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首页> 外文期刊>American Journal of Electromagnetics and Applications >Electromagnetic Problems Modeling Using Algebraic Topological Method
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Electromagnetic Problems Modeling Using Algebraic Topological Method

机译：使用代数拓扑方法建模的电磁问题

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We can solve electromagnetic problems using two main mathematical tools: vector calculus and differential equations. These tools command the computational electromagnetic domain. However, these tools are not always needed for the realistic modeling of electromagnetic problems. In reality, we are interested in the measurement of scalar quantities in electromagnetics, not vector quantities. Conventional electromagnetic simulation approaches are proving to be more mathematical than physical. Furthermore, the use of differential equations leads us along a different route for modeling fundamental physics. Since computers need discrete formulations, we can't directly transform continuous differential equations into numerical algorithms. The algebraic topological method is a direct discrete and computationally ambitious technique that uses only physically measurable scalar quantities. This paper simulates a parallel plate capacitor using global variables and calculating and comparing the potentials with the analytical method. The measured results show a good agreement between the analytical and the algebraic topological methods.
机译：我们可以使用两个主要数学工具解决电磁问题：矢量微积分和微分方程。这些工具命令计算电磁域。然而，电磁问题的现实建模并不总是需要这些工具。实际上，我们有兴趣测量电磁学中的标量度，而不是向量数量。传统的电磁模拟方法被证明与物理更加数学。此外，使用微分方程的使用沿着模拟基本物理学的不同路线引导我们。由于计算机需要离散配方，因此我们无法将连续微分方程直接转换为数字算法。代数拓扑方法是一种直接和计算雄心勃勃的技术，仅使用物理上可测量的标量数。本文使用全局变量模拟平行板电容，并计算和比较分析方法的电位。测量结果显示了分析和代数拓扑方法之间的良好一致性。

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