Discrete Simulation of a Class of Distributed Systems Using Functional Analytic Methods
Discrete Simulation of a Class of Distributed Systems Using Functional Analytic Methods
复制标题
使用泛函分析方法对一类分布式系统进行离散仿真
DOI：
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发表时间：
2006
影响因子：
2.5
通讯作者：
P. Steffen
中科院分区：
文献类型：
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作者：
V. Dymkou;R. Rabenstein;P. Steffen
本文研究了离散模拟的解决方案，通常出现在技术领域的初边值问题。由于它们中的许多导致无界和非自伴微分算子，我们必须使用一个相当普遍的理论作为数学基础。对于具有紧预解算子的扇形算子类，其初边值问题的解可用一个全纯半群表示。结果表明，该解决方案可以扩大关于所考虑的运营商的规范系统。这种扩展对应于频域中的多维函数变换。这一事实导致用于实现所得到的系统的简单结构。计算上有效的数值算法可以通过从数字信号处理理论中众所周知的适当方法导出。
This paper investigates the discrete simulation of the solution of initial-boundary-value problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value problem can be represented by means of a certain holomorphic semigroup. It is shown that the solution can be expanded with respect to the canonical system of the considered operator. Such an expansion corresponds to a multi-dimensional functional transformation in the frequency domain. This fact leads to simple structures for the realization of the resulting system. Computationally efficient numerical algorithms can be derived by proper methods well-known from the theory of digital signal processing.