Multem 3: An updated and revised version of the program for transmission and band calculations of photonic crystals

We present here Multem 3, an updated and revised version of Multem 2, which syntax has been upgraded to Fortran 2018, with the source code being divided into modules. Multem 3 is equipped with LAPACK, the state-of-the art Faddeeva complex error function routine, and the Bessel function package AMOS. The amendments significantly improve both the speed, convergence, and precision of Multem 2. Increased stability allows to freely increase the cut-off value LMAX on the number of spherical vector wave functions and the cut-off value RMAX controlling the maximal length of reciprocal vectors taken into consideration. An immediate bonus is that Multem 3 can be reliably used to describe bound states in the continuum (BICs). To ensure convergence of the layer coupling scheme, it appears that appreciably larger values of convergence paramaters LMAX and RMAX are required than those reported in numerous published work in the past using Multem 2. We hope that Multem 3 will become a reliable and fast alternative to generic commercial software, such as COMSOL Multiphysics, CST Microwave Studio, or Ansys HFSS, and that it will become the code of choice for various optimization tasks for a large number of research groups. The improvements concern the core part of Multem 2, which is common to the extensions of Multem 2 for acoustic and elastic multiple scattering and to the original layer-Kohn-Korringa-Rostocker (LKKR) code. Therefore, the enhancements presented here can be readily applied to the above codes as well. The previous version of this program may be found at https://doi.org/10.1016/S0010-4655(00)00131-4.

本文介绍Multem 3——即Multem 2的更新修订版本，其语法已升级至Fortran 2018标准，源代码采用模块化结构。Multem 3集成了LAPACK、当前最优的Faddeeva复误差函数程序，以及贝塞尔函数工具包AMOS。本次修订显著提升了Multem 2的运算速度、收敛性与计算精度。稳定性的增强使得用户可自由调高球面矢量波函数数量的截断阈值LMAX，以及控制所纳入倒易矢量最大长度的截断阈值RMAX。一项额外优势在于，Multem 3可可靠地用于描述连续域束缚态（bound states in the continuum, BICs）。为确保层耦合方案的收敛性，相较于过往使用Multem 2的诸多已发表研究，本次更新所需的收敛参数LMAX与RMAX的取值需显著更大。我们期望Multem 3能够成为通用商业软件（如COMSOL Multiphysics、CST Microwave Studio及Ansys HFSS）的可靠且高效替代方案，并成为众多研究团队各类优化任务的首选代码。本次改进涉及Multem 2的核心模块，该模块同时适配了Multem 2针对声学与弹性多散射问题的扩展版本，以及原始的层-Kohn-Korringa-Rostocker代码（layer-Kohn-Korringa-Rostocker, LKKR）。因此，本文所述的改进也可直接应用于上述代码。该程序的旧版可通过https://doi.org/10.1016/S0010-4655(00)00131-4获取。