The research of space-time coupled spectral element method for acoustic wave equations

A space-time coupled spectral element method based on Chebyshev polynomials is presented for solving time-dependent wave equations.Acoustic propagation problems in1+1,2+1,3+1 dimensions with the Dirichlet boundary conditions are simulated via space-time coupled spectral element method using quadrilateral,hexahedral and tesseractic elements respectively.Space-time coupled spectral element method can obtain high-order precision over time.With the same total number of nodes,higher numerical precision is obtained if the higher-order Chebyshev polynomials in space directions and lower-order Chebyshev polynomials in time direction are adopted.Numerical illustrations have indicated that the space-time algorithm provides higher precision than the semi-discretization.When space-time coupled spectral element method is used,time subdomain-by-subdomain approach is more economical than time domain approach.