This paper briefly reports the GeoMFree , a meshfree / meshless software package designed for analyzing the problems of large deformations and crack propagations of rock and soil masses in geotechnics. The GeoMFree is developed based on the meshfree RPIM, and accelerated by exploiting the parallel computing on multi-core CPU and many-core GPU. The GeoMFree is currently being under intensive dev...

Meshfree methods with discontinuous radial basis functions and their numerical implementation for elastic problems are presented. We study the following radial basis functions: the multiquadratic (MQ), the Gaussian basis functions and the thin-plate basis functions. These radial basis functions are combined with step function enrichments directly or with enriched Shepard functions. The formulat...

‎Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems‎. ‎They are often referred to as a meshfree method and can be spectrally accurate‎. ‎In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion‎. ‎We develop our approach in two-dimensional spaces for so...

In this paper, we propose a meshfree method based on the Gaussian radial basis function (RBF) to solve both classical and fractional PDEs. The proposed takes advantage of analytical Laplacian functions so as accommodate discretization in single framework avoid large computational cost for numerical evaluation derivatives. These important merits distinguish it from other methods Moreover, our is...

A phase-aware constitutive model is developed and integrated with the meshfree simulations to study failure mechanisms of space structural materials under oblique hypervelocity impact ice. The proposed covers material’s dynamic behavior in a wide range temperature, pressure, strain rates. numerical analysis combines Hot Optimal Transportation Meshfree method EigenErosion algorithm explicitly ac...