High-order finite element methods for singularly perturbed elliptic and parabolic problems
SIAM Journal on Applied Mathematics
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Heterogeneous Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems
SIAM Journal on Numerical Analysis
Multiquadric method for the numerical solution of a biphasic mixture model
Applied Mathematics and Computation
Solving partial differential equations by collocation using radial basis functions
Applied Mathematics and Computation
An efficient numerical scheme for Burgers' equation
Applied Mathematics and Computation
Meshless Galerkin methods using radial basis functions
Mathematics of Computation
Compactly supported radial basis functions for shallow water equations
Applied Mathematics and Computation
A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs
SIAM Journal on Scientific Computing
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods
SIAM Journal on Scientific Computing
Convergence of general meshless Schwarz method using radial basis functions
Applied Numerical Mathematics
Domain decomposition by radial basis functions for time dependent partial differential equations
ACST'06 Proceedings of the 2nd IASTED international conference on Advances in computer science and technology
A note on the Gibbs phenomenon with multiquadric radial basis functions
Applied Numerical Mathematics
A matrix decomposition RBF algorithm: Approximation of functions and their derivatives
Applied Numerical Mathematics
A note on the meshless method using radial basis functions
Computers & Mathematics with Applications
Radial function collocation solution of partial differential equations in irregular domains
International Journal of Computing Science and Mathematics
Applied Numerical Mathematics
Multiquadric collocation method with integralformulation for boundary layer problems
Computers & Mathematics with Applications
Iterative adaptive RBF methods for detection of edges in two-dimensional functions
Applied Numerical Mathematics
Spectral collocation and radial basis function methods for one-dimensional interface problems
Applied Numerical Mathematics
Preconditioning for radial basis functions with domain decomposition methods
Mathematical and Computer Modelling: An International Journal
Journal of Scientific Computing
Journal of Computational Physics
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In this paper, overlapping domain decomposition with both multiplicative and additive Schwarz iterative techniques are incorporated into the radial basis functions for solving partial differential equations. These decomposition techniques circumvent the ill-conditioning problem resulted from using the radial basis functions as a global interpolant. Both the multiplicative and additive Schwarz iterative techniques achieve high performances even without the Krylov subspace accelerators. The effectiveness of the algorithms are demonstrated by performing numerical experiments for both a regular elliptic problem and a singularly perturbed elliptic problem respectively.