The numerical simulation of sound fields helps us to understand how sound and noise propagate and supports the development of robust, efficient noise-reduction methods. For this reason, we develop and apply computational methods to describe the physical interactions between sound and objects. Our research includes models of structural dynamics, sound fields, and vibrations, with applications in environmental noise control, automotive audio, auditory perception, and speech production.
Our work includes:
developing and applying efficient boundary element methods (BEM) for the Helmholtz equation to simulate sound propagation in 2D, 2.5D, and 3D
developing efficient methods for modelling systems with hysteretic behaviour
modelling and psychoacoustically evaluating sound-mitigation methods
developing models and methods to simulate the human vocal tract
Computers become more powerful every year, yet the demands of real-world applications (for example, more detailed models, larger and more complex geometries, and real-time applications) grow even faster. It is therefore essential to continuously develop new, robust numerical methods and to introduce new ideas and concepts into numerical and applied mathematics. By working in close collaboration with the other groups at the institute, we can link advances in mathematical concepts (for example, in frame and wavelet theory) directly to real-world problems, such as the calculation of head-related transfer functions (HRTFs) for 3D virtual audio or the evaluation of noise-reduction measures. As part of our long-term research strategy, the Numerics department is contributing to the Lighthouse project From Noise Detection and Simulation to the Development of Effective Countermeasures.
Noise affects everyday life in many ways, and effective mitigation requires a precise understanding of how sound is generated, how it propagates, and how humans perceive it. The Lighthouse Project in the Numerics Cluster brings together mathematics, acoustics, signal processing, and psychoacoustics to develop numerical methods that model real acoustic environments with high realism and precision. This long-term effort supports research across multiple clusters and provides the computational foundations needed for designing future noise-control solutions.
Understanding and Modelling Noise
To develop effective noise-mitigation measures, we study the entire chain of acoustic processes—from noise generation and propagation to human perception. Numerical simulations play a central role, enabling the assessment of complex acoustic scenarios where physical measurements alone are insufficient.
Challenges in Current Modelling Approaches
Many commonly used modelling techniques, such as ray tracing, either lack realism or capture only selected aspects of acoustic behavior. Our research focuses on developing new numerical methods and models that increase the accuracy and applicability of simulations, enabling a more realistic representation of complex acoustic environments.
Localizing Noise Sources
Effective noise mitigation often requires identifying the precise position of noise sources. Microphone arrays are frequently used for this purpose, yet established array techniques—such as beamforming, acoustic holography, or inverse BEM—still face limitations. To improve these methods, we combine mathematical approaches, such as compressed sensing and sparsity, with engineering techniques to enhance speed, accuracy, and stability.
Next-Generation Simulation Methods
A major focus of the project is the development of advanced numerical methods for simulating sound propagation, particularly using the Boundary Element Method (BEM). In real-world applications, standard numerical methods often become impractical due to constraints on computing power, memory usage, or runtime. At the same time, the demands of realistic acoustic simulations continue to grow—for example, when modelling very high frequencies or complex geometries such as vehicle interiors.
Theoretical Foundations and Mathematical Innovation
Robust, theoretically grounded numerical methods are essential for solving complex acoustic problems efficiently and reliably. To this end, we investigate theoretical aspects of acoustic BEM, combinations of frames with adaptive BEM, and time-domain wave-field decomposition methods. These developments provide the mathematical basis for efficient, stable solutions in large-scale, real-world acoustic scenarios.
Commitment to Reproducible Research
Reproducibility is a key priority at the institute. Where appropriate, we make tools and datasets openly available. One example is Mesh2HRTF, an open-source package for calculating head-related transfer functions (HRTFs), which is freely accessible to the research community.
Earlier Projects in Noise Research
Over the past years, the ARI has carried out several research projects on noise generation, propagation, and mitigation, in cooperation with scientific and industrial partners. These include projects such as PAAB, Wiabahn, LARS, RELSKG, and SysBahnLärm. Their findings have contributed to the institute’s long-term expertise in numerical acoustics and form part of the foundation for the current Lighthouse Project.
