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
Meshless Galerkin methods using radial basis functions
Mathematics of 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
Overlapping domain decomposition method by radial basis functions
Applied Numerical Mathematics
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In this paper, we provide the theoretical justification of general meshless Schwarz method using radial basis functions. Using this meshless method, we only need to solve many small problems instead of one big ill-conditioned problem, and get the results with almost the same accurate. The only premise we need in our meshless method is that the resultant coefficient matrix of the linear algebra equations which we got when we solve the partial differential equations is positive definite, and which can usually be satisfied if we use meshless Galerkin method or meshless Hermitian-Birkhoff's collocation method.