Adaptive manifold interpolation techniques for acoustic metamaterial characterization in HPC environments

Abstract

Functionally graded acoustic metamaterials (FGAMs) can be designed to have specific waveguide properties dictated by a theory relevant to the application. Frequently, these material properties do not exist naturally, and must be fabricated by gradually layering manufactured unit cell microstructures, resulting in a (usually smooth) variation of properties. Tailoring these microstructures to the demands of the relevant theory requires assembling microstructures with very specific material properties—a process that often requires haphazardly searching a large domain space of unit cells for desirable parameter combinations. Moreover, the process of determining the material tensor of interest for a specific set of metamaterial cell design parameters typically involves solving a costly high dimensional finite element problem for each new microstructure cell of interest. This work presents a gradient-based, manifold interpolation technique to characterize acoustic metamaterial homogenized elastic tensors. An adaptive refinement method is used to seed the interpolation data allowing the method to reliably recover unit cell stiffness tensors within predefined error bounds—allowing for interpolation of a cell with desired properties within specified error tolerances while minimizing the number of unit cells that require high-fidelity, computationally-expensive simulation. Finally, an implementation of the process is presented in a massively parallel computing environment.