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

Author: GENG Yanhui; QIN Guoliang; WANG Yang; HE Wei 

Affiliation: Institute of Fluid Machinery, Xi'an Jiaotong University 

Abstract: 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.