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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A Compact FEM Implementation for Parabolic Integro-Differential Equations in 2D

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Reddy, Gujji Murali Mohan [1] ; Seitenfuss, Alan B. [2] ; Medeiros, Debora de Oliveira [2] ; Meacci, Luca [2] ; Assuncao, Milton [2] ; Vynnycky, Michael [3, 4]
Total Authors: 6
[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
Total Affiliations: 4
Document type: Journal article
Source: ALGORITHMS; v. 13, n. 10 OCT 2020.
Web of Science Citations: 0

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)

FAPESP's process: 16/19648-9 - Efficient numerical solution of the inverse Stefan problems using the method of fundamental solutions
Grantee:Gujji Murali Mohan Reddy
Support type: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 18/07643-8 - Industrial mathematics and practical asymptotics
Grantee:José Alberto Cuminato
Support type: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 17/11428-2 - Numerical Methods for Non-Newtonian Free Surface Flows: effects of surface tension
Grantee:Débora de Oliveira Medeiros
Support type: Scholarships in Brazil - Doctorate