This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent ...This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.展开更多
One of the open issues in principle scheme design of mechanical systems is principle representation, which not only outlines the physical principles, but also facilitates the design synthesis. An energy-based approach...One of the open issues in principle scheme design of mechanical systems is principle representation, which not only outlines the physical principles, but also facilitates the design synthesis. An energy-based approach to represent principle scheme design is proposed. Firstly, an energy interaction model of mechanical systems is established and an intermediate model is derived, in which principle scheme design is transformed into solving the energy functions of system. Then the energy functions are modeled with the language of bond graphs, and principle representation for components is presented. Finally, characteristics of the developed representation approach are analyzed and a design example of gate drive system is given to demonstrate this approach.展开更多
It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes？ To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which ...It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes？ To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which has been studied extensively for the phase field type equations. In this work, we will show that a stronger stability under the infinity norm can be established for the implicit-explicit discretization in time and central finite difference in space. In other words, this commonly used numerical method for the Allen-Cahn equation preserves the maximum principle.展开更多
基金supported by the National Natural Science Foundation of China(12126318,12126302).
文摘This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.
基金This project is supported by the National Natural Science Foundation of China (60174037, 50275013) and Foundation for University Key Teacher by the Ministry of Education.
文摘One of the open issues in principle scheme design of mechanical systems is principle representation, which not only outlines the physical principles, but also facilitates the design synthesis. An energy-based approach to represent principle scheme design is proposed. Firstly, an energy interaction model of mechanical systems is established and an intermediate model is derived, in which principle scheme design is transformed into solving the energy functions of system. Then the energy functions are modeled with the language of bond graphs, and principle representation for components is presented. Finally, characteristics of the developed representation approach are analyzed and a design example of gate drive system is given to demonstrate this approach.
文摘为解决燃料电池混合动力公交车中基于优化的能量管理策略难以实车应用的问题,在分析燃料电池公交车(Fuel cell hybrid bus,FCHB)行驶路线的固定性和片段性的基础上,提出了一种基于SOM-K-means(Self-organized mapping K-means)工况识别的能量管理策略。首先,根据公交车站点将行驶路线划分为多个行驶片段,在车辆停站时,运用SOM-K-means二阶聚类模型完成工况识别,获取车辆下一行驶片段的识别协态变量;当车辆在下一个行驶片段运行时,运用识别协态变量完成基于庞特里亚金极值原理(Pontryagin s maximum principle,PMP)求解的能量管理策略的实时应用。其次,建立基于公交车实际运行数据的仿真实验,最后建立硬件在环实验,将所提出的策略移植入整车控制器(Vehicle control unit,VCU)中进行实验。实验结果表明,与基于规则的能量管理策略相比,本研究提出的能量管理策略降低了19.77%的平均等效氢气消耗。且该策略在VCU中每一步的计算时间大约为30 ms,计算结果与仿真结果完全一致,满足车辆对能量管理策略的时效性和准确性的要求。
文摘It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes？ To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which has been studied extensively for the phase field type equations. In this work, we will show that a stronger stability under the infinity norm can be established for the implicit-explicit discretization in time and central finite difference in space. In other words, this commonly used numerical method for the Allen-Cahn equation preserves the maximum principle.
