572 citations · 804 across the 24 of their papers we have counts for
28 papers
On a robust inf-sup condition for the Stokes problem in slender domains -- with application to preconditioning
Espen Sande, Timo Koch, Miroslav Kuchta +1
We identify a norm on the pressure variable in the Stokes equation that allows us to prove a continuous inf-sup condition with a constant independent of the domain's aspect ratio.…
Parameter-robust preconditioner for Stokes-Darcy coupled problem with Lagrange multiplier
Xiaozhe Hu, Miroslav Kuchta, Kent-Andre Mardal +1
In this paper, we propose a parameter-robust preconditioner for the coupled Stokes-Darcy problem equipped with various boundary conditions, enforcing the mass conservation at the i…
Parameter-Robust Preconditioners for A Four-Field Thermo-Poroelasticity Model
Mingchao Cai, Miroslav Kuchta, Jingzhi Li +2
We study a thermo-poroelasticity model which describes the interaction between the deformation of an elastic porous material and fluid flow under non-isothermal conditions. The mod…
Robust Preconditioning of mixed-dimensional PDEs on 3d-1d domains coupled with Lagrange multipliers
Nunzio Dimola, Miroslav Kuchta, Kent-Andre Mardal +1
In the context of micro-circulation, the coexistence of two distinct length scales - the vascular radius and the tissue/organ scale - with a substantial difference in magnitude, po…
Algebraic multigrid methods for metric-perturbed coupled problems
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta +2
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriora…
The modelling error in multi-dimensional time-dependent solute transport models
Rami Masri, Marius Zeinhofer, Miroslav Kuchta +1
Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsat…
Domain decomposition solvers for operators with fractional interface perturbations
Miroslav Kuchta
Operators with fractional perturbations are crucial components for robust preconditioning of interface-coupled multiphysics systems. However, in case the perturbation is strong, st…
HAZniCS -- Software Components for Multiphysics Problems
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta +2
We introduce the software toolbox HAZniCS for solving interface-coupled multiphysics problems. HAZniCS is a suite of modules that combines the well-known FEniCS framework for finit…
Rational approximation preconditioners for multiphysics problems
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta +2
We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the…
Investigating molecular transport in the human brain from MRI with physics-informed neural networks
Bastian Zapf, Johannes Haubner, Miroslav Kuchta +3
In recent years, a plethora of methods combining deep neural networks and partial differential equations have been developed. A widely known and popular example are physics-informe…
Learning Mesh Motion Techniques with Application to Fluid-Structure Interaction
Johannes Haubner, Ottar Hellan, Marius Zeinhofer +1
Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion…
Robust approximation of generalized Biot-Brinkman problems
Q. Hong, J. Kraus, M. Kuchta +3
The generalized Biot-Brinkman equations describe the displacement, pressures and fluxes in an elastic medium permeated by multiple viscous fluid networks and can be used to study c…
Parameter-robust methods for the Biot-Stokes interfacial coupling without Lagrange multipliers
Wietse M. Boon, Martin Hornkjøl, Miroslav Kuchta +2
In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a…
Robust monolithic solvers for the Stokes-Darcy problem with the Darcy equation in primal form
Wietse M. Boon, Timo Koch, Miroslav Kuchta +1
We construct mesh-independent and parameter-robust monolithic solvers for the coupled primal Stokes-Darcy problem. Three different formulations and their discretizations in terms o…
Hybrid FEM-NN models: Combining artificial neural networks with the finite element method
Sebastian K. Mitusch, Simon W. Funke, Miroslav Kuchta
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural net…
Robust preconditioners for perturbed saddle-point problems and conservative discretizations of Biot's equations utilizing total pressure
Wietse M. Boon, Miroslav Kuchta, Kent-Andre Mardal +1
We develop robust solvers for a class of perturbed saddle-point problems arising in the study of a second-order elliptic equation in mixed form (in terms of flux and potential), an…
Analysis and approximation of mixed-dimensional PDEs on 3D-1D domains coupled with Lagrange multipliers
Miroslav Kuchta, Federica Laurino, Kent-Andre Mardal +1
Coupled partial differential equations defined on domains with different dimensionality are usually called mixed dimensional PDEs. We address mixed dimensional PDEs on three-dimens…
Robust preconditioning for coupled Stokes-Darcy problems with the Darcy problem in primal form
Karl Erik Holter, Miroslav Kuchta, Kent-Andre Mardal
The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditione…
Robust preconditioning of monolithically coupled multiphysics problems
Karl Erik Holter, Miroslav Kuchta, Kent-Andre Mardal
In many applications, one wants to model physical systems consisting of two different physical processes in two different domains that are coupled across a common interface. A cruc…
Assembly of multiscale linear PDE operators
Miroslav Kuchta
In numerous applications the mathematical model consists of different processes coupled across a lower dimensional manifold. Due to the multiscale coupling, finite element discreti…
An Observation On The Uniform Preconditioners For The Mixed Darcy Problem
Trygve Bærland, Miroslav Kuchta, Kent-Andre Mardal +1
When solving a multi-physics problem one often decomposes a monolithic system into simpler, frequently single-physics, subproblems. A comprehensive solution strategy may commonly b…
Deep Reinforcement Learning achieves flow control of the 2D Karman Vortex Street
Jean Rabault, Ulysse Reglade, Nicolas Cerardi +2
The Karman Vortex Street has been investigated for over a century and offers a reference case for investigation of flow stability and control of high dimensionality, non-linear sys…
Artificial Neural Networks trained through Deep Reinforcement Learning discover control strategies for active flow control
Jean Rabault, Miroslav Kuchta, Atle Jensen +2
We present the first application of an Artificial Neural Network trained through a Deep Reinforcement Learning agent to perform active flow control. It is shown that, in a 2D simul…
Multigrid Methods for Discrete Fractional Sobolev Spaces
Trygve Bærland, Miroslav Kuchta, Kent-Andre Mardal
Coupled multiphysics problems often give rise to interface conditions naturally formulated in fractional Sobolev spaces. Here, both positive- and negative fractionality are common.…