fasshauer meshfree approximation methods with matlab

‘A kernel-based collocation method for elliptic partial differential equations with random coefficients’. Meshfree Methods for Partial Differential Equations VI.

‘Kernel-based collocation methods versus Galerkin finite element methods for approximating elliptic stochastic partial differential equations’.

‘Reproducing kernels of generalized Sobolev spaces via a green function approach with distributional operators’. Singapore:World Scientific Publishing Co. Meshfree Approximation Methods with Matlab. ‘Approximation of stochastic partial differential equations by a kernel-based collocation method’. Reproducing Kernel Hilbert Spaces in Probability and Statistics.ĭordrecht:Kluwer Academic Publishers Google Scholar ‘A stochastic collocation method for elliptic partial differential equations with random input data’. The numerical experiments of Sobolev-spline kernels for Klein-Gordon SPDEs show that the kernel-based collocation method produces the well-behaved approximate probability distributions of the SPDE solutions. For a fixed kernel function, the convergence of kernel-based collocation solutions only depends on the fill distance of the chosen collocation points for the bounded domain of SPDEs. Its random expansion coefficients are computed by a random optimisation problem with constraint conditions induced by the nonlinear SPDEs. The kernel-based collocation solution is a linear combination of the reproducing kernel with the differential and boundary operators of SPDEs at the given collocation points placed in the related high-dimensional domains. A reproducing kernel is used to construct an approximate basis. In this paper, we present a new idea to approximate high-dimensional nonlinear stochastic partial differential equations (SPDEs) by a kernel-based collocation method, which is a meshfree approximation method.

Fasshauer meshfree approximation methods with matlab