# Kent-Andre Mardal

## ProfessorAdjunct Chief Research Scientist

- Department
- Numerical Analysis and Scientific Computing
- Organisation
- Simula Research Laboratory

- kent-and@simula.no

## Publications

### 2024

#### Book Chapters

N. Dimola, M. Kuchta, K. Mardal and P. Zunino

Robust Preconditioning of mixed-dimensional PDEs on 3d-1d domains coupled with Lagrange multipliers

Quantitative approaches to microcirculation: mathematical models, computational methods, measurements and data analysis (SEMA/SIMAI Collection on Microcirculation)

### 2023

#### Journal Articles

B. Gomez-Vargas, K. Mardal, R. Ruiz-Baier and V. Vinje

Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion

SIAM Journal on Numerical Analysis

T. Koch, V. Vinje and K. Mardal

Estimates of the permeability of extra-cellular pathways through the astrocyte endfoot sheath

Fluids and Barriers of the CNS

V. Vinje, B. Zapf, G. Ringstad, P. K. Eide, M. E. Rognes and K. Mardal

Human brain solute transport quantified by glymphatic MRI-informed biophysics during sleep and sleep deprivation

Fluids and Barriers of the Central Nervous System

A. Budisa, X. Hu, M. Kuchta, K. Mardal and L. T. Zikatanov

Algebraic multigrid methods for metric-perturbed coupled problems

SIAM J. Sci. Comput.

L. Bojarskaite, A. Vallet, D. M. Bjørnstad, K. M. G. Binder, C. Cunen, K. Heuser, M. Kuchta, K. Mardal and R. Enger

Sleep cycle-dependent vascular dynamics in male mice and the predicted effects on perivascular cerebrospinal fluid flow and solute transport

Nature Communications

#### Proceedings, refereed

A. Budisa, X. Hu, M. Kuchta, K. Mardal and L. T. Zikatanov

Rational approximation preconditioners for multiphysics problems

Numerical Methods and Applications (NMA 2022)

### 2022

#### Journal Articles

A. Budisa, X. Hu, M. Kuchta, K. Mardal and L. T. Zikatanov

HAZniCS – Software Components for Multiphysics Problems

ACM Transactions on Mathematical Software

M. Kuchta, S. G. Wubshet, N. K. Afseth, K. Mardal and K. H. Liland

Encoder–decoder neural networks for predicting future

Journal of Biophotonics

L. Bojarskaite, D. M. Bjørnstad, A. Vallet, K. M. G. Binder, C. Cunen, K. Heuser, M. Kuchta, K. Mardal and R. Enger

Sleep cycle-dependent vascular dynamics enhance perivascular cerebrospinal fluid flow and solute transport

bioRxiv

B. Zapf, J. Haubner, M. Kuchta, G. Ringstad, P. K. Eide and K. Mardal

Investigating molecular transport in the human brain from MRI with physics-informed neural networks

Scientific Reports

W. M. Boon, T. Koch, M. Kuchta and K. Mardal

Robust Monolithic Solvers for the Stokes--Darcy Problem with the Darcy Equation in Primal Form

SIAM Journal on Scientific Computing

W. M. Boon, M. Hornkjøl, M. Kuchta, K. Mardal and R. Ruiz-Baier

Parameter-robust methods for the Biot–Stokes interfacial coupling without Lagrange multipliers

Journal of Computational Physics

T. Bohr, P. G. Hjorth, S. C. Holst, S. Hrabětová, V. Kiviniemi, T. Lilius, I. Lundgaard, K. Mardal, E. A. Martens, Y. Mori, V. Nägerl, C. Nicholson, A. Tannenbaum, J. H. Thomas, J. Tithof, H. Benveniste, J. J. Iliff, D. H. Kelley and M. Nedergaard

The glymphatic system: Current understanding and modeling

iScience

J. Schreiner and K. Mardal

Simulating epileptic seizures using the bidomain model

Scientific Reports

K. Mardal, J. Sogn and S. Takacs

Robust Preconditioning and Error Estimates for Optimal Control of the Convection--Diffusion--Reaction Equation with Limited Observation in Isogeometric Analysis

SIAM Journal on Numerical Analysis

M. Hornkjøl, L. M. Valnes, G. A. Ringstad, M. E. Rognes, P. K. Eide, K. Mardal and V. Vinje

CSF circulation and dispersion yield rapid clearance from intracranial compartments

Frontiers in Bioengineering and Biotechnology

Q. Hong, J. Kraus, M. Kuchta, M. Lymbery, K. Mardal and M. E. Rognes

Robust approximation of generalized Biot-Brinkman problems

Journal on Scientific Computing

#### Books

K. Mardal, M. E. Rognes, T. B. Thompson and L. M. Valnes

Mathematical modeling of the human brain: from magnetic resonance images to finite element simulation

Simula SpringerBriefs on Computing

#### Talks, invited

M. Kuchta

Parameter-robust monolithic solvers for Stokes-Darcy/Biot systems

The 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), Oslo, Norway

M. Kuchta, W. M. Boon, K. E. Holter, M. Hornkjøl, T. Koch, K. Mardal and R. Ruiz-Baier

Fractional operators in coupled multiphysics problems with implicit coupling

Numerical Solution of Fractional Differential Equations and Applications NSFDE&A’22

