47 citations · 190 across the 24 of their papers we have counts for
31 papers
Mixed Consistent PINNs for Elliptic Obstacle Problems with Stability Analysis
Arbaz Khan, Kent-Andre Mardal, Shiv Mishra
We propose a consistent physics-informed neural networks (CPINNs) framework for elliptic obstacle problems formulated as variational inequalities. The method is based on a mixed lo…
A robust and time-parallel preconditioner for parabolic reconstruction problems using Isogeometric Analysis
Kent-Andre Mardal, Jarle Sogn, Stefan Takacs
We consider a PDE-constrained optimization problem of tracking type with parabolic state equation. The solution to the problem is characterized by the Karush-Kuhn-Tucker (KKT) syst…
Variational Formulations of the Strong Formulation -- Forward and Inverse Modeling using Isogeometric Analysis and Physics-Informed Networks
Kent-Andre Mardal, Jarle Sogn, Marius Zeinhofer
The recently introduced Physics-Informed Neural Networks (PINNs) have popularized least squares formulations of both forward and inverse problems involving partial differential equ…
A Unified Framework for the Error Analysis of Physics-Informed Neural Networks
Marius Zeinhofer, Rami Masri, Kent-André Mardal
We prove a priori and a posteriori error estimates for physics-informed neural networks (PINNs) for linear PDEs. We analyze elliptic equations in primal and mixed form, elasticity,…
Robust preconditioning and error estimates for optimal control of the convection-diffusion-reaction equation with limited observation in Isogeometric analysis
Kent-Andre Mardal, Jarle Sogn, Stefan Takacs
In this paper we analyze an optimization problem with limited observation governed by a convection--diffusion--reaction equation. Motivated by a Schur complement approach, we arriv…
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…
Accurate Discretization Of Poroelasticity Without Darcy Stability -- Stokes-Biot Stability Revisited
Kent-Andre Mardal, Marie E. Rognes, Travis B. Thompson
In this manuscript we focus on the question: what is the correct notion of Stokes-Biot stability? Stokes-Biot stable discretizations have been introduced, independently by several…
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…
Parameter robust preconditioning for multi-compartmental Darcy equations
Eleonora Piersanti, Marie E. Rognes, Kent-Andre Mardal
In this paper, we propose a new finite element solution approach to the multi-compartmental Darcy equations describing flow and interactions in a porous medium with multiple fluid…
Parameter robust preconditioning by congruence for multiple-network poroelasticity
Eleonora Piersanti, Jeonghun J. Lee, Travis Thompson +2
The mechanical behaviour of a poroelastic medium permeated by multiple interacting fluid networks can be described by a system of time-dependent partial differential equations know…
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…
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…
Can diffusion alone explain brain-wide distribution of a CSF tracer within 24 hours?
Lars Magnus Valnes, Sebastian K. Mitusch, Geir Ringstad +3
The recently proposed glymphatic system suggests that bulk flow is important for clearing waste from the brain, and as such may underlie the development of e.g. Alzheimer's disease…
Laplacian preconditioning of elliptic PDEs: Localization of the eigenvalues of the discretized operator
Tomáš Gergelits, Kent-André Mardal, Bjørn Fredrik Nielsen +1
In the paper \textit{Preconditioning by inverting the {L}aplacian; an analysis of the eigenvalues. IMA Journal of Numerical Analysis 29, 1 (2009), 24--42}, Nielsen, Hackbusch and T…
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.…
A mixed finite element method for nearly incompressible multiple-network poroelasticity
Jeonghun J. Lee, Eleonora Piersanti, Kent-Andre Mardal +1
In this paper, we present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. The MPET equation…
Slope limiting the velocity field in a discontinuous Galerkin divergence free two-phase flow solver
Tormod Landet, Kent-Andre Mardal, Mikael Mortensen
Solving the Navier-Stokes equations when the density field contains a large sharp discontinuity---such as a water/air free surface---is numerically challenging. Convective instabil…
Sub-voxel perfusion modeling in terms of coupled 3d-1d problem
Karl Erik Holter, Miroslav Kuchta, Kent-André Mardal
We study perfusion by a multiscale model coupling diffusion in the tissue and diffusion along the one-dimensional segments representing the vasculature. We propose a block-diagonal…
Multi-resolution Bayesian CMB component separation through Wiener-filtering with a pseudo-inverse preconditioner
D. S. Seljebotn, T. Bærland, H. K. Eriksen +2
We present a Bayesian model for multi-resolution CMB component separation based on Wiener filtering and/or computation of constrained realizations, extending a previously developed…
Weakly imposed symmetry and robust preconditioners for Biot's consolidation model
Trygve Baerland, Jeonghun J. Lee, Kent-Andre Mardal +1
We discuss the construction of robust preconditioners for finite element approximations of Biot's consolidation model in poroelasticity. More precisely, we study finite element met…
Preconditioning trace coupled 3-1 systems using fractional Laplacian
Miroslav Kuchta, Kent-Andre Mardal, Mikael Mortensen
Multiscale or multiphysics problems often involve coupling of partial differential equations posed on domains of different dimensionality. In this work we consider a simplified mod…
On the Singular Neumann Problem in Linear Elasticity
Miroslav Kuchta, Kent-Andre Mardal, Mikael Mortensen
The Neumann problem of linear elasticity is singular with a kernel formed by the rigid motions of the body. There are several tricks that are commonly used to obtain a non-singular…
Variational data assimilation for transient blood flow simulations
S. W. Funke, M. Nordaas, Øyvind Evju +2
Several cardiovascular diseases are caused from localised abnormal blood flow such as in the case of stenosis or aneurysms. Prevailing theories propose that the development is caus…