A meshless solution algorithm for the full potential equation has been developed by applying the principles of the Taylor Least Squares (TLS) method. This method allows for a PDE to be discretized on a local cloud of scattered nodes without the need of connectivity data. The process for discretizing the full potential equation within a meshless framework is outlined along with a novel Hermite T...

The Rajendran-Grove (RG) ceramic damage model is a three-dimensional internal variable based constitutive model for ceramic materials, with the considerations of micro-crack extension and void collapse. In the present paper, the RG ceramic model is implemented into the newly developed computational framework based on the Meshless Local Petrov-Galerkin (MLPG) method, for solving high-speed impac...

This paper advocates a method for real-time physical deformation and arbitrary cutting simulation of heterogeneous objects with multi-material distribution, whose originality centers on the tight coupling of domain-specific finite element method (FEM) 1 and material-distance-aware meshless approach in a CUDA-centric parallel simulation framework. We employ hierarchical hexahedron serving as bas...

This paper develops a class of meshless methods that are well-suited to statistical inverse problems involving partial differential equations (PDEs). The methods discussed in this paper view the forcing term in the PDE as a random field that induces a probability distribution over the residual error of a symmetric collocation method. This construction enables the solution of challenging inverse...

The linear systems arising from MFS calculations share certain numerical effects with other systems involving radial basis functions. These effects concern approximation error and stability, which are closely related, and they can already be studied for simple interpolation problems without PDEs. In MFS calculations, they crucially depend on the position and density of the source points and the...