On the Equivalence of the Digital Waveguide and Finite Difference Time Domain Schemes

JULIUS O. SMITH III

Center for Computer Research in Music and Acoustics (CCRMA)
Department of Music, Stanford University, Stanford, California 94305 USA

Date: July 21, 2004

Abstract:

It is known that the digital waveguide (DW) method for solving the wave equation numerically on a grid can be manipulated into the form of the standard finite-difference time-domain (FDTD) method (also known as the ``leapfrog'' recursion). This paper derives a simple rule for going in the other direction, that is, converting the state variables of the FDTD recursion to corresponding wave variables in a DW simulation. Since boundary conditions and initial values are more intuitively transparent in the DW formulation, the simple means of converting back and forth can be useful in initializing and constructing boundaries for FDTD simulations.