32 citations · 130 across the 12 of their papers we have counts for
12 papers
Data Clustering as an Emergent Consensus of Autonomous Agents
Piotr Minakowski, Jan Peszek
We present a data segmentation method based on a first-order density-induced consensus protocol. We provide a mathematically rigorous analysis of the consensus model leading to the…
Comparison of the Symmetric Hyperbolic Thermodynamically Compatible framework with Hamiltonian mechanics of binary mixtures
Martin Sykora, Michal Pavelka, Ilya Peshkov +3
How to properly describe continuum thermodynamics of binary mixtures where each constituent has its own momentum? The Symmetric Hyperbolic Thermodynamically Consistent (SHTC) frame…
A priori and a posteriori error estimates for the Deep Ritz method applied to the Laplace and Stokes problem
Piotr Minakowski, Thomas Richter
We analyze neural network solutions to partial differential equations obtained with Physics Informed Neural Networks. In particular, we apply tools of classical finite element erro…
On the Impact of Fluid Structure Interaction in Blood Flow Simulations: Stenotic Coronary Artery Benchmark
Lukas Failer, Piotr Minakowski, Thomas Richter
We study the impact of using fluid-structure interactions (FSI) to simulate blood flow in a large stenosed artery. We compare typical flow configurations using Navier-Stokes in a r…
Density-induced Consensus Protocol
Piotr Minakowski, Piotr B. Mucha, Jan Peszek
The paper introduces a model of collective behavior where agents receive information only from sufficiently dense crowds in their immediate vicinity. The system is an asymmetric, d…
Numerical benchmarking of fluid-rigid body interactions
Henry von Wahl, Thomas Richter, Christoph Lehrenfeld +2
We propose a fluid-rigid body interaction benchmark problem, consisting of a solid spherical obstacle in a Newtonian fluid, whose centre of mass is fixed but is free to rotate. A n…
Finite Element Error Estimates on Geometrically Perturbed Domains
Piotr Minakowski, Thomas Richter
We develop error estimates for the finite element approximation of elliptic partial differential equations on perturbed domains, i.e. when the computational domain does not match t…
Singular Cucker-Smale Dynamics
Piotr Minakowski, Piotr B. Mucha, Jan Peszek +1
The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mes…
A Gibbs-potential-based framework for ideal plasticity of crystalline solids treated as a material flow through an adjustable crystal lattice space and its application to three-dimensional micropillar compression
Jan Kratochvíl, Josef Málek, Piotr Minakowski
We propose an Eulerian thermodynamically compatible model for ideal plasticity of crystalline solids treated as a material flow through an adjustable crystal lattice space. The mod…
Finite Volume approximations of the Euler system with variable congestion
Pierre Degond, Piotr Minakowski, Laurent Navoret +1
We are interested in the numerical simulations of the Euler system with variable congestion encoded by a singular pressure. This model describes for instance the macroscopic motion…
Stress-diffusive regularizations of non-dissipative rate-type materials
Jan Burczak, Josef Málek, Piotr Minakowski
We consider non-dissipative (elastic) rate-type material models that are derived within the Gibbs-potential-based thermodynamic framework. Since the absence of any dissipative mech…
Transport of congestion in two-phase compressible/incompressible flows
Pierre Degond, Piotr Minakowski, Ewelina Zatorska
We study the existence of weak solutions to the two-phase model of crowd motion. The model encompasses the flow in the uncongested regime (compressible) and the congested one (inco…