Modified space-time radial basis function collocation method for long-time simulation of transient heat conduction in 3D anisotropic composite materials

In this paper, the standard and the localized space-time radial basis function (RBF) collocation methods are modified and combined with the time-marching scheme and space-time domain decomposition technique for simulating the long-time transient heat conduction in 3D anisotropic composite materials. In the proposed approaches, we set the source points outside the whole space-time domain in the standard space-time RBF collocation method or outside the established subdomain in the localized approach by introducing the space and time magnification factors, instead of distributing them inside the original domain. In addition, the space-time regulating factor is defined and added to the conventional schemes to improve the stability of numerical methods. The modified approaches are resulted in a simple and effective time-marching process which can achieve long-time simulation, resting on the property that the coefficient matrices generated by these two methods are only related to the space-time distance between the collocation points and source points. Our ultimate aim is to develop a computing system for resolving dynamic problems in composite materials by designing a space-time domain decomposition technique. Numerical experiments are conducted to demonstrate the accuracy, efficiency and stability of the presented methodologies.