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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, Michelangelo G. Garroni, Ilario Mazzieri, Nicola Parolini

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.

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 (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.
Paper Structure (15 sections, 24 equations, 27 figures, 1 table, 3 algorithms)

This paper contains 15 sections, 24 equations, 27 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Multi-physics problem formulation for large PMUT array simulations
  3. Space discretization: Discontinous Galerkin Spectral Element Method
  4. Algebraic formulation and time integration
  5. Parallel implementation strategies for PMUT simulations
  6. Setup of the computational domain structure
  7. Load balancing strategy for Omegaout U OmegaPML
  8. Mesh generation and load balancing strategy for Omegain
  9. Fast assembly of interface terms for non-matching grids
  10. Numerical results
  11. Single PMUT excitation in TX phase
  12. Single PMUT with an obstacle in TX-RX phase
  13. Multi-array PMUT simulation
  14. Performance comparisons and scalability test
  15. Conclusions and future developements

Figures (27)

  • Figure 1: Cross-section of a representative PMUT stack, illustrating the multilayer structure in which each layer has a defined thickness and distinct material properties.
  • Figure 2: A three-dimensional view of the domain decomposition (left) and the corresponding two-dimensional slice with boundary labels (right) for (\ref{['eq:full_problem']}).
  • Figure 3: Example of mesh employed in the DG-SE approach. Different mesh sizes and polynomial degrees are employed for $\Omega_\text{in}$ and $\Omega_\text{out}$, resulting in a non-conforming mesh.
  • Figure 4: Representation of two adjacent hexahedra $K^{+}$ and $K^{-}$ with the shared face $F$ and the corresponding normal vectors $\bm{n}^{+}$ and $\bm{n}^{-}$.
  • Figure 5: Schematic illustration of the outer domain decomposition: non-optimized partitioning (left), DG layer $\Omega_\text{DG}$ (middle), optimal partitioning (right). The set of processors is $\{P_1, P_2, P_3, P_4\} = \{\textcolor{c1}{$\bullet$},\, \textcolor{c2}{$\bullet$},\, \textcolor{c3}{$\bullet$},\, \textcolor{c4}{$\bullet$}\}$.
  • ...and 22 more figures