90 citations · 340 across the 24 of their papers we have counts for
25 papers
The role of porosity in the transition to inertial regime in porous media flows
Dawid Strzelczyk, Gregor Kosec, Maciej Matyka
In this work, we investigate the fundamental physical mechanism of the transition from Darcy to inertial (Darcy-Forchheimer) regime in steady-state flows through porous media, with…
Spatially-varying meshless approximation method for enhanced computational efficiency
Mitja Jančič, Miha Rot, Gregor Kosec
In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatial variation of computational no…
Computational Electromagnetics with the RBF-FD Method
Andrej Kolar-Požun, Gregor Kosec
One of the most popular methods employed in computational electromagnetics is the Finite Difference Time Domain (FDTD) method. We generalise it to a meshless setting using the Radi…
Discretization of non-uniform rational B-spline (NURBS) models for meshless isogeometric analysis
Urban Duh, Varun Shankar, Gregor Kosec
We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more spec…
Oscillatory behaviour of the RBF-FD approximation accuracy under increasing stencil size
Andrej Kolar-Požun, Mitja Jančič, Miha Rot +1
When solving partial differential equations on scattered nodes using the Radial Basis Function generated Finite Difference (RBF-FD) method, one of the parameters that must be chose…
Strong form mesh-free -adaptive solution of linear elasticity problem
Mitja Jančič, Gregor Kosec
We present an algorithm for -adaptive collocation-based mesh-free numerical analysis of partial differential equations. Our solution procedure follows a well-established iterat…
A Meshless Solution of a Small-Strain Plasticity Problem
Filip Strniša, Mitja Jančič, Gregor Kosec
When the deformations of a solid body are sufficiently large, parts of the body undergo a permanent deformation commonly refereed to as plastic deformation. Several plasticity mode…
Implicit-Explicit Error Indicator based on Approximation Order
Mitja Jančič, Filip Strniša, Gregor Kosec
With the immense computing power at our disposal, the numerical solution of partial differential equations (PDEs) is becoming a day-to-day task for modern computational scientists.…
Dynamic mode decomposition as an analysis tool for time-dependent partial differential equations
Miha Rot, Martin Horvat, Gregor Kosec
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningf…
A hybrid RBF-FD and WLS mesh-free strong-form approximation method
Mitja Jančič, Gregor Kosec
Since the advent of mesh-free methods as a tool for the numerical analysis of systems of Partial Differential Equations (PDEs), many variants of differential operator approximation…
A sharp-interface mesoscopic model for dendritic growth
Mitja Jančič, Miha Založnik, Gregor Kosec
The grain envelope model (GEM) describes the growth of envelopes of dendritic crystal grains during solidification. Numerically the growing envelopes are usually tracked using an i…
Parallel domain discretization algorithm for RBF-FD and other meshless numerical methods for solving PDEs
Matjaž Depolli, Jure Slak, Gregor Kosec
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 numeric…
Stability analysis of RBF-FD and WLS based local strong form meshless methods on scattered nodes
Mitja Jančič, Gregor Kosec
The popularity of local meshless methods in the field of numerical simulations has increased greatly in recent years. This is mainly due to the fact that they can operate on scatte…
Uncertainty Assessment of Dynamic Thermal Line Rating for Operational Use at Transmission System Operators
Aleksandra Rashkovska, Mitja Jančič, Matjaž Depolli +2
Transmission system operators (TSOs) in recent years have faced challenges in order to ensure maximum transmission capacity of the system to satisfy market needs, while maintaining…
p-refined RBF-FD solution of a Poisson problem
Mitja Jančič, Jure Slak, Gregor Kosec
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 spatial…
Discretized boundary surface reconstruction
Mitja Jančič, Viktor Cvrtila, Gregor Kosec
Domain discretization is an essential part of the solution procedure in numerical simulations. Meshless methods simplify the domain discretization to positioning of nodes in the in…
GPU accelerated RBF-FD solution of Poisson's equation
Mitja Jančič, Jure Slak, Gregor Kosec
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…
Fast variable density node generation on parametric surfaces with application to mesh-free methods
Urban Duh, Gregor Kosec, Jure Slak
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…
RBF-FD analysis of 2D time-domain acoustic wave propagation in heterogeneous media
Jure Močnik - Berljavac, Pankaj K Mishra, Jure Slak +1
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…
Medusa: A C++ Library for solving PDEs using Strong Form Mesh-Free methods
Jure Slak, Gregor Kosec
Medusa, a novel library for implementation of strong form mesh-free methods, is described. We identify and present common parts and patterns among many such methods reported in the…
Monomial augmentation guidelines for RBF-FD from accuracy vs. computational time perspective
Mitja Jančič, Jure Slak, Gregor Kosec
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 dimensi…
Refined Meshless Local Strong Form solution of Cauchy-Navier equation on an irregular domain
Jure Slak, Gregor Kosec
This paper considers a numerical solution of a linear elasticity problem, namely the Cauchy-Navier equation, using a strong form method based on a local Weighted Least Squares (WLS…
On generation of node distributions for meshless PDE discretizations
Jure Slak, Gregor Kosec
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 a…
Adaptive Radial Basis Function-generated Finite Differences method for contact problems
Jure Slak, Gregor Kosec
This paper proposes an original adaptive refinement framework using Radial Basis Functions-generated Finite Differences method. Node distributions are generated with a Poisson Disk…