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

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.