格子法是申请者提出的一类基于非规则、非结构网格的高精度地震波数值模拟方法。该项目将在GPU计算环境下，改进和发展这一方法，使其在保持高精度等优点的同时，获得更高的加速比，形成新的适用于GPU的高阶格子法。高阶格子法将为基于双程波方程的地震成像方法，如逆时偏移、全波形反演提供重要的工具，也将为精细考虑复杂地表形状的强地震动模拟提供有效的方法。研究工作将聚焦于弹性波方程，以形成新的算法架构为核心；成果可容易应用到声波、复杂各向异性、孔隙介质等地震波模拟问题。研究工作包括速度相关的非规则、非结构网格最优剖分，基于双重网格的GPU格子法，精细考虑介质突变界面和界面内介质非均匀的高精度GPU格子法，基于GPU的空间-时间高阶格子法。研究的重点是根据GPU的特点改变算法架构，通过减少读取存储来发挥GPU的并行计算能力，并通过引入高阶近似提升格子法的频散特性。研究工作将形成一类新的波动方程数值解法。

Grid method, which has been put forward by us, is an irregular, unstructured mesh based numerical scheme for seismic wave modeling with high-accuracy. The project will improve the grid method on GPU devices, and try to yield a GPU high-order grid method which has a higher speed-up rate when using GPU and persists the high qualities of the grid method. High-order grid method will provide a key tool for the two-way wave equation based imaging methods such as RTM and FWI, and the in-site strong earthquake motion simulation under complex near-surface velocities and surface topography. The research will focus on elastic wave equations, and the key is to yield a new computational architecture. It is easy to extend the resulted algorithm into the acoustic, anisotropic, poroelastic wave equations. The research content includes velocity related irregular, unstructured mesh generation and optimization, double-mesh based GPU grid method, high-accuracy GPU grid method which can accurately describe the medium interfaces with high velocity contrasts and the medium inhomogeneous inside the interfaces, and spatial-temporal high-order grid method on GPU. The key is to modify the computational architecture according to the calculating characteristic of GPU. We will create the intensive computation for GPU by reducing memory access and improve the dispersion characteristic of the grid method by using high-order approximation. The project will yield a new kind of numerical schemes for solving wave equation.