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[1] Donne, K.E., Marotin, A. & Al-Hussany, A., Modified dual reciprocity boundary ele-ment modeling of collimated light fluence distribution in normal and cancerous prostate tissue during photodynamic therapy. 34th International Conference on Boundary Ele-ments and other Mesh Reduction Methods, Split, Croatia, 2012.
[2] Wrobel, L.C., The Boundary Element Method Vol 1: Applications in Thermofluids and Acoustics, Wiley, 2002.
[3] Brebbia, C.A, Telles, J.C.F. & Wrobel, L.C., Boundary Element Techniques, Springer-Verlag, 1984.
[4] Daniel, G., Donne, K.E., Song, L., Computer Modelling of Photodynamic Therapy, IPEM Annual Scientific meeting, York, UK, 2004.
[5] MAYA, available at: http://www.mayahtt.com/expertise/thermal
[6] Carslaw, H.S. & Jaeger, J.C., Conduction of Heat in Solids, 2nd edn., Oxford Clarendon Press, 1959.
[7] Van der Beek, N., Donne, K., Bjerring, P. & Neumann, M., The Effect of Pulse Train Profile on the Efficacy of PDL Treatments for PWS. Br J Dermatol, July 2015. [Crossref]
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Open Access
Research article

Solution of the Transient Thermal Diffusion Equation Using the Time-Dependent Boundary Element Method

donne, k.e.,
marotin, a.,
bashford, t.
Faculty of Architecture, Computing & Engineering, University of Wales Trinity Saint David, Swansea, UK
International Journal of Computational Methods and Experimental Measurements
|
Volume 5, Issue 3, 2017
|
Pages 260-270
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: 03-31-2017
View Full Article|Download PDF

Abstract:

A time-dependent fully-parallelised formulation of the BEM is applied to transient thermal problems in the context of light-based medical devices. The method is initially verified against benchmark problems. The limitations of the model are discussed, particularly the singularity challenge inherent in the fundamental solution. The method is then applied for a representative 3D clinical problem, further illustrating the singularity challenge.

Keywords: boundary element, diffusion, parallel, thermal
References
[1] Donne, K.E., Marotin, A. & Al-Hussany, A., Modified dual reciprocity boundary ele-ment modeling of collimated light fluence distribution in normal and cancerous prostate tissue during photodynamic therapy. 34th International Conference on Boundary Ele-ments and other Mesh Reduction Methods, Split, Croatia, 2012.
[2] Wrobel, L.C., The Boundary Element Method Vol 1: Applications in Thermofluids and Acoustics, Wiley, 2002.
[3] Brebbia, C.A, Telles, J.C.F. & Wrobel, L.C., Boundary Element Techniques, Springer-Verlag, 1984.
[4] Daniel, G., Donne, K.E., Song, L., Computer Modelling of Photodynamic Therapy, IPEM Annual Scientific meeting, York, UK, 2004.
[5] MAYA, available at: http://www.mayahtt.com/expertise/thermal
[6] Carslaw, H.S. & Jaeger, J.C., Conduction of Heat in Solids, 2nd edn., Oxford Clarendon Press, 1959.
[7] Van der Beek, N., Donne, K., Bjerring, P. & Neumann, M., The Effect of Pulse Train Profile on the Efficacy of PDL Treatments for PWS. Br J Dermatol, July 2015. [Crossref]
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K.e., D., A., M., & T., B. (2017). Solution of the Transient Thermal Diffusion Equation Using the Time-Dependent Boundary Element Method. Int. J. Comput. Methods Exp. Meas., 5(3), 260-270. https://doi.org/10.2495/CMEM-V5-N3-260-270
D. K.e., M. A., and B. T., "Solution of the Transient Thermal Diffusion Equation Using the Time-Dependent Boundary Element Method," Int. J. Comput. Methods Exp. Meas., vol. 5, no. 3, pp. 260-270, 2017. https://doi.org/10.2495/CMEM-V5-N3-260-270
@research-article{K.e.2017SolutionOT,
title={Solution of the Transient Thermal Diffusion Equation Using the Time-Dependent Boundary Element Method},
author={Donne, K.E. and Marotin, A. and Bashford, T.},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2017},
page={260-270},
doi={https://doi.org/10.2495/CMEM-V5-N3-260-270}
}
Donne, K.E., et al. "Solution of the Transient Thermal Diffusion Equation Using the Time-Dependent Boundary Element Method." International Journal of Computational Methods and Experimental Measurements, v 5, pp 260-270. doi: https://doi.org/10.2495/CMEM-V5-N3-260-270
Donne, K.E., Marotin, A., Bashford and T.. "Solution of the Transient Thermal Diffusion Equation Using the Time-Dependent Boundary Element Method." International Journal of Computational Methods and Experimental Measurements, 5, (2017): 260-270. doi: https://doi.org/10.2495/CMEM-V5-N3-260-270
K E D， Marotin, A.， T. B. Solution of the Transient Thermal Diffusion Equation Using the Time-Dependent Boundary Element Method[J]. International Journal of Computational Methods and Experimental Measurements， 2017， 5(3)： 260-270. https://doi.org/10.2495/CMEM-V5-N3-260-270