Mesh-based numerical methods such as the Finite Element Method (FEM) and Finite Difference Method (FDM) are widely used in various fields of science and engineering. However, the shortcomings of mesh-based methods are becoming increasingly obvious mainly due to the distorted or broken elements when analyzing the problems of large deformation or crack propagation. To overcome the above problems, meshfree methods such as the Meshless Local Petrov–Galerkin (MLPG) and Radial Point Interpolation Method (RPIM) were proposed, which can eliminate or partially eliminate the difficulties triggered by mesh-dependence. In geotechnics, the numerical modeling of deformations and failures of soil and rock masses is one of the most important approaches to understand and prevent geohazards, such as landslides and ground subsidence. In this paper, a local RPIM-based meshfree software package GeoMFree${}^{\mathrm{3D}}$ is specifically developed for analyzing the deformations and failures of soil and rock masses. To enhance the computing capability of GeoMFree${}^{\mathrm{3D}}$, (1) effective memory storage strategies are adopted to solve the memory requirement bottleneck; and (2) parallel computing strategies are utilized and heterogeneously implemented on multi-core CPU and many-core GPU to improve the computational efficiency. To demonstrate the performance of GeoMFree${}^{\mathrm{3D}}$, three simple verification examples and one application case are presented in this paper. The verification examples indicate that the computational accuracy and efficiency of the package GeoMFree${}^{\mathrm{3D}}$ is acceptable. Furthermore, the application case indicates that GeoMFree${}^{\mathrm{3D}}$ is capable of analyzing the displacements of complex rock slopes. GeoMFree${}^{\mathrm{3D}}$ is currently under intensive development, plans for future work on the development of GeoMFree${}^{\mathrm{3D}}$ are also introduced.

诸如有限元法（FEM）和有限差分法（FDM）之类的基于网格的数值方法已广泛应用于科学和工程学的各个领域。然而，基于网格的方法的缺点变得越来越明显，主要是由于在分析大变形或裂纹扩展问题时元素变形或破裂。为了克服上述问题，提出了无网格方法，如无网格局部Petrov-Galerkin（MLPG）和径向点插值方法（RPIM），它们可以消除或部分消除由网格相关性引起的困难。在岩土工程中，对土壤和岩体的变形和破坏进行数值模拟是了解和预防地质灾害（例如滑坡和地面沉降）的最重要方法之一。在本文中，基于RPIM的本地无网格软件包GeoMFree${}^{\mathrm{3D}}$专为分析土壤和岩体的变形和破坏而开发。增强GeoMFree的计算能力${}^{\mathrm{3D}}$，（1）采用有效的内存存储策略来解决内存需求瓶颈；（2）利用并行计算策略，并在多核CPU和多核GPU上异构实现，以提高计算效率。演示GeoMFree的性能${}^{\mathrm{3D}}$本文介绍了三个简单的验证示例和一个应用案例。验证示例表明，GeoMFree软件包的计算准确性和效率${}^{\mathrm{3D}}$是可以接受的。此外，该应用案例表明，GeoMFree${}^{\mathrm{3D}}$能够分析复杂岩石边坡的位移。免费版${}^{\mathrm{3D}}$ 目前正处于密集开发中，有关GeoMFree开发的未来工作计划${}^{\mathrm{3D}}$ 也介绍了。