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- Title
An Efficient Element-Free Galerkin Method Based on Adaptive TR-AB2 Scheme for Transient Heat Conduction Problems.
- Authors
Shuyi Xiang; Xiaohua Zhang
- Abstract
Meshless methods have numerous advantages over mesh-based approaches, but their high computational cost has significantly hindered their progress, particularly for timedependent problems. In this study, we propose a time-adaptive meshless approach aimed at improving the computational efficiency of the method for addressing time-dependent issues. Specifically, we use the element-free Galerkin (EFG) method for spatial discretization, and the trapezoidal rule (TR) with adaptive time stepping for time integration. Additionally, we incorporate the explicit second-order Adams-Bashforth (AB2) method to control the error. The adaptive control of the time step effectively resolves issues related to non-convergence and low computational efficiency caused by inappropriate selection of the time step. To validate the efficacy and accuracy of the algorithm, we provide several numerical examples. The numerical results demonstrate that the EFG method combined with TR-AB2 method (EFG-TR-AB2) exhibits significant potential in solving two-dimensional transient heat conduction problems, which can maintain computational accuracy and improve computational efficiency.
- Subjects
HEAT conduction; GALERKIN methods; ADAPTIVE control systems; ELECTRIC transients; DISCRETIZATION methods
- Publication
IAENG International Journal of Applied Mathematics, 2023, Vol 53, Issue 4, p1520
- ISSN
1992-9978
- Publication type
Article