Efficient Computation of 3D Engineered (Anisotropic) Materials

研究概述和constitutivesinterest在复杂的电磁现象的建模显着增长，近年来。这在很大程度上受到两个因素的影响：越来越强大的计算机和求解算法的进步。因此，时域技术的建模能力，如传输线建模方法（TLM），正在不断扩展，以实现具有复杂特性的三维材料的有效表示。这项工作的重点是TLM算法及其衍生物，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，即短期中期目标和长期目标，具体如下：短期/中期目标是：1.研究TLM中的各种完全匹配层（PML）公式，旨在改善与反射性能差和后期不稳定性相关的问题.除此之外，我们也将研究一种将PML技术整合到UTLM演算法中的公式。探索的机会所提出的坐标变换作为一种方法来设计一个UTLM制定散装各向异性材料，从而为四面体TLM grids.METHODOLOGY /方法的原始PML所提出的方法，以实现短期/长期的目标包括：1。探索坐标变换及其与材料参数的等价性。特别是，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TLM方法制定遵循TLM理念的SCB PML的实现。还将采用一种混合方法在UTLM中实现PML，该方法涉及在计算域中采用非结构化网格，在PML区域中采用结构化网格。到目前为止，所有现有的TLM-PML公式都表现出弱稳定性和较差的性能，他们的有限差分时域对应。因此，对这些问题的任何改进都将被证明是新颖的。到目前为止，PML还没有被证明在原来的四面体TLM网格。实现这一点将是该领域的一个重大进展，因此展示了新颖性。到目前为止，PML尚未通过混合方法在UTLM网格中得到证明。因此，简单地将PML引入UTLM将是对该领域的重大贡献，因为与PML相比，目前采用的截断方法在计算上是低效的。

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.