21 citations · 53 across the 11 of their papers we have counts for
14 papers
Point Cloud Quality for Meshfree Methods
Mohsen Abdolahzadeh, Oleg Davydov, Isabel Michel +1
Mesh quality is very well studied and widely used to quantify a good mesh. In contrast, a systematic study of quality of meshfree point clouds is lacking. This gap makes it difficu…
Overlap Splines and Meshless Finite Difference Methods
Oleg Davydov
We consider overlap splines that are defined by connecting the patches of piecewise functions via common values at given finite sets of nodes, without using any partitions of the c…
Improved Stencil Selection for Meshless Finite Difference Methods in 3D
Oleg Davydov, Dang Thi Oanh, Ngo Manh Tuong
We introduce a geometric stencil selection algorithm for Laplacian in 3D that significantly improves octant-based selection considered earlier. The goal of the algorithm is to choo…
Approximation with Conditionally Positive Definite Kernels on Deficient Sets
Oleg Davydov
Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown t…
Error Bounds for a Least Squares Meshless Finite Difference Method on Closed Manifolds
Oleg Davydov
We present an error bound for a least squares version of the kernel based meshless finite difference method for elliptic differential equations on smooth compact manifolds of arbit…
Selection of Sparse Sets of Influence for Meshless Finite Difference Methods
Oleg Davydov
We suggest an efficient algorithm for the selection of sparse subsets of a set of influence for the numerical discretization of differential operators on irregular nodes with polyn…
Optimal approximation order of piecewise constants on convex partitions
Oleg Davydov, Oleksandr Kozynenko, Dmytro Skorokhodov
We prove that the error of the best nonlinear -approximation by piecewise constants on convex partitions is , where the number of…
An application of numerical differentiation formulas to discontinuity curve detection from irregularly sampled data
Cesare Bracco, Oleg Davydov, Carlotta Giannelli +1
We present a method to detect discontinuity curves, usually called faults, from a set of scattered data. The scheme first extracts from the data set a subset of points close to the…
Approximation by Splines on Piecewise Conic Domains
Oleg Davydov, Wee Ping Yeo
We develop a Hermite interpolation scheme and prove error bounds for bivariate piecewise polynomial spaces of Argyris type vanishing on the boundary of curved domains enclose…
Optimal Stencils in Sobolev Spaces
Oleg Davydov, Robert Schaback
This paper proves that the approximation of pointwise derivatives of order of functions in Sobolev space by linear combinations of function values cannot have a c…
Minimal Numerical Differentiation Formulas
Oleg Davydov, Robert Schaback
We investigate numerical differentiation formulas on irregular centers in two or more variables that are exact for polynomials of a given order and minimize an absolute seminorm of…
Adaptive RBF-FD Method for Elliptic Problems with Point Singularities in 2D
Dang Thi Oanh, Oleg Davydov, Hoang Xuan Phu
We describe and test numerically an adaptive meshless generalized finite difference method based on radial basis functions that competes well with the finite element method on stan…
Quintic Splines on Domains Enclosed by Piecewise Conics and Numerical Solution of Fully Nonlinear Elliptic Equations
Oleg Davydov, Abid Saeed
We introduce bivariate piecewise quintic finite element spaces for curved domains enclosed by piecewise conics satisfying homogeneous boundary conditions, construct local bas…
Polynomial Finite Element Method for Domains Enclosed by Piecewise Conics
Oleg Davydov, Georgii Kostin, Abid Saeed
We consider bivariate piecewise polynomial finite element spaces for curved domains bounded by piecewise conics satisfying homogeneous boundary conditions, construct stable local b…