The particle-in-cell method (PIC), especially the latest version of it, the material point method (MPM), has shown significant advantage over the pure Lagrangian method or the pure Eulerian method in numerical simulations of problems involving large deformations. It avoids the mesh distortion and tangling issues associated with Lagrangian methods and the advection errors associated with Euleria...

The theory and algorithm for the Material Point Method (MPM) are documented, with a detailed discussion on the treatments of boundary conditions and shock wave problems. A step-by-step solution scheme is written based on direct inspection of the two-dimensional MPM code currently used at the University of Missouri-Columbia (which is, in turn, a legacy of the University of New Mexico code). To t...

The two-point angular correlation function is a traditional method used to search for deviations from expectations of isotropy. In this paper we develop and explore a statistically descriptive three-point method with the intended application being the search for deviations from isotropy in the highest energy cosmic rays. We compare the sensitivity of a two-point method and a “shape-strength” me...

In this paper we present the results obtained in the solution of sparse and large systems of non-linear equations by inexact Newton methods combined with an block iterative row-projection linear solver of Cimmino-type. Moreover, we propose a suitable partitioning of the Jacobian matrix A. In view of the sparsity, we obtain a mutually orthogonal row-partition of A that allows a simple solution o...