高精度浮点数在电场积分方程低频崩溃时的应用

      Application of high-precision floating-point numbers to the low-frequency breakdown of electric field integral equations

      • 摘要: 电场积分方程(electric field integral equation, EFIE)“低频崩溃”现象是指当电磁波波长远大于离散单元的尺寸时,分析结果不准确的现象。它的发生与计算机浮点数的字长有关,高精度浮点数的普及有助于缓解低频崩溃现象的发生,但目前还没有关于不同精度的浮点数的低频崩溃临界阈值的研究报道。本文定量研究了不同字长浮点数的EFIE不发生低频崩溃的适用范围,以便在该适用范围内,研究人员仅须简单地修改现有EFIE代码的浮点数字长就可以进行电磁特性的准确分析而不发生低频崩溃,避免现有低频问题都需要修改基函数或积分方程等分析技术,为低频电磁分析增加了一种可选择的简便解决办法。经过数值算例的验证,高精度浮点数的EFIE可以将低频崩溃现象发生的离散网格的电尺寸降低到2.5×10−13,这已经能够处理我们常见的低频崩溃问题。

         

        Abstract: Electric field integral equation (EFIE) “low-frequency breakdown” phenomenon refers to the phenomenon that when the wavelength of the electromagnetic wave is much larger than the size of the discrete unit, the analysis results are not correct. Its occurrence is related to the word length of computer floating-point numbers, and the popularization of high-precision floating-point numbers can help alleviate the phenomenon of “low-frequency breakdown” phenomenon, but there is no research report on the critical threshold of low-frequency breakdown for floating-point numbers with different precision. In this paper, we quantitatively investigate the application range of EFIE with different word lengths of floating-point numbers without low-frequency crashes, so that within this application range, researchers only need to simply modify the lengths of floating-point numbers in the existing EFIE codes to accurately analyze the electromagnetic properties without “low-frequency breakdown”, thus avoiding the need to modify analysis techniques such as basis functions or integral equations for all existing low-frequency problems. This avoids the need to modify the base functions or integral equations of existing low-frequency problems, and adds an optional and simple solution for low-frequency electromagnetic analysis. As verified by numerical examples, the high-precision floating-point EFIE can reduce the electrical size of the discrete mesh where the “low-frequency breakdown” phenomenon occurs to 2.5×10−13, which is able to deal with the “low-frequency breakdown” problem that we generally encounter.

         

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