Publications [#68085] of Qing H. Liu

Papers Published

1. Joon-Ho Lee and Liu, Q.H., A 3-D spectral element time-domain (SETD) method for electromagnetic wave problems, 2006 IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No. 06CH37758C) (2006), pp. 675 -, Albuquerque, NM, USA
   (last updated on 2007/04/17)

   Abstract:
   Summary form only given. In this paper, we developed a 3-D spectral element time-domain (SETD) method to solve the first-order Maxwell's equations as well as their second-order wave equations. Galerkin method is used for spatial discretization, and a fourth-order, four-stage Runge-Kutta scheme is employed for the time integration. Because the basis functions are orthogonal and because the Gauss-Lobato-Legendre (GLL) quadrature is used, the mass matrix is block-diagonal and thus it can be easily inverted with little cost. After we obtain the inexpensive inversion of the mass matrix, it is moved to the right-hand side and multiplied by stiffness matrices and the resulting matrices will be still sparse. Finally, only a trivial vector-matrix product is required in each time step

   Keywords:
   electromagnetic waves;Galerkin method;matrix inversion;Maxwell equations;polynomials;Runge-Kutta methods;time-domain analysis;wave equations;