TY - JOUR
T1 - The generalized finite difference method for an inverse time-dependent source problem associated with three-dimensional heat equation
AU - Gu, Yan
AU - Lei, Jun
AU - Fan, Chia-Ming
AU - He, Xiao-Qiao
PY - 2018/6
Y1 - 2018/6
N2 - This paper presents a meshless numerical scheme for recovering the time-dependent heat source in general three-dimensional (3D) heat conduction problems. The problem considered is ill-posed and the determination of the unknown heat source is achieved here by using the boundary condition, initial condition and the extra measured data from a fixed point placed inside the domain. The extra measured data are used to guarantee the uniqueness of the solution. The generalized finite difference method (GFDM), a recently-developed meshless method, is then adopted to solve the resulting time-dependent boundary-value problem. In our computations, the second-order Crank–Nicolson scheme is employed for the temporal discretization and the proposed GFDM for the spatial discretization. Several benchmark test problems with both smooth and piecewise smooth geometries have been studied to verify the accuracy and efficiency of the proposed method. No need to apply any well-known regularization strategy, the accurate and stable solution could be obtained with a comparatively large level of noise.
AB - This paper presents a meshless numerical scheme for recovering the time-dependent heat source in general three-dimensional (3D) heat conduction problems. The problem considered is ill-posed and the determination of the unknown heat source is achieved here by using the boundary condition, initial condition and the extra measured data from a fixed point placed inside the domain. The extra measured data are used to guarantee the uniqueness of the solution. The generalized finite difference method (GFDM), a recently-developed meshless method, is then adopted to solve the resulting time-dependent boundary-value problem. In our computations, the second-order Crank–Nicolson scheme is employed for the temporal discretization and the proposed GFDM for the spatial discretization. Several benchmark test problems with both smooth and piecewise smooth geometries have been studied to verify the accuracy and efficiency of the proposed method. No need to apply any well-known regularization strategy, the accurate and stable solution could be obtained with a comparatively large level of noise.
KW - Generalized finite difference method
KW - Inverse problems
KW - Meshless method
KW - Three-dimensional problems
KW - Time-dependent heat source
UR - http://www.scopus.com/inward/record.url?scp=85044517866&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85044517866&origin=recordpage
U2 - 10.1016/j.enganabound.2018.03.013
DO - 10.1016/j.enganabound.2018.03.013
M3 - RGC 21 - Publication in refereed journal
SN - 0955-7997
VL - 91
SP - 73
EP - 81
JO - Engineering Analysis with Boundary Elements
JF - Engineering Analysis with Boundary Elements
ER -