A subwoofer generates the lowest frequency range in loudspeaker systems. Subwoofers are used in audio systems for live concerts, movie theatres, home theatres, gaming consoles, cars, etc. During the last decades, numerical simulations have emerged as a cost- and time-efficient complement to traditional experiments in the design process of different products. The aim of this study is to reduce the computational time of simulating the average response for a given subwoofer design. To this end, we propose a hybrid 2D–3D model that reduces the computational time significantly compared to a full 3D model. The hybrid model describes the interaction between different subwoofer components as interacting modules whose acoustic properties can partly be pre-computed. This allows us to efficiently compute the performance of different subwoofer design layouts. The results of the hybrid model are validated against both a lumped element model and a full 3D model over a frequency band of interest. The hybrid model is found to be both accurate and computationally efficient.

By using topology optimization, we consider the problem of designing a passive acoustic device that allows for one-way flow of sound waves; such a device is often colloquially referred to as an acoustic diode. The Helmholtz equation is used to model the time harmonic linear wave propagation together with a Dirichlet-to-Neumann (DtN) type boundary condition, and the finite element method is used for discretization. The objective of this study is to maximize the wave propagation in one direction (from left to right) and minimize the wave propagation in the reverse direction (from right to left) for planar incoming waves. The method of moving asymptotes (MMA) solves the optimization problem, and a continuation approach is used for the penalizing intermediate design variables. The results for the optimized waveguide show that more than 99.8% of the power of planar incoming waves get transmitted from left to right while less than 0.3% gets transmitted in the reverse direction for planar incoming waves in the specified frequency range. Since a true diode is a non-reciprocal device and here we used a linear acoustic wave model, which is basically reciprocal, we discuss details about how it appears to be possible to obtain a one-way waveguiding effect using this linear model.

We use material-distribution-based topology optimization to design a three-port frequency dividing multiplexer at microwave frequencies. That is, by placing a good electric conductor inside the design domain, we aim to design a passive device that splits the incoming signal’s frequencies into two frequency bands and transmits them to their respective output ports. The Helmholtz equation models the time-harmonic wave propagation problem. We solve the governing equation using the finite element method. The adjoint variable method provides the required gradients, and we solve the topology optimization problem using Svanberg’s MMA algorithm. In this study, we present a technique for modeling the distribution of a good electric conductor within the design domain. In addition, we derive a power balance expression, which aids in formulating a series of three objective functions. In each successive objective function, we add more information and evaluate its impact on the results. The results show that by selecting a suitable objective function, we achieve more than $$93.7\,\%$$ 93.7 % transmission for both the frequency bands. Moreover, the numerical experiments suggest that the optimization problem is self penalized and is sensitive to the initial design.