In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topo...In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(R<sup>n</sup>) of functions of class C<sup>∞ </sup>on R<sup>n</sup> which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn</sup>) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C<sup>∞</sup> with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.展开更多
以氮化镓(GaN)为代表的第三代半导体正促使着固态微波功率器件向着更高功率、更高效率、集成化的方向不断发展,但这会导致器件内部电磁场分布效应更为显著,单一的路仿真已无法满足分析设计的精度需求,亟需建立有源GaN器件与无源电磁结...以氮化镓(GaN)为代表的第三代半导体正促使着固态微波功率器件向着更高功率、更高效率、集成化的方向不断发展,但这会导致器件内部电磁场分布效应更为显著,单一的路仿真已无法满足分析设计的精度需求,亟需建立有源GaN器件与无源电磁结构的一体化协同仿真技术.针对这一需求,本文提出基于时域不连续伽辽金技术的GaN基高功率微波器件高效场路协同仿真方法,将所提取的GaN HEMT(high electron mobility transistor)器件大信号紧凑模型引入电磁场方程中,采用局部时间步进技术以消除非线性紧凑模型及多尺度网格对全局算法稳定性条件的限制,实现有源器件-无源电磁结构、多尺度粗细网格的高效自适应求解.通过数值仿真算例与实验测试及软件计算结果对比展示了本文所提方法准确性和高效性,可为先进大功率微波器件的高可靠研发提供理论基础与设计参考.展开更多
文摘In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(R<sup>n</sup>) of functions of class C<sup>∞ </sup>on R<sup>n</sup> which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn</sup>) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C<sup>∞</sup> with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.
文摘以氮化镓(GaN)为代表的第三代半导体正促使着固态微波功率器件向着更高功率、更高效率、集成化的方向不断发展,但这会导致器件内部电磁场分布效应更为显著,单一的路仿真已无法满足分析设计的精度需求,亟需建立有源GaN器件与无源电磁结构的一体化协同仿真技术.针对这一需求,本文提出基于时域不连续伽辽金技术的GaN基高功率微波器件高效场路协同仿真方法,将所提取的GaN HEMT(high electron mobility transistor)器件大信号紧凑模型引入电磁场方程中,采用局部时间步进技术以消除非线性紧凑模型及多尺度网格对全局算法稳定性条件的限制,实现有源器件-无源电磁结构、多尺度粗细网格的高效自适应求解.通过数值仿真算例与实验测试及软件计算结果对比展示了本文所提方法准确性和高效性,可为先进大功率微波器件的高可靠研发提供理论基础与设计参考.
