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

Paola F. Antonietti, Omer M. O. Abdalla+3 more|arXiv (Cornell University)|Mar 6, 2026

Ultrasound Imaging and Elastography0 citations

TL;DR

The paper presents a hybrid framework combining reduced-order PMUT modal models with a high-fidelity DG-SEM acoustic solver to efficiently simulate large PMUT arrays, including TX/RX phases and non-conforming mesh handling.

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.

Motivation & Objective

• Develop a scalable computational framework for large PMUT arrays by coupling reduced-order PMUT models with a high-fidelity acoustic solver.
• Enable accurate simulation of both transmission and reception phases for PMUT arrays.
• Incorporate non-conforming mesh interfaces and DG-SEM for high-order accuracy in the acoustic domain.
• Leverage parallel computing (MPI, METIS) and domain decomposition to achieve scalability.
• Validate accuracy, efficiency, and scalability through numerical experiments.

Proposed method

• Extract a reduced basis of PMUT vibration modes from a 3D piezoelectric eigenproblem for each PMUT.
• Couple the reduced-order PMUT model to an acoustic DG-SEM domain describing the array as bi-dimensional membranes.
• Discretize the coupled problem with a Discontinuous Galerkin Spectral Element Method and use a Newmark time integration scheme.
• Employ domain decomposition and non-conforming mesh handling to enable flexible meshing and efficient parallel computation.
• Implement the framework in SPEED, an open-source platform, with MPI-based parallelism and METIS partitioning.

Experimental results

Research questions

• RQ1 Can a hybrid reduced-order and high-fidelity DG-SEM framework accurately simulate large PMUT arrays while reducing computational cost?
• RQ2 How effectively can non-conforming meshes and interfaces be handled in the acoustic domain without sacrificing accuracy?
• RQ3 What is the performance (accuracy, scalability) of the proposed approach for PMUT transmission and reception scenarios?

Key findings

• The framework demonstrates accuracy, scalability, and efficiency for large PMUT array simulations.
• Non-conforming mesh refinement and variable approximation orders are effectively managed via DG interfaces.
• A reduced modal basis for PMUTs reduces computational complexity while preserving essential electromechanical coupling.
• Open-source SPEED provides a parallelized platform leveraging domain decomposition, high-order polynomials, METIS, and MPI.
• The method supports both TX and RX phases of PMUT operation within a single coupled framework.