Subdivision Based Isogeometric Analysis driven Electro-Acoustic Design

Michigan State University, East Lansing MI

Investigators

Abstract

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.