The generalized finite-element method (GFEM) has been applied frequently to solve harmonic wave equations, but its use in the simulation of transient wave propagation is still limited. We have applied GFEM for the simulation of the acoustic wave equation in models relevant to exploration seismology. We also perform an assessment of its accuracy and efficiency. The main advantage of GFEM is that it provides an enhanced solution accuracy compared to the standard finite-element method (FEM). This is attained by adding user-defined enrichment functions to standard FEM approximations. For the acoustic wave equation, we consider plane waves oriented in different directions as the enrichments, whose argument includes the largest wavenumber of the wavefield. We combine GFEM with an unconditionally stable time integration scheme with a constant time step. To assess the accuracy and efficiency of GFEM, we compare the GFEM simulation results against those obtained with the spectral-element method (SEM). We use SEM because it is the method of choice for wave propagation simulation due to its proven accuracy and efficiency. In the numerical examples, we first perform a convergence study in space and time, evaluating the accuracy of both methods against a semianalytical solution. Then, we consider simulations of relevant models in exploration seismology that include low-velocity features, an inclusion with a complex geometric boundary and topography. Results using these models indicate that GFEM presents comparable accuracy and efficiency to those based on SEM. For the given examples, the GFEM efficiency stems from the combined effect of local mesh refinement, nonconforming or unstructured, and the unconditionally stable time integration scheme with a constant time step. Moreover, these features provide great flexibility to the GFEM implementations, proving advantageous when using, for example, unstructured grids that impose severe time step size restrictions in SEM.

中文翻译：

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广义有限元法在勘探地震波模拟中的应用

广义有限元法（GFEM）已被广泛用于求解谐波方程，但在瞬态波传播模拟中的应用仍然受到限制。我们已将GFEM应用到与勘探地震学相关的模型中的声波方程模拟中。我们还将对其准确性和效率进行评估。GFEM的主要优点是，与标准有限元方法（FEM）相比，它提供了更高的求解精度。这是通过将用户定义的扩展功能添加到标准FEM逼近中来实现的。对于声波方程，我们将面向不同方向的平面波视为丰富度，其论点包括波场的最大波数。我们将GFEM与具有恒定时间步长的无条件稳定时间积分方案结合在一起。为了评估GFEM的准确性和效率，我们将GFEM模拟结果与通过光谱元素法（SEM）获得的结果进行比较。我们使用SEM是因为它具有经过验证的准确性和效率，因此是进行波传播模拟的首选方法。在数值示例中，我们首先在时空上进行收敛研究，并针对半解析解评估两种方法的准确性。然后，我们考虑对勘探地震学中相关模型的模拟，这些模型包括低速特征，复杂的几何边界和地形。使用这些模型的结果表明，GFEM与基于SEM的精度和效率相当。对于给定的示例，GFEM效率源于局部网格细化，不合格或非结构化，以及具有恒定时间步长的无条件稳定时间积分方案。此外，这些功能为GFEM实现提供了极大的灵活性，例如在使用非结构化网格（在SEM中施加严格的时间步长限制）时证明是有利的。