A direct method to computational acoustics

The exact knowledge of the sound field within an enclosure is essential for a number of applications in electro-acoustics. Conventional methods for the assessment of room acoustics model the sound propagation in analogy to the propagation of light. More advanced computational methods rely on the numerical solution of the wave equation. A recently presented method is based on multidimensional wave digital principles. It allows a physically exact numerical modelling of the relevant acoustical effects and yields robust algorithms. This contribution presents a new foundation of the multidimensional wave digital principle as applied to room acoustics. It starts from the first principles of physics. From there, the derivation of the algorithm only involves basic knowledge of numerical mathematics, linear algebra, and multidimensional system theory. An example for the simulation of dynamic three-dimensional sound propagation demonstrates the capability of the method.