A multiregion-integral-equation method for wearable and implantable device design and evaluation : modeling, high-performance algorithms, and postprocessing

Computational bioelectromagnetics has an essential role during the design phase of wireless devices that operate near, on, or inside the human body. Simulating the electromagnetic interaction of devices with a nearby human body, however, presents significant challenges that manifest in three areas of the simulation process: (i) Modeling challenges arise when simultaneously modeling devices (with complex geometrical features) and bodies (with inhomogeneous tissues); interfacing such models and creating consistent (conformal) discretizations/meshes is difficult, especially when high-fidelity device and anatomical body models are used, because the two types of models are often developed independently and because they exhibit large differences in length scales, model sizes, and material properties. (ii) Solution challenges arise due to the size of the problem, potentially reaching to 10⁸–10⁹ unknowns, as well as the multitude of simulations that are of interest, e.g., to quantify the impact of variations in anatomy, posture, and device position/orientation on the performance of the design. (iii) Postprocessing challenges arise also because of the problem size and because of the increasing demand for more accurate and numerous secondary quantities, e.g., for multiphysics simulations. Calculating such secondary quantities quickly becomes the bottleneck of the simulation process, especially when powerful modeling methods and solution algorithms are developed to address the other challenges. This dissertation presents an integral-equation based approach to address these challenges and enable more advanced designs of body-worn and implanted devices. The dissertation presents a formulation that hybridizes a multiregion surface-integral equation formulation with a volume-integral equation pertinent to scattering from inhomogeneous tissues. The proposed formulation sidesteps many of the modeling challenges by allowing devices to be modeled and meshed independently of the anatomical human body model and mesh, by coupling them using an equivalent surface, and by simultaneously solving the resulting fully-coupled linear system of equations. To address the solution challenges, a scalable fast iterative algorithm that is accelerated by the multiple-grid adaptive integral method and parallelized using a hybrid shared-memory/distributed-memory (OpenMP/MPI) scheme is presented; moreover, a Schur-complement based algorithm is developed to harness the relatively small size of the system of equations corresponding to the equivalent surface and to rapidly perform the multitude of simulations needed during the design process. To accelerate the postprocessing stage, auxiliary-grid-based methods to rapidly compute far-field and near-field distributions are proposed. The dissertation also presents a benchmark suite that can be used to evaluate competitive computational bioelectromagnetics methods empirically and objectively; this suite is used to quantify the performance of the presented methods. Finally, three classes of problems are simulated to demonstrate the utility of the proposed work: a wearable antenna near an anatomical human model, an ingestible device inside an anatomical human model, and an anatomical human model under MRI exposure