Applied Mathematics and Computation
Meshless Galerkin methods using radial basis functions
Mathematics of Computation
An upwind finite difference scheme for meshless solvers
Journal of Computational Physics
Mesh deformation based on radial basis function interpolation
Computers and Structures
Meshfree explicit local radial basis function collocation method for diffusion problems
Computers & Mathematics with Applications
An Introduction to Meshfree Methods and Their Programming
An Introduction to Meshfree Methods and Their Programming
Implicit fully mesh-less method for compressible viscous flow calculations
Journal of Computational and Applied Mathematics
GPU computing of compressible flow problems by a meshless method with space-filling curves
Journal of Computational Physics
| Hi-index | 31.45 |
The primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud. Multicloud is well-founded in the mathematical basis of multigrid, but relies on a meshless operator on coarse levels. The meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes. The performance of multicloud is compared with established multigrid techniques for structured and unstructured meshes for the Euler equations on two-dimensional test cases. Results indicate comparable convergence rates per unit work for multicloud and multigrid. However, because of its mesh and scheme transparency, multicloud may be applied to a wide array of problems with no modification of fine level schemes as is often required with agglomeration techniques. The implication is that multicloud can be implemented in a completely modular fashion, allowing researchers to develop fine level algorithms independent of the convergence accelerator for complex three-dimensional problems.