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Combining MFS and PGD methods to solve transient heat equation
Author(s) -
Kpogan Kékéli,
Tri Abdeljalil,
Sogah Amen,
Mathieu Norman,
Zahrouni Hamid,
PotierFerry Michel
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22196
Subject(s) - representation (politics) , transient (computer programming) , range (aeronautics) , reduction (mathematics) , computer science , variable (mathematics) , heat equation , mathematics , algorithm , mathematical optimization , mathematical analysis , materials science , geometry , politics , political science , law , composite material , operating system
We propose in this article a numerical algorithm based on the combination of the method of fundamental solutions (MFS) and the proper generalized decomposition technique (PGD) to solve time‐dependent heat equation. The MFS is considered as a truly meshless technique well adapted for a wide range of physical problems and the PGD approach can be considered as a reduction technique based on the separated representation of the variable functions. The proposed study relates to a separation between the spatial and temporal coordinates. To show the effectiveness of the proposed algorithm, several examples are presented and compared to the reference results.