M. Kuchta, W. M. Boon, M. Hornkjøl, T. Koch, K. Mardal and R. Ruiz-Baier

Parameter-robust Methods for Biot-Stokes and Darcy-Stokes Interfacial Coupling without Lagrange Multipliers

15th World Congress on Computation Mechanics

M. Kuchta, A. Budisa, X. Hu, L. T. Zikatanov and K. Mardal

Fractional Laplacians and Hybridized DG

Simula's Workshop on computational mechanics models on domains of heterogeneous dimensionality, Split, Croatia

#### Talks, contributed

C. Daversin-Catty, V. Vinje, I. Gjerde, K. Mardal and M. E. Rognes

Modeling fluid flow in perivascular networks

ECCOMAS22, Oslo (Norway)

M. Kuchta, W. M. Boon, T. Koch, K. Mardal and R. Ruiz-Baier

Parameter-robust monolithic solvers for coupled Biot/Darcy-Stokes models

27th International Domain Decomposition Conference, DD27

### 2021

#### Journal Articles

W. M. Boon, M. Kuchta, K. Mardal and R. Ruiz-Baier

Robust Preconditioners for Perturbed Saddle-Point Problems and Conservative Discretizations of Biot's Equations Utilizing Total Pressure

SIAM Journal on Scientific Computing

P. K. Eide, L. M. Valnes, E. K. Lindstrøm, K. Mardal and G. Ringstad

Direction and magnitude of cerebrospinal fluid flow vary substantially across central nervous system diseases

Fluids and Barriers of the CNS

B. A. Young, J. Adams, J. M. Beary, K. Mardal, R. Schneider and T. Kondrashova

Variations in the cerebrospinal fluid dynamics of the American alligator (Alligator mississippiensis)

Fluids and Barriers of the CNS

P. K. Eide, V. Vinje, A. H. Pripp, K. Mardal and G. A. Ringstad

Sleep deprivation impairs molecular clearance from the human brain

Brain

M. Kuchta, F. Laurino, K. Mardal and P. Zunino

Analysis and approximation of mixed-dimensional PDEs on 3D-1D domains coupled with Lagrange multipliers

SIAM Journal on Numerical Analysis

K. Mardal, M. E. Rognes and T. Thompson

Accurate discretization of poroelasticity without Darcy stability – Stokes-Biot revisited

BIT Numerical Mathematics

#### Book Chapters

M. Kuchta, K. Mardal and M. E. Rognes

Solving the EMI Equations using Finite Element Methods

Modeling Excitable Tissue: The EMI Framework

Å. Telle, S. Wall and J. Sundnes

Modeling Cardiac Mechanics on a Sub-Cellular Scale

Modeling Excitable Tissue: The EMI Framework

M. Kuchta and K. Mardal

Iterative Solvers for EMI Models

Modeling Excitable Tissue: The EMI Framework

A. P. Buccino, M. Kuchta, J. Schreiner and K. Mardal

Improving Neural Simulations with the EMI Model

Modeling Excitable Tissue: The EMI Framework

K. H. Jæger, K. G. Hustad, X. Cai and A. Tveito

Operator Splitting and Finite Difference Schemes for Solving the EMI Model

Modeling Excitable Tissue: The EMI Framework

K. H. Jæger and A. Tveito

Derivation of a Cell-Based Mathematical Model of Excitable Cells

Modeling Excitable Tissue: The EMI Framework

#### Edited books

Modeling Excitable Tissue: The EMI Framework

#### Talks, invited

C. Daversin-Catty, I. Gjerde, K. Mardal, M. E. Rognes and V. Vinje

Modeling fluid flow in perivascular networks

Oslo glymphatics symposium, Oslo (Norway)

### 2020

#### Journal Articles

C. Daversin-Catty, V. Vinje, K. Mardal and M. E. Rognes

The mechanisms behind perivascular fluid flow

PLOS ONE

L. M. Valnes, S. Mitusch, G. Ringstad, P. K. Eide, S. W. Funke and K. Mardal

Apparent diffusion coefficient estimates based on 24 hours tracer movement support glymphatic transport in human cerebral cortex

Scientific Reports

K. E. Holter, M. Kuchta and K. Mardal

Robust preconditioning for coupled Stokes–Darcy problems with the Darcy problem in primal form

Computers & Mathematics with Applications

W. M. Boon, M. Kuchta, K. Mardal and R. Ruiz-Baier

Robust preconditioners for perturbed saddle-point problems and conservative discretizations of Biot's equations utilizing total pressure

arXiv preprint arXiv:2011.05236

T. Bærland, M. Kuchta, K. Mardal and T. Thompson

An observation on the uniform preconditioners for the mixed Darcy problem

Numerical Methods for Partial Differential Equations

K. E. Holter, M. Kuchta and K. Mardal

Robust preconditioning of monolithically coupled multiphysics problems

arXiv preprint arXiv:2001.05527