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Wave propagation effects such as resonance and interference effects complicate the design of many acoustic devices, particularly when the dimensions of the device are in the order of the operating wavelength. At the same time, these complications also offer an opportunity for numerical optimization schemes to outperform designs achieved using traditional methodology. An example of a device sensitive to resonance and interference effects is the compression driver, the standard sound source for midrange acoustic horns in public address systems. Although ingenious and rather simple design guidelines have been developed, these unfortunately only apply to particular conceptual compression driver layouts. Here, we address a configuration for which no simple rules exist and apply numerical shape optimization for the design task. We employ a level-set geometry description of the crucial part of the compression driver interior. To avoid mesh changes when the level-set function is updated by a gradient-based optimization algorithm, we rely on the cut finite element (CutFEM) technique for the acoustic modeling. A particular modeling challenge here is that viscothermal losses cannot be ignored, due to narrow chambers and slits in the device. Up to quite recently, the modeling of such losses has required computationally expensive solutions of the linearized, compressible Navier–Stokes equations, making the use of shape optimization extremely challenging. Fortunately, a recently developed, accurate, but computationally inexpensive boundary-layer model is applicable in this case. For the first time in the context of a CutFEM/level-set method, the shape calculus needed to compute derivatives for the optimization algorithm is carried out in the fully discrete case, taking into account the discontinuities along the design boundary of the pressure derivatives and the normal field. Applying these techniques, the algorithm was able to successfully design the interior of a compression driver so that the final frequency response very closely matches an ideal response, derived by a lumped circuit model where wave interference effects are not accounted for.

We propose an extended family of structured spatial priors that incorporates the total variation (TV) function with ℓp norms. The prior is proven to be proper and incorporated into a Bayesian regression framework to enable uncertainty quantification in T1 mapping, with posterior inference performed using the No-U-Turn Sampler (NUTS). This TV– ℓp construction is proven to constitute a well-defined family of prior distributions, and it naturally enforces spatial consistency and smooth variations in the estimated parameter maps. The method was evaluated in comparison to maximum-likelihood estimation and several Bayesian alternative priors based on the uniform, Gamma, and bounded TV priors. The evaluation includes experiments on synthetic brain and cardiac T1 mapping datasets, as well as a real in-vivo breast T1 mapping dataset. The results show that the TV–ℓp prior yields more concentrated posterior densities, indicating reduced uncertainty. It also consistently achieves lower variance and smaller (negative) bias, leading to more reliable estimates. Overall, embedding a TV-based structured penalty along with ℓp norms in a prior in a Bayesian model improves spatial coherence in T1 maps and enhances uncertainty quantification, offering a robust approach for T1 mapping with uncertainties.

This review focuses on material distribution-based topology optimization methods for boundary-effect-dominated problems. More precisely, it addresses problems where the behavior at or near the boundaries of the domain significantly influences the physics, such as problems involving boundary layers or the skin effect. While traditional topology optimization techniques have been highly successful in idealized settings, boundary-sensitive problems introduce unique challenges. We survey the historical development of relevant ideas, including fictitious-domain methods and filtering techniques, and provide a detailed account of modern approaches for handling boundary effects. Key topics include cascades of filters, multi-field representations, and methods for controlling length scale and interface sharpness. We also review specialized strategies for pressure and thermal loads, as well as recent advances in the design of coated structures and impedance-based modeling of boundary layers. This article aims to provide a comprehensive and structured overview of the field.

Structured regularization allows machine learning models to consider spatial relationships among parameters, leading to results that generalize better and are more interpretable compared to norm penalties. In this study, we evaluated a novel structured regularization method that incorporates approximate morphology operators defined using harmonic mean-based fW-filters. We extended this method to multiclass classification and conducted experiments aimed at classifying magnetic resonance images (MRI) of subjects into four stages of Alzheimer's disease progression. The experimental results demonstrate that the novel structured regularization method not only performs better than standard sparse and structured regularization methods in terms of prediction accuracy (ACC), F1 scores, and the area under the receiver operating characteristic curve (AUC), but also produces interpretable coefficient maps.

We propose a novel way to incorporate morphology operators through structured regularization of machine learning models. Specifically, we introduce a feature map in the models that performs structured variable selection. The feature map is automatically processed by approximate morphology operators and is learned together with the model coefficients. Experiments were conducted with linear regression on both synthetic data, demonstrating that the proposed methods are effective in selecting groups of parameters with much less noise than baseline models, and on three-dimensional T1-weighted brain magnetic resonance images (MRI) for age prediction, demonstrating that the proposed methods enforce sparsity and select homogeneous regions of non-zero and relevant regression coefficients. The proposed methods improve interpretability in pattern analysis. The minimum size of features in the structured variable selection can be controlled by adjusting the structuring element in the approximate morphology operator, tailored to the specific study of interest. With these added benefits, the proposed methods still perform on par with commonly used variable selection and structured variable selection methods in terms of the coefficient of determination and the Pearson correlation coefficient.

