High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response
Journal of Computational Physics
Smoothing and accelerated computations in the element free Galerkin method
Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
Introduction to algorithms
A Particle-Partition of Unity Method--Part II: Efficient Cover Construction and Reliable Integration
SIAM Journal on Scientific Computing
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Review: Meshless methods: A review and computer implementation aspects
Mathematics and Computers in Simulation
Meshfree Approximation Methods with MATLAB
Meshfree Approximation Methods with MATLAB
Meshfree Particle Methods
Adaptive computations on conforming quadtree meshes
Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
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Novel numerical methods, known as Meshless Methods or Meshfree Methods and, in a wider perspective, Partition of Unity Methods, promise to overcome most of disadvantages of the traditional finite element techniques. The absence of a mesh makes meshfree methods very attractive for those problems involving large deformations, moving boundaries and crack propagation. However, meshfree methods still have significant limitations that prevent their acceptance among researchers and engineers, namely the computational costs. This paper presents an in-depth analysis of computational techniques to speed-up the computation of the shape functions in the Reproducing Kernel Particle Method and Moving Least Squares, with particular focus on their bottlenecks, like the neighbour search, the inversion of the moment matrix and the assembly of the stiffness matrix. The paper presents numerous computational solutions aimed at a considerable reduction of the computational times: the use of kd-trees for the neighbour search, sparse indexing of the nodes-points connectivity and, most importantly, the explicit and vectorized inversion of the moment matrix without using loops and numerical routines.