On Adaptive Unsymmetric Meshless Collocation
نویسندگان
چکیده
The set Λ consists of infinitely many linear real–valued functionals λ that usually take the form of point evaluations of functions or derivatives at points inside a domain or on some boundary or interface layer. If several differential or boundary operators are involved, we simply put everything into a single set Λ of functionals of various types. We call (1) a generalized interpolation problem. Discretization just consists in replacing the infinite set Λ by some finite unstructured subset {λ1, . . . ,λN}. The space spanned by these functionals can be called the test space. The trial space consists of a meshless space U of functions spanned by a basis {u1, . . . ,uM}, and then the discretized problem reads as
منابع مشابه
Stable and Convergent Unsymmetric Meshless Collocation Methods
In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. Kansa’s well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent m...
متن کاملResults on Meshless Collocation Techniques
Though the technique introduced by E. Kansa [7, 8] is very successful in engineering applications, there were no proven results so far on the unsymmetric meshless collocation method for solving PDE boundary value problems in strong form. While the original method cannot be proven to be fail–safe in general, we prove asymptotic feasibility for a generalized variant using separated trial and test...
متن کاملCoupling Projection Domain Decomposition Method and Meshless Collocation Method Using Radial Basis Functions in Electromagnetics
This paper presents an efficient meshless approach for solving electrostatic problems. This novel approach is based on combination of radial basis functions-based meshless unsymmetric collocation method with projection domain decomposition method. Under this new method, we just need to solve a Steklov-Poincaré interface equation and the original problem is solved by computing a series of indepe...
متن کاملConvergence of Unsymmetric Kernel-Based Meshless Collocation Methods
This paper proves convergence of variations of the unsymmetric kernel-based collocation method introduced by E. Kansa in 1986. Since then, this method has been very successfully used in many applications, though it may theoretically fail in special situations, and though it had no error bound or convergence proof up to now. Thus it is necessary to add assumptions or to make modifications. Our m...
متن کاملH-Adaptive Local Radial Basis Function Collocation Meshless Method
This paper introduces an effective H-adaptive upgrade to solution of the transport phenomena by the novel Local Radial Basis Function Collocation Method (LRBFCM). The transport variable is represented on overlapping 5-noded influence-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the variable are calculated from the ...
متن کامل