Efficient Computation of 3D Engineered (Anisotropic) Materials

研究综述与目的近年来，人们对复杂电磁现象建模的兴趣显著增长。这在很大程度上受到两个因素的影响：日益强大的计算机，以及求解器算法的进步。因此，诸如传输线建模方法(TLM)的时域技术的建模能力正在不断扩展，以使得能够有效地表示具有复杂属性的三维材料。本文重点研究了TLM算法及其衍生的非结构化传输线建模(UTLM)方法。该项目的目标可以分为两个阶段，即较短的中期目标和较长期的目标，具体如下：1.研究TLM中的各种完美匹配层(PML)配方，以改善与较差的反射性能和后期不稳定性有关的问题。此外，还将研究将PML技术集成到UTLM算法中的公式。长期目标是：3.探索坐标变换带来的机会，作为一种方法来设计用于块状各向异性材料的UTLM公式，从而设计用于四面体TLM网格的原始PML。方法/方法为了实现短期/长期目标，所提出的方法包括：1.探索坐标变换及其与材料参数的等价性。尤其是在基于拉伸的坐标(SCB)PML解释的情况下。2.将为结构化和非结构化的TLM方法制定符合TLM理念的SCB PML的实施。还将采取一种在UTLM中实施PML的混合方法，包括在计算域中使用非结构化网格，在PML区域中使用结构化网格。到目前为止，所有现有的TLM-PML公式都表现出较弱的稳定性和较差的性能。因此，在这些问题上的任何改进都将被证明是新奇的。到目前为止，PML还没有在原始的四面体TLM网格中得到演示。实现这一点将是该领域的一大进步，因此显示出新颖性。到目前为止，PML还没有通过混合方法在UTLM网格中进行演示。因此，简单地将PML引入UTLM将是对该领域的重大贡献，因为目前使用的截断方法与PML相比在计算上效率低下。

RESEARCH OVERVIEW AND OBJECTIVESInterest in the modelling of complex electromagnetic phenomena has grown significantly in recent years. This has largely been influenced by two factors: increasingly more powerful computers, and advancements in solver algorithms. As such, the modelling capabilities of time domain techniques, such as the transmission line modelling methods (TLM), are continually being expanded to enable an efficient representation of three dimensional materials with complex properties. This work focuses on the TLM algorithm and its derivative, the unstructured transmission line modelling (UTLM) method. The objectives of the project can be divided into two phases, namely the shorter intermediate aims and longer term goal which are given below:Short/Intermediate aim is to: 1. To investigate the various perfectly matched layer (PML) formulations in TLM with the aim of improving the issues relating to the inferior reflection performance and late-time instabilities.2. In addition to this, a formulation that integrates the PML technique into the UTLM algorithm will also be investigated.Long term aim is to: 3. Explore the opportunities presented by coordinate transformations as an approach to devise a UTLM formulation for bulk anisotropic materials and thus an original PML for tetrahedral TLM grids.METHODOLOGY / APPROACH The proposed methodology to achieve the short/long term goal involves:1. Exploring coordinate transformations and its equivalence with material parameters. Particularly, in the case of the stretched based coordinate (SCB) PML interpretation. 2. An implementation of the SCB PML that follows a TLM philosophy will be formulated for the structured and unstructured TLM methods.3. An hybrid approach to implementing the PML in UTLM will also be taken which involves employing an unstructured mesh in the computational domain and a structured mesh in the PML region.NOVELTY1. To date, all existing TLM-PML formulations have demonstrated weak stability and inferior performance to their finite-difference time domain counterpart. Therefore, any improvement on these issues will prove novel.2. To date, the PML has not been demonstrated in an original tetrahedral TLM mesh. Achieving this will be a major advance in the field and thus demonstrates novelty.3. To date, the PML has not been demonstrated in a UTLM mesh via an hybrid approach. Therefore, simply introducing the PML into UTLM will be a major contribution to the field, seeing that the truncation methods currently employed are computationally inefficient in comparison to the PML.