícies livres: efeitos da tensão superficial |
| Beneficiário: | Débora de Oliveira Medeiros |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |