Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs
SIAM Journal on Scientific Computing
Overlapping domain decomposition method by radial basis functions
Applied Numerical Mathematics
Radial function collocation solution of partial differential equations in irregular domains
International Journal of Computing Science and Mathematics
The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems
Journal of Computational Physics
An adaptive domain decomposition method for the Hamilton---Jacobi---Bellman equation
Journal of Global Optimization
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In the last years, there has been an increased investigation of efficient algorithms to solve problems of great scale. The main restriction of the traditional methods, like finite difference methods and finite element methods, is the mesh generation. In this work, we investigate the overlapping domain decomposition method applied to time dependent partial differential equations with unsymmetric radial basis function collocation method. Numerical experiments performed with thin-plate splines as kernel function, for an evolutionary problem in two dimensions, show a drastic time reduction as we increase the number of subdomains, high numerical accuracy and lower numerical diffusion. The numerical results suggest that the scheme proposed can be useful to tackle large scale time dependent problems.