J. Slak
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View article: Parallel domain discretization algorithm for RBF-FD and other meshless numerical methods for solving PDEs
Parallel domain discretization algorithm for RBF-FD and other meshless numerical methods for solving PDEs Open
In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on…
View article: Parallel domain discretization algorithm for RBF-FD and other meshless numerical methods for solving PDEs
Parallel domain discretization algorithm for RBF-FD and other meshless numerical methods for solving PDEs Open
In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on…
View article: p-refined RBF-FD solution of a Poisson problem
p-refined RBF-FD solution of a Poisson problem Open
Local meshless methods obtain higher convergence rates when RBF approximations are augmented with monomials up to a given order. If the order of the approximation method is spatially variable, the numerical solution is said to be p-refined…
View article: GPU accelerated RBF-FD solution of Poisson's equation
GPU accelerated RBF-FD solution of Poisson's equation Open
The Radial Basis Function-generated finite differences became a popular variant of local meshless strong form methods due to its robustness regarding the position of nodes and its controllable order of accuracy. In this paper, we present a…
View article: p-refined RBF-FD solution of a Poisson problem
p-refined RBF-FD solution of a Poisson problem Open
Local meshless methods obtain higher convergence rates when RBF\napproximations are augmented with monomials up to a given order. If the order\nof the approximation method is spatially variable, the numerical solution is\nsaid to be p-refi…
View article: Fast Variable Density Node Generation on Parametric Surfaces with Application to Mesh-Free Methods
Fast Variable Density Node Generation on Parametric Surfaces with Application to Mesh-Free Methods Open
Domain discretization is considered a dominant part of solution procedures for solving partial differential equations. It is widely accepted that mesh generation is among the most cumbersome parts of the FEM analysis and often requires hum…
View article: GPU accelerated RBF-FD solution of Poisson’s equation
GPU accelerated RBF-FD solution of Poisson’s equation Open
The Radial Basis Function-generated finite differences became a popular\nvariant of local meshless strong form methods due to its robustness regarding\nthe position of nodes and its controllable order of accuracy. In this paper, we\npresen…
View article: Fast variable density node generation on parametric surfaces with application to mesh-free methods
Fast variable density node generation on parametric surfaces with application to mesh-free methods Open
Domain discretization is considered a dominant part of solution procedures for solving partial differential equations. It is widely accepted that mesh generation is among the most cumbersome parts of the FEM analysis and often requires hum…
View article: RBF-FD analysis of 2D time-domain acoustic wave propagation in heterogeneous Earth's subsurface.
RBF-FD analysis of 2D time-domain acoustic wave propagation in heterogeneous Earth's subsurface. Open
Radial Basis Function-generated Finite Differences (RBF-FD) is a popular variant of local strong-form meshless methods that do not require a predefined connection between the nodes, making it easier to adapt node-distribution to the proble…
View article: Monomial augmentation guidelines for RBF-FD from accuracy vs. computational time perspective
Monomial augmentation guidelines for RBF-FD from accuracy vs. computational time perspective Open
Local meshless methods using RBFs augmented with monomials have become increasingly popular, due to the fact that they can be used to solve PDEs on scattered node sets in a dimension-independent way, with the ability to easily control the …
View article: Analysis of high order dimension independent RBF-FD solution of Poisson's equation.
Analysis of high order dimension independent RBF-FD solution of Poisson's equation. Open
The RBF-FD solution of a Poisson problem with mixed boundary conditions is analyzed in 1D, 2D and 3D domains discretized with scattered nodes. The results are presented in terms of convergence analyses for different orders of RBF-FD approx…
View article: ADAPTIVE RBF-FD METHOD FOR POISSON’S EQUATION
ADAPTIVE RBF-FD METHOD FOR POISSON’S EQUATION Open
Solutions to many physical problems governed by partial differential equations (PDEs) often vary significantly in magnitude throughout the problem domain.Although in some special cases the areas with high error are known in advance, in gen…
View article: On Generation of Node Distributions for Meshless PDE Discretizations
On Generation of Node Distributions for Meshless PDE Discretizations Open
In this paper we present an algorithm that is able to generate locally regular node layouts with spatially variable nodal density for interiors of arbitrary domains in two, three and higher dimensions. It is demonstrated that the generated…
View article: FAST GENERATION OF VARIABLE DENSITY NODE DISTRIBUTIONS FOR MESH-FREE METHODS
FAST GENERATION OF VARIABLE DENSITY NODE DISTRIBUTIONS FOR MESH-FREE METHODS Open
Problems with pronounced differences in intensity, such as those that appear in contact mechanics, where locally concentrated high stresses are present, are usually attacked with a spatially variable nodal distribution.In a meshless contex…
View article: RBF-FD BASED DYNAMIC THERMAL RATING OF OVERHEAD POWER LINES
RBF-FD BASED DYNAMIC THERMAL RATING OF OVERHEAD POWER LINES Open
The essential limiting factor of the power transmission line transfer capabilities is the maximal allowed temperature of the conductor that should not be exceeded to avoid excessive sags.A commonly used conservative approach is to limit tr…