Subdivision Based Isogeometric Analysis driven Electro-Acoustic Design

现代社会的许多重要设备都依赖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的影响：附近相互作用的物体的形状和位置在系统的性能中起着至关重要的作用。 为了实现最佳性能，有必要同时考虑发射或接收设备的设计以及其环境中的对象的设计。这项研究将研究基于计算机的方法来优化这些设备的形状及其环境，考虑到附近物体的影响，优化它们的形状或位置，以实现最佳的电磁或声学性能。我们的目标是开发一种基于计算机的框架，促进对新颖设计概念的探索，并有可能产生非凡的设计，其应用范围从用于数字通信的可穿戴或可变形技术，到用于医学成像、威胁检测或降噪的设备。 我们的方法依赖于等几何分析和细分曲面，并进行这种表示跨越几何描述，分析和优化。为了分析，我们制定了一个isogeometric积分方程版本的波散射问题的细分表面的基础上，在计算机动画中流行的几何表示技术，并在细分表面上的特征基的扩展。对于优化，我们依赖于一个新的配方拓扑优化方法，支持细分曲面表示和相关的特征基扩展，允许同时修改形状和拓扑结构，并支持灵敏度分析。为了便于探索的设计空间，我们建立映射的解决方案本征基和远场的频谱内容，这决定了电磁和声学性能。因此，每个本征基与给定形状的对象相关联，并且它对反映对象的形状和电磁或声学行为的信息进行编码。这将对象的形状及其行为结合到一个单一的实体中，作为多对象设计中可能的构建块进行优化和研究。其结果将是一个设计框架，允许设计人员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，并用于评估不同环境中的设计性能。

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.