A hybrid reduced-order and high-fidelity discontinuous Galerkin Spectral Element framework for large-scale PMUT array simulations

TL;DR

This paper introduces a scalable hybrid computational framework combining reduced-order modeling and high-fidelity discontinuous Galerkin methods to efficiently simulate large-scale PMUT arrays for ultrasonic sensing and imaging.

Contribution

It presents a novel combined approach using model order reduction and DGSEM for large PMUT array simulation, enabling efficient and accurate electromechanical-acoustic modeling.

Findings

Framework achieves high accuracy in large PMUT array simulations

Method demonstrates excellent scalability and computational efficiency

Open-source implementation facilitates further research and development

Abstract

Piezoelectric Micromachined Ultrasonic Transducers (PMUTs) are essential for next-generation ultrasonic sensing and imaging due to their bidirectional electromechanical behavior, compact design, and compatibility with low-voltage electronics. As PMUT arrays grow in size and complexity, efficiently modeling their coupled electromechanical-acoustic behavior becomes increasingly challenging. This work presents a novel computational framework that combines model order reduction with a Discontinuous Galerkin Spectral Element Method (DGSEM) paradigm to simulate large PMUT arrays. Each PMUT's mechanical behavior is represented using a reduced set of vibration modes, which are coupled to an acoustic domain model to describe the full array. To further improve efficiency, a secondary acoustic domain is connected via DG interfaces, enabling non-conforming mesh refinement, with variable approximation order, and accurate wave propagation. The framework is implemented in the SPectral Elements in Elastodynamics with Discontinuous Galerkin (SPEED) software, an open-source, parallelized platform leveraging domain decomposition, high-order polynomials, METIS graph partitioning, and MPI for scalable performance. The proposed methodology addresses key challenges in meshing, supporting high-fidelity simulations for both PMUT transmission and reception phases. Numerical results demonstrate the framework's accuracy, scalability, and efficiency for large PMUT array simulations.