Efficient Broadband Simulation of Fluid-Structure Coupling for Membrane-Type Acoustic Transducer Arrays Using the Multilevel Fast Multipole Algorithm

Abstract

A boundary element model provides great flexibility for the simulation of membrane-type micromachined ultrasonic transducers (MUTs) in terms of membrane shape, actuating mechanism, and array layout. Acoustic crosstalk is accounted for through a mutual impedance matrix which captures the primary crosstalk mechanism of dispersive-guided modes generated at the fluid-solid interface. However, finding the solution to the fully-populated boundary element matrix equation using standard techniques requires computation time and memory usage which scales by the cube and by the square of the number of nodes, respectively, limiting simulation to a small number of membranes. We implement a solver with improved speed and efficiency through the application of a multi-level fast multipole algorithm (FMA). By approximating the fields of collections of nodes using multipole expansions of the free-space Green’s function, an FMA solver can enable the simulation of hundreds of thousands of nodes while incurring an approximation error that is controllable. Convergence is drastically improved using a problem-specific block-diagonal preconditioner. We demonstrate the solver’s capabilities by simulating a 32-element 7 MHz 1-D CMUT phased array with 2880 membranes. The array is simulated using 233,280 nodes for a very wide frequency band up to 50 MHz. For a simulation with 15,210 nodes, the FMA solver performed 10-times faster and used 32-times less memory than a standard solver based on LU decomposition We investigate the effects of mesh density and phasing on the predicted array response and find that it is necessary to use about 7 nodes over the width of the membrane to observe convergence of the solution–even below the first membrane resonance frequency–due to the influence of higher-order membrane modes.

Squeeze film damping and stiffening in circular CMUT with air-filled cavity: Influence of the lateral venting boundary conditions and the bias voltage

“…However, the DC bias voltage causes the static deflection of the membrane, making the cavity non-uniform. The models based on finite difference plate equation discretization take into account this effect [21][22][23][24][25]. Therefore, the air stiffness of non-uniform circular cavity ( Fig.…”

“…1.b). Therefore, an accurate implementation of the squeeze film effects in existing analytical and numerical CMUTs models as described in [21][22][23][24][25]33] requires the characterization of the stiffness of non-uniform airfilled gap. The problem is handled only for large squeeze number, typical for CMUT operation.…”

A Hybrid Boundary Element Model for Simulation and Optimization of Large Piezoelectric Micromachined Ultrasonic Transducer Arrays

“…This code is built on several open source tools: Python (Python Software Foundation), Cython (optimising compiler), NumPy (multi-dimensional arrays), and SciPy (scientific programming). For implementation details of our solver, please refer to [27].…”

“…Membrane dynamics such as stiffness and piezoelectrically-induced actuation loading are extracted from finite element method (FEM) simulation of a single membrane structure. Acoustic interactions are calculated using a multi-level fast multipole algorithm (ML-FMA), which we have reported on previously [27]. This approach has a number of distinct advantages when compared with previous models.…”

“…First, because acoustic interactions are calculated on a node-to-node basis, membranes are not restricted to simple axisymmetric deflection. In fact, we have shown previously that high-order modes and anti-symmetric modes may contribute to cross-talk, even within the first frequency band of the transducer [27]. Second, by utilizing FEM simulation, the BEM model is generalized to cover more complicated membrane structures.…”