Accurate simulations of sound propagation in narrow geometries need to account for viscous and thermal losses. In this respect, effective boundary conditions that model viscothermal losses in frequency-domain acoustics have recently gained in popularity. Here, we investigate the time-domain analogue of one such boundary condition. We find that the thermal part of the boundary condition is passive in time domain as expected, while the viscous part is not. More precisely, we demonstrate that the viscous part is responsible for exponentially growing normal modes with unbounded temporal growth rates, which indicates ill-posedness of the considered model. A finite-difference-time-domain scheme is developed for simulations of lossy sound propagation in a duct. If viscous losses are neglected the obtained transmission characteristics are found to be in excellent agreement with frequency-domain simulations. In the general case, the simulations experience an instability much in line with the theoretical findings.

Near-field and radiation coupling between nearby radiating elements is unavoidable, and it is considered a limiting factor for applications in wireless communications and active sensing. This article proposes a density-based topology optimization approach to design decoupling networks for such systems. The decoupling network is designed by formulating an optimization problem that considers both energy transmission and reflection at the network ports. We replace the radiating elements by their time-domain impulse response for efficient computations and to enable the solution of the design problem using gradient-based optimization methods. We use the adjoint-field method to compute the gradients of the optimization objectives. Additionally, nonlinear filters are applied during the optimization procedure to impose minimum-size control on the optimized designs. We demonstrate the concept by designing the decoupling network for a two-element planar antenna array; the antenna is designed in a separate optimization problem. The optimized decoupling networks provide a signal path that destructively interferes with the coupling between the radiating elements while preserving their individual matching to the feeding ports. Compact decoupling networks capable of suppressing the mutual coupling by more than 10 dB between two closely separated planar antennas operating around 2.45 GHz are presented and validated experimentally.

We use a density-based topology optimization approach to design dualband planar metallic antennas. The design problem is formulated based on the time-domain Maxwell's equations, solved using the finite-difference timedomain (FDTD) method. The antenna design is formulated as an optimization problem where the received and reflected energy by the antenna in two frequency bands, centered around 2.5 GHz and 5.5 GHz, are optimized. Two design examples that exhibit outstanding performance are presented. In one design case, we employ a nonlinear filtering scheme to impose size control on the optimized design and ensure manufacturability.

Sonic black holes (SBHs) are waveguides intended to slow down the wave propagation speed and focus the energy towards the end of the device. However, the extent to which these effects occur, as well as the degree of wave dispersion introduced, has not been systematically quantified. This article investigates these aspects through transient finite-element computations, analyzing the properties of a novel, numerically optimized SBH with enhanced wave-focusing capabilities. The investigation utilizes the lossless acoustic wave equation as well as a linearized compressible flow formulation to account for viscothermal losses. We analyze the wave focusing and filtering properties of the SBH by monitoring the pressure amplitude and the transmission and reflection coefficients. Moreover, we examine the effective wave propagation speed along the centerline of SBH and assess the similarity of pressure wave packets using cross-correlations. Our results reveal that the optimized SBH not only enhances wave focusing but also on average effectively slows down wave propagation, demonstrating the device's potential as a true sonic black hole. By investigating two crucial aspects - wave-slowing effect and signal dispersion - that were not previously explored, we provide a deeper understanding of the device's functionality and operational mechanisms, including how its design influences wave-focusing performance and local wave speed.

The waveguide acoustic black hole (WAB) effect is a promising approach for controlling wave propagation in various applications, especially for attenuating sound waves. While the wave-focusing effect of structural acoustic black holes has found widespread applications, the classical ribbed design of waveguide acoustic black holes (WABs) acts more as a resonance absorber than a true wave-focusing device. In this study, we employ a computational design optimization approach to achieve a conceptual design of a WAB with enhanced wave-focusing properties. We investigate the influence of viscothermal boundary losses on the optimization process by formulating two distinct cases: one neglecting viscothermal losses and the other incorporating these losses using a recently developed material distribution topology optimization technique. We compare the performance of optimized designs in these two cases with that of the classical ribbed design. Simulations using linearized compressible Navier–Stokes equations are conducted to evaluate the wave-focusing performance of these different designs. The results reveal that considering viscothermal losses in the design optimization process leads to superior wave-focusing capabilities, highlighting the significance of incorporating these losses in the design approach. This study contributes to the advancement of WAB design and opens up new possibilities for its applications in various fields.