Veröffentlichungen und Präsentationen

Ultrasound phased arrays are central to modern nondestructive testing (NDT) and medical imaging, yet the underlying beamforming principles — constructive and destructive interference of individually delayed element signals — are difficult to convey with static teaching material. Interactive simulation apps let students explore beam steering and focusing directly, but only if the response to a parameter change is near-instantaneous. A full finite element solution of the acoustic field takes on the order of one minute, which is prohibitive for classroom interaction. This work presents a workflow, built from scratch in COMSOL Multiphysics® version 6.4, that combines parametric FEM simulation, deep neural network (DNN) surrogate models, and browser-based deployment to deliver responsive phased array teaching apps for two audiences: an entry-level course on wave physics and an advanced course on ultrasound NDT. The model is a 2D frequency-domain setup using the Solid Mechanics interface of the Structural Mechanics Module, in combination with the Surrogate Model Training study; no other add-on modules or LiveLink™ products are used for this app. The geometry is a 15-cm-radius steel half-disc with a low-reflecting curved outer boundary. On the flat edge, up to 32 transducer elements at a pitch of λ/2 (longitudinal wavelength) are driven as sources at 2.25 MHz with individually controlled phase shifts. Two beamforming modalities are implemented: beam steering (constant inter-element delay producing a plane wave at a set angle) and beam focusing (delays computed for a chosen focal distance and angle). Inputs are steering angle, number of active elements, and focal distance; the output is the steady-state von Mises stress distribution over the half-space. To achieve interactive response times, a DNN is trained on approximately 2000 precomputed parameter combinations. The FEM mesh must resolve the wavelength with roughly five elements per λ, yielding fields far too data-intensive for training; the DNN is therefore trained on a 10× downsampled grid of the solution, which still resolves the focal spot and lobe structure. The trained surrogate is embedded in an app built with the Application Builder and served to students and teachers via COMSOL Server™, where field predictions appear effectively instantaneously upon parameter changes. The FEM results agree well with analytical expectations: simulated beam angles and focal positions match the prescribed inputs, and side lobes emerge at larger steering angles, as expected. Training and validation losses converge to approximately 0.012 (mean squared error on the normalized field) with no signs of overfitting. A second app, currently in development, extends the setup to the time domain with pulsed excitation as used in ultrasound imaging, based on the Elastic Waves, Time Explicit interface of the Acoustics Module. The FEM model is fully functional, and DNN training on the transient data is in progress, with the goal of displaying animations of the time-varying field. Classroom deployment begins next semester, and limited internal trial runs have already produced positive feedback. The presented FEM–surrogate–app pipeline generalizes readily to other computation-heavy physics topics, enabling interactive, browser-based teaching tools wherever direct simulation is too slow for live use.