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A compact FEM implementation for parabolic integro-differential equations in 2D

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Show simple item record Reddy, Gujji Murali Mohan Seitenfuss, Alan B. de Oliveira Medeiros, Débora Meacci, Luca Assunção, Milton Vynnycky, Michael 2020-10-28T12:31:02Z 2020-10-28T12:31:02Z 2020
dc.description peer-reviewed en_US
dc.description.abstract 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 the 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 2DPIDEs 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. en_US
dc.language.iso eng en_US
dc.publisher MDPI en_US
dc.relation PROEX-9740044/D en_US
dc.relation.ispartofseries Algorithms;13, 242
dc.subject parabolic integro-differential equations en_US
dc.subject backward-Euler en_US
dc.subject Crank–Nicolson en_US
dc.title A compact FEM implementation for parabolic integro-differential equations in 2D en_US
dc.type info:eu-repo/semantics/article en_US
dc.type.supercollection all_ul_research en_US
dc.type.supercollection ul_published_reviewed en_US
dc.identifier.doi 10.3390/a13100242
dc.contributor.sponsor FAPESP en_US
dc.contributor.sponsor KTH Royal Institute of Technology en_US
dc.relation.projectid 2016/19648-9 en_US
dc.relation.projectid 2017/11428-228-2 en_US
dc.relation.projectid 2018/07643-8 en_US
dc.rights.accessrights info:eu-repo/semantics/openAccess en_US
dc.internal.rssid 2996163

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