TY - JOUR
T1 - A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems
AU - Johansson, B. Tomas
AU - Lesnic, Daniel
AU - Reeve, Thomas
N1 - Special Issue: Proceedings of the 8th UK Conference on Boundary Integral Methods, July 4th–5th, 2011, held at the University of Leeds, UK.
PY - 2012
Y1 - 2012
N2 - We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.
AB - We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.
KW - heat conduction
KW - method of fundamental solutions
KW - MFS
KW - axisymmetric heat equation
KW - radially symmetric heat equation
KW - backward inverse problem
UR - http://www.tandfonline.com/10.1080/00207160.2012.680448
U2 - 10.1080/00207160.2012.680448
DO - 10.1080/00207160.2012.680448
M3 - Special issue
VL - 89
SP - 1555
EP - 1568
JO - International Journal of Computer Mathematics
JF - International Journal of Computer Mathematics
SN - 0020-7160
IS - 11
T2 - 8th UK Conference on Boundary Integral Methods
Y2 - 4 July 2011 through 5 July 2011
ER -