In this paper,we present a dual-horizon nonlocal diffusion model,in which the influence area at each point consists of a standard sphere horizon and an irregular dual horizon and its geometry is determined by the dist...In this paper,we present a dual-horizon nonlocal diffusion model,in which the influence area at each point consists of a standard sphere horizon and an irregular dual horizon and its geometry is determined by the distribution of the varying horizon parameter.We prove the mass conservation and maximum principle of the proposed nonlocal model,and establish its well-posedness and convergence to the classical diffusion model.Noticing that the dual horizon-related term in fact vanishes in the corresponding variational formof themodel,we then propose a finite element discretization for its numerical solution,which avoids the difficulty of accurate calculations of integrals on irregular intersection regions between the mesh elements and the dual horizons.Various numerical experiments in two and three dimensions are also performed to illustrate the usage of the variable horizon and demonstrate the effectiveness of the numerical scheme.展开更多
基金supported by the National Natural Science Foundation of China(Grants 11801533,11871454)Fundamental Research Funds for the Central Universities(Grant 202042008)Natural Science Foundation of Shandong Province(Grant ZR2019ba031).
文摘In this paper,we present a dual-horizon nonlocal diffusion model,in which the influence area at each point consists of a standard sphere horizon and an irregular dual horizon and its geometry is determined by the distribution of the varying horizon parameter.We prove the mass conservation and maximum principle of the proposed nonlocal model,and establish its well-posedness and convergence to the classical diffusion model.Noticing that the dual horizon-related term in fact vanishes in the corresponding variational formof themodel,we then propose a finite element discretization for its numerical solution,which avoids the difficulty of accurate calculations of integrals on irregular intersection regions between the mesh elements and the dual horizons.Various numerical experiments in two and three dimensions are also performed to illustrate the usage of the variable horizon and demonstrate the effectiveness of the numerical scheme.
