32 citations · 50 across the 6 of their papers we have counts for
6 papers
An RBF partition of unity method for geometry reconstruction and PDE solution in thin structures
Elisabeth Larsson, Pierre-Frédéric Villard, Igor Tominec +3
The main respiratory muscle, the diaphragm, is an example of a thin structure. We aim to perform detailed numerical simulations of the muscle mechanics based on individual patient…
Stability estimates for radial basis function methods applied to linear scalar conservation laws
Igor Tominec, Murtazo Nazarov, Elisabeth Larsson
We derive stability estimates for three commonly used radial basis function (RBF) methods to solve hyperbolic time-dependent PDEs: the RBF generated finite difference (RBF-FD) meth…
Residual viscosity stabilized RBF-FD methods for solving nonlinear conservation laws
Igor Tominec, Murtazo Nazarov
In this paper, we solve nonlinear conservation laws using the radial basis function generated finite difference (RBF-FD) method. Nonlinear conservation laws have solutions that ent…
An unfitted radial basis function generated finite difference method applied to thoracic diaphragm simulations
Igor Tominec, Pierre-Frederic Villard, Elisabeth Larsson +2
The thoracic diaphragm is the muscle that drives the respiratory cycle of a human being. Using a system of partial differential equations (PDEs) that models linear elasticity we co…
An unfitted RBF-FD method in a least-squares setting for elliptic PDEs on complex geometries
Igor Tominec, Eva Breznik
Radial basis function generated finite difference (RBF-FD) methods for PDEs require a set of interpolation points which conform to the computational domain . One of the requirem…
A least squares radial basis function finite difference method with improved stability properties
Igor Tominec, Elisabeth Larsson, Alfa Heryudono
Localized collocation methods based on radial basis functions (RBFs) for elliptic problems appear to be non-robust in the presence of Neumann boundary conditions. In this paper we…