Modeling elastic waves in complex media, with varying physical properties, require very accurate algorithms and a great computational effort to avoid nonphysical effects. Among the numerical methods the spectral elements (SEM) have a high precision and ease in modeling such problems and the physical domains can be discretized using very coarse meshes with elements of constant properties. In many cases, models with very complex geometries and small heterogeneities, shorter than the minimum wavelength, require grid resolution down to the thinnest scales, resulting in an extremely large problem size and greatly reducing accuracy and computational efficiency. In this paper, a poly-grid method (PG-CSEM) is presented that can overcome this limitation. To accurately deal with continuous variations or even small-scale fluctuations in elastic properties, temporary auxiliary grids are introduced that prevent the need to use large meshes, while at the macroscopic level wave propagation is solved maintaining the SEM accuracy and computational efficiency as confirmed by the numerical results.

在具有不同物理特性的复杂介质中模拟弹性波需要非常精确的算法和大量的计算工作来避免非物理效应。在数值方法中，光谱元素 (SEM) 具有高精度并且易于对此类问题进行建模，并且可以使用具有恒定属性元素的非常粗糙的网格对物理域进行离散化。在许多情况下，具有非常复杂几何形状和小异质性且比最小波长短的模型需要网格分辨率达到最薄的尺度，从而导致问题规模极大，并大大降低准确性和计算效率。在本文中，提出了一种可以克服此限制的多网格方法 (PG-CSEM)。为了准确处理弹性特性的连续变化甚至小规模波动，