Subdivision Based Isogeometric Analysis driven Electro-Acoustic Design

许多对现代社会很重要的设备依靠声波或电磁波来实现其目的：小型化天线、可穿戴设备中的传感器、声学工程材料。这些设备的性能受到其附近物体存在的影响：附近物体的形状和位置，相互作用的物体在系统性能中起着至关重要的作用。为了达到最佳性能，有必要同时考虑发射或接收设备的设计以及其环境中物体的设计。本研究将研究基于计算机的方法，以优化此类设备的形状及其环境，考虑到附近物体的影响，优化其形状或放置，以实现最佳的电磁或声学性能。目标是开发一个基于计算机的框架，促进对新颖设计概念的探索，并有可能产生非凡的设计，其应用范围从数字通信的可穿戴或可变形技术，到医疗成像、威胁检测或降噪设备。我们的方法依赖于等几何分析和细分曲面，并在几何描述、分析和优化中使用这种表示。为了进行分析，我们基于细分表面（一种在计算机动画中流行的几何表示技术）和细分表面上的特征基展开，建立了波散射问题的等几何积分方程版本。对于优化，我们依赖于拓扑优化方法的新公式，该方法支持细分表面表示和相关的特征基扩展，允许同时进行形状和拓扑修改，并支持灵敏度分析。为了便于探索设计空间，我们建立了解特征基与远场频谱含量之间的映射关系，这决定了电磁和声学性能。因此，每个特征基都与给定形状的物体相关联，并且它编码反映物体形状和电磁或声学行为的信息。这将对象的形状及其行为结合成一个单一的实体，作为多对象设计的可能构建块进行优化和研究。结果将是一个设计框架，允许设计师从预先计算的构建块构建场景，并探索对象的最佳放置及其在各种场景中的优化。将构建涉及常见对象的标准场景目录，并用于评估设计在不同环境中的性能。

Many devices important to modern society rely on acoustic or electromagnetic waves to achieve their purpose: miniaturized antennas, sensors in wearable devices, acoustic engineered materials. The performance of these devices is affected by the presence of objects in their vicinity: the shape and location of near-by, interacting objects play a crucial role in the performance of the system. To achieve optimum performance it is necessary to consider, simultaneously, the design of the transmitting or receiving device, as well as the design of objects in its environment. This research will investigate computer-based methodologies to optimize the shape of such devices and their environment, taking into account the effect of close-by objects, optimizing their shape or placement to achieve optimal electromagnetic or acoustic performance. The goal is to develop a computer based framework that facilitates exploration of novel design concepts and has the potential to generate extraordinary designs, with applications ranging from wearable or deformable technologies for digital communications, to devices for medical imaging, for threat detection, or for noise mitigation. Our approach relies on isogeometric analysis and subdivision surfaces, and carries this representation across geometric description, analysis, and optimization. For analysis, we formulate an isogeometric integral equation version of wave scattering problems based on subdivision surfaces, a geometry representation technique popular in computer animation, and on an expansion of eigenbasis on the subdivision surface. For optimization, we rely on a new formulation for topology optimization methods that supports a subdivision surface representation and the associated eigenbasis expansion, allows simultaneous shape and topology modifications, and supports sensitivity analysis. To facilitate exploration of the design space, we establish mappings between the solution eigenbasis and the spectral content of far fields, which determine electromagnetic and acoustic performance. Thus, each eigenbasis is associated with an object of given shape, and it encodes information that reflects both the shape and the electromagnetic or acoustic behavior of the object. This combines the shape of the object and its behavior into a single entity, to be optimized and investigated as a possible building block in multi-object designs. The outcome will be a design framework that allows designers to build scenes from pre-computed building blocks, and explore the optimal placement of objects and their optimization in various scenes. Catalogs of standard scenes involving common objects will be constructed and used to evaluate design performance in different environments.