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

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 (DG-SEM) 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 within the SPectral Elements in Elastodynamics with Discontinuous Galerkin (SPEED) software, an open-source library. A key contribution of this work is the introduction of a novel parallel computational framework based on a domain decomposition procedure, high-order polynomial discretizations, METIS graph partitioning, and MPI communications. This new feature enables efficient large-scale wave propagation simulations involving very large PMUT arrays on distributed-memory architectures. 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.