A numerical study of a technique for shifting eigenvalues of radial basis function differentiation matrices
نویسندگان
چکیده
Radial Basis Function (RBF) collocation methods for time-dependent PDEs, in particular hyperbolic PDEs, are known to be difficult to implement in a way so that they are stable for time integration. It has been hypothesized that the instability is due to the way that boundary conditions are applied and to the relatively large errors in boundary regions. We describe a preconditioning technique that deemphasizes data in boundary regions and reformulates derivative calculations to focus on interior data. The preconditioning technique improves the eigenvalue stability of RBF methods for time-dependent PDEs. Unfortunately, the technique seems to only be applicable on domains that are simply shaped. keywords: Radial Basis Functions, Numerical Partial Differential Equations, Time-Dependent Partial Differential Equations, Eigenvalue Stability, Collocation Methods. 1
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