Source points placement in the method of fundamental solutions for parabolic problems / Colocação de pontos de fonte no método de soluções fundamentais para problemas parabólicos

Authors

  • Carlos Eduardo Polatschek Kopperschmidt
  • Bruno Henrique Marques Margotto
  • Wellington Betencurte da Silva
  • Júlio César Sampaio Dutra

DOI:

https://doi.org/10.34117/bjdv6n3-041

Keywords:

Method of Fundamental Solutions, Time-dependent, Parabolic, Heat conduction problem.

Abstract

In this paper, the placement of the source points for Method of Fundamental Solutions in one-dimensional parabolic partial differential equations is evaluated for two different traditional benchmark problems one with Dirichlet condition and other with mixed boundary conditions. Four source points placement strategies are used. The approximate results from Method of Fundamental Solutions are sensitive to strategy used, and when the positive timed source points are used the approximate results are instable.

References

Chantasiriwan, S., Johansson, B. T., & Lesnic, D. (2009). “The Method of Fundamental Solutions for free surface Stefan problems”. Engineering Analysis with Boundary Elements, 33(4), 529–538.

Grabski, J. K. (2019). “On the sources placement in the Method Of Fundamental Solutions for time-dependent heat conduction problems”. Computers and Mathematics with Applications, https://doi.org/10.1016/j.camwa. 2019.04.023.

Lin, C. Y., Gu, M.H., Young, D. L. (2010), “The Time-Marching Method of Fundamental Solutions for Multi-Dimensional Telegraph Equations”. Tech Science Press. CMC, vol. 18, no. 1, pp. 43-68.

Mathon, R., Johnston, R. L. (1977). “The approximate solution of elliptic boundary-value problems by fundamental solutions”. SIAM J. Numer. Anal. 14, 638-650.

Mera, N. S. (2005). The Method of Fundamental Solutions for the backward heat conduction problem. Inverse Problems in Science and Engineering, 13(1), 65–78.

Johansson, B. T., & Lesnic, D. (2009). “A Method of Fundamental Solutions for transient heat conduction in layered materials”. Engineering Analysis with Boundary Elements, 33(12), 1362–1367. doi:10.1016/j.enganabound.2009.04.014.

Johansson, B. T. (2017). “Properties of a Method of Fundamental Solutions for the parabolic heat equation”. Applied Mathematics Letters, 65, 83–89.doi:10.1016/j.aml.2016.08.021

Kupradze, V. D., & Aleksidze, M. A. (1964). “The method of functional equations for the approximate solution of certain boundary value problems”. USSR Computational Mathematics and Mathematical Physics, 4(4), 82–126.doi:10.1016/0041-5553(64)90006-0

Valtchev, S. S., & Roberty, N. C. (2008). “A time-marching MFS scheme for heat conduction problems”. Engineering Analysis with Boundary Elements, 32(6), 480–493.

Yan, L., Yang, F., & Fu, C. (2009). “A Bayesian inference approach to identify a Robin coefficient in one-dimensional parabolic problems”. Journal of Computational and Applied Mathematics, 231(2), 840–850. Lanzhou University, China.

Downloads

Published

2020-03-04

How to Cite

Kopperschmidt, C. E. P., Margotto, B. H. M., Silva, W. B. da, & Dutra, J. C. S. (2020). Source points placement in the method of fundamental solutions for parabolic problems / Colocação de pontos de fonte no método de soluções fundamentais para problemas parabólicos. Brazilian Journal of Development, 6(3), 10118–10129. https://doi.org/10.34117/bjdv6n3-041

Issue

Section

Original Papers