Fourier spectral method for acoustic simulation with domain enclosed by curved boundary

Curved geometries often make sound propagation complex. Such complexity may cause acoustical problems including flutter echo and sound focusing. When designing the geometry, acoustic simulation can be helpful to prevent such problems. Fourier spectral method (FSM) is a simulation method by approximation using the Fourier basis. Although FSM has many advantages such as its high convergence rate, the application range of the conventional FSM is limited to a simply-shaped domain with a specific boundary condition. In a realistic acoustics room setting, there exist a lot of room shapes beyond the scope of FSM. At the same time, the Fourier extension (FE) has been proposed for approximating a function on a complicated domain by the Fourier basis. It can be expected that the FE expands the application range of FSM. In this paper, we introduce FE into FSM for extending it to make a computational domain enclosed by curved boundaries tractable.