In this work, we propose the investigation of unsteady nonlinear heat conduction by using the radial point interpolation method (RPIM) in high-order continuation coupled with homotopy transformation for the first time. In this resolution strategy, the Euler implicit time scheme is used to transform the unsteady nonlinear continuous problem into a sequence of stationary continuous problems. Moreover, by using the RPIM, we transform the sequence of stationary nonlinear continuous problems into discrete problems. Then, homotopy transformation is applied by introducing an arbitrary invertible pre-conditioner $\left[{K}^{*}\right]$ and a dimensionless parameter $a$. These nonlinear problems are transformed into a sequence of linear problems thanks to Taylor series expansions used in a continuation technique to compute the whole solution branch by branch. Numerical examples have been investigated to show the accuracy and efficiency of the proposed approach in this type of problem. The results obtained by the proposed high-order homotopic continuation with the RPIM are compared with those computed by the Newton–Raphson method coupled with the RPIM, high-order homotopic continuation with moving least squares, and high-order homotopic continuation with the finite element method.

Revised:

Accepted:

Published online:

Said Mesmoudi ^{1};
Omar Askour ^{1};
Bouazza Braikat ^{1}

@article{CRMECA_2020__348_8-9_745_0, author = {Said Mesmoudi and Omar Askour and Bouazza Braikat}, title = {Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems}, journal = {Comptes Rendus. M\'ecanique}, pages = {745--758}, publisher = {Acad\'emie des sciences, Paris}, volume = {348}, number = {8-9}, year = {2020}, doi = {10.5802/crmeca.49}, language = {en}, }

TY - JOUR AU - Said Mesmoudi AU - Omar Askour AU - Bouazza Braikat TI - Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems JO - Comptes Rendus. Mécanique PY - 2020 SP - 745 EP - 758 VL - 348 IS - 8-9 PB - Académie des sciences, Paris DO - 10.5802/crmeca.49 LA - en ID - CRMECA_2020__348_8-9_745_0 ER -

%0 Journal Article %A Said Mesmoudi %A Omar Askour %A Bouazza Braikat %T Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems %J Comptes Rendus. Mécanique %D 2020 %P 745-758 %V 348 %N 8-9 %I Académie des sciences, Paris %R 10.5802/crmeca.49 %G en %F CRMECA_2020__348_8-9_745_0

Said Mesmoudi; Omar Askour; Bouazza Braikat. Radial point interpolation method and high-order continuation for solving nonlinear transient heat conduction problems. Comptes Rendus. Mécanique, Volume 348 (2020) no. 8-9, pp. 745-758. doi : 10.5802/crmeca.49. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.49/

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