IMPLEMENTATION OF MULTI-TRANSMITTING BOUNDARY CONDITION FOR WAVE MOTION SIMULATION BY SPECTRAL ELEMENT METHOD:TWO DIMENSION CASE

The spectral element scheme of multi-transmitting formula (MTF) which proposed by Xing and Li is developed and expanded to numerical simulation of SH-type wave motion in homogeneous linear medium. The spectral elements adjacent to the artificial boundaries are supposed to be rectilinear quadrilateral elements, in order that each node on the artificial boundary locates on a unique grid line pointing to the interior domain, hence the displacement of a particular artificial boundary node at a certain time can be inferred from displacements of nodes on the grid line at earlier times. Two numerical examples, the plane wave propagation with a certain angle (outer-source problem) and the free spread of a pulse wave originated from a point (inner-source problem), are employed for verification of this wave motion simulation procedure which combines the spectral element method with MTF boundary. The main parameters affecting reflection error of the MTF scheme, such as order of interpolation polynomial, artificial wave speed and transmitting order, are investigated in time domain via a series of initial-value problems. The results show that the order of interpolation polynomial influences the reflection error very little, while higher interpolation order may lead to better accuracy. For the choice of artificial wave speed, it is preferable to choose values equal or slightly greater than the physical wave speed, otherwise bigger reflection errors come about. Transmitting order exerts the most significant impact on reflection error, which would be reduced greatly with the increase of transmitting order of MTF, but the undesired drift instability may arise when transmitting order reaches three or two for inner-source and outer-source problems, respectively. Although the work combining MTF boundary with spectral element method is conducted on simulation of SH wave propagation in infinite homogeneous medium in this paper, it has laid the foundation of research on more complicated situations, such as issues of layered soil sites, propagation of P-SV wave or Rayleigh wave, etc.