Improved adjustable boundary condition for the 2-D finite-difference time-domain mesh

Antti Kelloniemi
DAFx-2005 - Madrid
The digital waveguide (DWG) mesh is a method for simulating wave propagation in multiple dimensions. Boundary conditions are needed for modeling changes in wave propagation media such as walls and furniture in a room or boundaries of a resonating membrane of a musical instrument. The boundary conditions have been solved for a one-dimensional DWG structure, but there is no known exact solution for the multi-dimensional mesh. In this work, a new boundary structure is introduced for modeling reflection coefficient values −1 ≤ r ≤ 1 in two dimensions. The new method gives remarkably more accurate results than the earlier approximations, especially at the low absolute values of r. At incident angles of Θ < 60o , the absolute error of reflection coefficient r is below 0.1 at frequencies 0.004 < f < 0.222 relative to the sampling frequency and at 60o ≤ Θ ≤ 80o the same result is reached at 0.005 < f < 0.114.