We present a new high-order, local meshfree method for numerically solving reaction diffusion equations on smooth surfaces of codimension 1 embedded in Rd. The novelty of the method is in the approximation of the Laplace–Beltrami operator for a given surface using Hermite radial basis function (RBF) interpolation over local node sets on the surface. This leads to compact (or implicit) RBF gener...

The well-known Laplace–Beltrami operator, established as a basic tool in shape processing, builds on a long history of mathematical investigations that have induced several numerical models for computational purposes. However, the Laplace–Beltrami operator is only one special case of many possible generalizations that have been researched theoretically. Thereby it is natural to supplement some ...

Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is bas...

We present a new high-order, local meshfree method for numerically solving reaction 5 diffusion equations on smooth surfaces of co-dimension one embedded in Rd. The novelty of the 6 method is in the approximation of the Laplace-Beltrami operator for a given surface using Hermite 7 radial basis function (RBF) interpolation over local node sets on the surface. This leads to compact 8 (or implicit...

Classical scattering theory, by which we mean the scattering of acoustic and electromagnetic waves and quantum particles, is a very old discipline with roots in mathematical physics. It has also become an important part of the modern theory of linear partial differential equations. Spectral geometry is a slightly more recent subject, the goal of which is to understand the connections between th...

Abstract The problem of determining the domain closure Laplace-Beltrami operator on a 2D almost-Riemannian manifold is considered. Using tools from theory Lie groupoids natural domains perturbations are found. main novelty that presented method allows us to treat geometries with tangency points. This kind singularity difficult since those points do not have tubular neighbourhood compatible metr...