A Legendre spectral element method (SEM) based on the modified bases for solving neutral delay distributed-order fractional damped diffusion-wave equation

2018 ◽  
Vol 41 (9) ◽  
pp. 3476-3494 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mostafa Abbaszadeh
Keyword(s):  
Wave Equation ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Neutral Delay ◽  
Diffusion Wave ◽  
Legendre Spectral Element Method ◽  
Distributed Order ◽  
Element Method

scholarly journals Space-time spectral element method solution for the acoustic wave equation and its dispersion analysis

2017 ◽  
Vol 38 (6) ◽  
pp. 303-313 ◽  
Author(s):  
Yanhui Geng ◽  
Guoliang Qin ◽  
Jiazhong Zhang ◽  
Wenqiang He ◽  
Zhenzhong Bao ◽  
...  
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Dispersion Analysis ◽  
Space Time ◽  
Acoustic Wave Equation ◽  
Element Method

scholarly journals Efficiency of the spectral element method with very high polynomial degree to solve the elastic wave equation

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. T33-T43
Author(s):  
Chao Lyu ◽  
Yann Capdeville ◽  
Liang Zhao
Keyword(s):  
Wave Equation ◽  
Spectral Element Method ◽  
Computing Time ◽  
Spectral Element ◽  
Two Dimensions ◽  
Elastic Model ◽  
Time Step ◽  
High Degree ◽  
Very High ◽  
Element Method

The spectral element method (SEM) has gained tremendous popularity within the seismological community to solve the wave equation at all scales. Classic SEM applications mostly rely on degrees 4–8 elements in each tensorial direction. Higher degrees are usually not considered due to two main reasons. First, high degrees imply large elements, which make the meshing of mechanical discontinuities difficult. Second, the SEM’s collocation points cluster toward the edge of the elements with the degree, degrading the time-marching stability criteria and imposing a small time step and a high numerical cost. Recently, the homogenization method has been introduced in seismology. This method can be seen as a preprocessing step before solving the wave equation that smooths out the internal mechanical discontinuities of the elastic model. It releases the meshing constraint and makes use of very high degree elements more attractive. Thus, we address the question of memory and computing time efficiency of very high degree elements in SEM, up to degree 40. Numerical analyses reveal that, for a fixed accuracy, very high degree elements require less computer memory than low-degree elements. With minimum sampling points per minimum wavelength of 2.5, the memory needed for a degree 20 is about a quarter that of the one necessary for a degree 4 in two dimensions and about one-eighth in three dimensions. Moreover, for the SEM codes tested in this work, the computation time with degrees 12–24 can be up to twice faster than the classic degree 4. This makes SEM with very high degrees attractive and competitive for solving the wave equation in many situations.

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