A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems

作者：Johansson B Tomas^*; Lesnic Daniel; Reeve Thomas

来源：International Journal of Computer Mathematics, 2012, 89(11): 1555-1568.

DOI：10.1080/00207160.2012.680448

• heat conduction
• method of fundamental solutions (MFS)
• axisymmetric heat equation
• radially symmetric heat equation
• backward inverse problem

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.

• 出版日期2012