Polynomial Time-Marching for Three-Dimensional Wave Equations

As a continuation of the efficient and accurate polynomial interpolation time-marching technique in one-dimensional and two-dimensional cases, this paper proposes a method to extend it to threedimensional problems. By stacking all two-dimensional (x, y) slice matrices along Z direction, threedimensional derivative matrices are constructed so that the polynomial interpolation time-marching can be performed in the same way as one-dimensional and two-dimensional cases. Homogeneous Dirichlet and Neumann boundary conditions are also incorporated into the matrix operators in a similar way as in one- and two-dimensional problems. A simple numerical example of scalar wave propagation in a closed-cube has validated this extended method. KEY WORDS: Time-marching; Chebyshev collocation; boundary value problems; differentiation matrix; three-dimensional problems 1 Introduction In order to obtain balanced spectral accuracy in both time and space when numerically solving wave equations, Tal-Ezer (1..