A high-order leap-frog based non-dissipative discontinuous Galerkin time- domain method for solving Maxwell＇s equations is introduced and analyzed. The pro- posed method combines a centered approximation for the eval...A high-order leap-frog based non-dissipative discontinuous Galerkin time- domain method for solving Maxwell＇s equations is introduced and analyzed. The pro- posed method combines a centered approximation for the evaluation of fluxes at the in- terface between neighboring elements, with a Nth-order leap-frog time scheme. More- over, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary level hanging nodes. The method is proved to be stable under some CFL-like condition on the time step. The convergence of the semi-discrete approximation to Maxwelrs equations is established rigorously and bounds on the global divergence error are provided. Numerical experiments with high- order elements show the potential of the method.展开更多
The partial differential equation(PDE)solution of the telegrapher is a promising fault location method among time-domain and model-based techniques.Recent research works have shown that the leap-frog process is superi...The partial differential equation(PDE)solution of the telegrapher is a promising fault location method among time-domain and model-based techniques.Recent research works have shown that the leap-frog process is superior to other explicit methods for the PDE solution.However,its implementation is challenged by determining the initial conditions in time and the boundary conditions in space.This letter proposes two implicit solution methods for determining the initial conditions and an analytical way to obtain the boundary conditions founded on the signal decomposition.The results show that the proposal gives fault location accuracy superior to the existing leap-frog scheme,particularly in the presence of harmonics.展开更多
基金supported by a grant from the French National Ministry of Education and Research(MENSR,19755-2005)
文摘A high-order leap-frog based non-dissipative discontinuous Galerkin time- domain method for solving Maxwell＇s equations is introduced and analyzed. The pro- posed method combines a centered approximation for the evaluation of fluxes at the in- terface between neighboring elements, with a Nth-order leap-frog time scheme. More- over, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary level hanging nodes. The method is proved to be stable under some CFL-like condition on the time step. The convergence of the semi-discrete approximation to Maxwelrs equations is established rigorously and bounds on the global divergence error are provided. Numerical experiments with high- order elements show the potential of the method.
基金Izudin Dzafic was supported by the Federal Ministry of Education and ScienceBosniathrough funding
文摘The partial differential equation(PDE)solution of the telegrapher is a promising fault location method among time-domain and model-based techniques.Recent research works have shown that the leap-frog process is superior to other explicit methods for the PDE solution.However,its implementation is challenged by determining the initial conditions in time and the boundary conditions in space.This letter proposes two implicit solution methods for determining the initial conditions and an analytical way to obtain the boundary conditions founded on the signal decomposition.The results show that the proposal gives fault location accuracy superior to the existing leap-frog scheme,particularly in the presence of harmonics.
基金国家自然科学基金重点项目( the key Project of National Natural Science Foundation of China under Grant No.50539140) 国家自然科 学基金( the National Natural Science Foundation of China under Grant No.50579022)高等院校博士学科点专项科研基金( the China Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20050487062)
