Kernel Based Meshless Methods
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Special Techniques for Kernel-Based Reconstruction of Functions from Meshless Data
Here are three short stories on meshless methods using kernel techniques: • Any well–posed linear problem in the native space NΦ of a symmetric (strictly) positive definite kernel Φ can be successfully solved by symmetric meshless collocation. This applies to a large variety of standard linear PDE problems. • Relaxing interpolation conditions by allowing some small absolute error can significan...
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This work explores the application of kernel based local meshless method for solving multi-dimensional wave equations in irregular domain. The method is tested for various types of boundary conditions in irregular shaped domain. The method is capable of solving multi-dimension large scaled problems in complex shaped domain.
متن کاملRecovery of Functions From Weak Data Using Unsymmetric Meshless Kernel-Based Methods
Recent engineering applications successfully introduced unsymmetric meshless local Petrov-Galerkin (MLPG) schemes. As a step towards their mathematical analysis, this paper investigates nonstationary unsymmetric Petrov-Galerkin-type meshless kernel-based methods for the recovery of L2 functions from finitely many weak data. The results cover solvability conditions and error bounds in negative S...
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A general framework for proving error bounds and convergence of a large class of unsymmetric meshless numerical methods for solving well-posed linear operator equations is presented. The results provide optimal convergence rates, if the test and trial spaces satisfy a stability condition. Operators need not be elliptic, and the problems can be posed in weak or strong form without changing the t...
متن کاملOn the Scope of Meshless Kernel Methods
Under very weak conditions any well–posed linear problem of Applied Analysis can be solved by certain meshless kernel methods to any prescribed accuracy.
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