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pro vyhledávání: '"Tominec, Igor"'
This paper shows that the Stokes problem is well-posed when both velocity and pressure vanish on the domain boundary. This result is achieved by extending Ne\v{c}as' inequality to square-integrable functions that vanish in a small band covering the b
Externí odkaz:
http://arxiv.org/abs/2407.15971
Autor:
Tominec, Igor, Ahlkrona, Josefin
The Shallow Ice Approximation (SIA) model on strong form is commonly used for inferring the flow dynamics of grounded ice sheets. The solution to the SIA model is a closed-form expression for the velocity field. When that velocity field is used to ad
Externí odkaz:
http://arxiv.org/abs/2403.06811
Autor:
Larsson, Elisabeth, Villard, Pierre-Frédéric, Tominec, Igor, Sundin, Ulrika, Michael, Andreas, Cacciani, Nicola
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 data. This requires a representation of the diaphragm geometry extract
Externí odkaz:
http://arxiv.org/abs/2403.01486
Publikováno v:
In Applied Mathematics and Computation 15 January 2025 485
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) method, the RBF partition of unity method (RBF-PUM) and Kansa's (global) R
Externí odkaz:
http://arxiv.org/abs/2110.14548
Autor:
Tominec, Igor, Nazarov, Murtazo
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 entail strong discontinuities and shocks, which give rise to numerical in
Externí odkaz:
http://arxiv.org/abs/2109.07183
Autor:
Tominec, Igor, Villard, Pierre-Frederic, Larsson, Elisabeth, Bayona, Victor, Cacciani, Nicola
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 compute displacements and stresses in a two-dimensional cross section of
Externí odkaz:
http://arxiv.org/abs/2103.03673
Autor:
Tominec, Igor, Breznik, Eva
Radial basis function generated finite difference (RBF-FD) methods for PDEs require a set of interpolation points which conform to the computational domain $\Omega$. One of the requirements leading to approximation robustness is to place the interpol
Externí odkaz:
http://arxiv.org/abs/2007.07775
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 overcome this issue by formulating the RBF-generated finite difference
Externí odkaz:
http://arxiv.org/abs/2003.03132
Autor:
Tominec, Igor, Villard, Pierre-Frédéric, Larsson, Elisabeth, Bayona, Víctor, Cacciani, Nicola
Publikováno v:
In Journal of Computational Physics 15 November 2022 469