# Aslak Tveito

## ProfessorSimula Fellow

- Department
- Administration and Management
- Organisation
- Simula Research Laboratory
- Research Interests
- Computational physiology Biophysics Scientific computing

- aslak@simula.no

## Publications

### 2023

#### Books

K. H. Jæger and A. Tveito

Differential Equations for Studies in Computational Electrophysiology

#### Journal Articles

K. H. Jæger, E. Ivanovic, J. P. Kucera and A. Tveito

Nano-scale solution of the Poisson-Nernst-Planck (PNP) equations in a fraction of two neighboring cells reveals the magnitude of intercellular electrochemical waves

PLoS Computational Biology

K. H. Jæger and A. Tveito

Efficient, cell-based simulations of cardiac electrophysiology; The Kirchhoff Network Model (KNM)

npj Systems Biology and Applications

K. H. Jæger and A. Tveito

The simplified Kirchhoff network model (SKNM): a cell‐based reaction–diffusion model of excitable tissue

Nature Scientific Reports

### 2022

#### Journal Articles

V. Charwat, B. Charrez, B. A. Siemons, H. Finsberg, K. H. Jæger, A. G. Edwards, N. Huebsch, S. Wall, E. Miller, A. Tveito and K. E. Healy

Validating the Arrhythmogenic Potential of High-, Intermediate-, and Low-Risk Drugs in a Human-Induced Pluripotent Stem Cell-Derived Cardiac Microphysiological System

ACS Pharmacology & Translational Science

K. H. Jæger and A. Tveito

Deriving the Bidomain Model of Cardiac Electrophysiology From a Cell-Based Model; Properties and Comparisons

Frontiers in Physiology

K. H. Jæger, A. G. Edwards, W. R. Giles and A. Tveito

Arrhythmogenic influence of mutations in a myocyte‑based computational model of the pulmonary vein sleeve

Nature Scientific Reports

N. Huebsch, B. Charrez, G. Neiman, B. Siemons, S. C. Boggess, S. Wall, V. Charwat, K. H. Jæger, D. Cleres, Å. Telle, F. T. Lee-Montiel, N. C. Jeffreys, N. Deveshwar, A. G. Edwards, J. Serrano, M. Snuderl, A. Stahl, A. Tveito, E. W. Miller and K. E. Healy

Metabolically driven maturation of human-induced-pluripotent-stem-cell-derived cardiac microtissues on microfluidic chips

Nature Biomedical Engineering

### 2021

#### Book Chapters

A. J. Ellingsrud, C. Daversin-Catty and M. E. Rognes

A cell-based model for ionic electrodiffusion in excitable tissue

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

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

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

Solving the EMI Equations using Finite Element Methods

Modeling Excitable Tissue: The EMI Framework

#### Edited books

Modeling Excitable Tissue: The EMI Framework

#### Journal Articles

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

Efficient numerical solution of the EMI model representing the extracellular space (E), cell membrane (M) and intracellular space (I) of a collection of cardiac cells

Frontiers in Physics

K. H. Jæger, V. Charwat, S. Wall, K. E. Healy and A. Tveito

Identifying drug response by combining measurements of the membrane potential, the cytosolic calcium concentration, and the extracellular potential in microphysiological systems

Frontiers in Pharmacology

K. H. Jæger, S. Wall and A. Tveito

Computational prediction of drug response in short QT syndrome type 1 based on measurements of compound effect in stem cell-derived cardiomyocytes

PLoS Computational Biology

K. H. Jæger, A. G. Edwards, W. R. Giles and A. Tveito

A computational method for identifying an optimal combination of existing drugs to repair the action potentials of SQT1 ventricular myocytes

PLoS Computational Biology

K. H. Jæger, A. G. Edwards, W. R. Giles and A. Tveito

From Millimeters to Micrometers; Re-introducing Myocytes in Models of Cardiac Electrophysiology

Frontiers in Physiology

### 2020

#### Journal Articles

K. H. Jæger, V. Charwat, B. Charrez, H. Finsberg, M. Maleckar, S. Wall, K. E. Healy and A. Tveito

Improved computational identification of drug response using optical measurements of human stem cell derived cardiomyocytes in microphysiological systems

Frontiers in Pharmacology

A. Tveito, K. H. Jæger, M. Maleckar, W. R. Giles and S. Wall

Computational translation of drug effects from animal experiments to human ventricular myocytes

Nature Scientific Reports

### 2019

#### Journal Articles

A. P. Buccino, M. Kuchta, K. H. Jæger, T. V. Ness, P. Berthet, K. Mardal, G. Cauwenberghs and A. Tveito

How does the presence of neural probes affect extracellular potentials?

Journal of Neural Engineering

K. H. Jæger, A. G. Edwards, A. D. McCulloch and A. Tveito

Properties of cardiac conduction in a cell-based computational model

PLoS Computational Biology

K. H. Jæger, S. Wall and A. Tveito

Detecting undetectables: Can conductances of action potential models be changed without appreciable change in the transmembrane potential?

Chaos

#### Posters

Å. Telle, B. Charrez, K. E. Healy, A. Tveito and S. Wall

A numerical model of mechanical properties of cardiac tissue in heart-on-a-chip devices

#### Talks, contributed

Å. Telle, B. Charrez, K. E. Healy, A. Tveito and S. Wall

A Numerical Model of Heart -on -a-Chip Systems – A Tool for Cardiotoxicity Screening

Melbourne, Australia

Å. Telle, B. Charrez, K. E. Healy, A. Tveito and S. Wall

Finite element modeling of cardiac tissue in heart-on-a-chip systems

Washington DC, USA

### 2018

#### Journal Articles

A. Tveito, M. Maleckar and G. T. Lines

Computing Optimal Properties of Drugs Using Mathematical Models of Single Channel Dynamics

Computational and Mathematical Biophysics

A. Tveito, K. H. Jæger, N. Huebsch, B. Charrez, A. G. Edwards, S. Wall and K. E. Healy

Inversion and computational maturation of drug response using human stem cell derived cardiomyocytes in microphysiological systems

Nature Scientific Reports

N. Huebsch, B. Charrez, B. Siemons, S. C. Boggess, S. Wall, V. Charwat, K. Jaeger, F. L. T. Montiel, N. C. Jeffreys, N. Deveshwar, A. G. Edwards, J. Serrano, M. Snuderl, A. Stahl, A. Tveito, E. W. Miller and K. E. Healy

Metabolically-Driven Maturation of hiPSC-Cell Derived Heart-on-a-Chip

{bioRxiv

#### Posters

S. Wall, K. H. Jæger, N. Huebsch, B. Charrez, K. Healy and A. Tveito

In Silico - Augmented Cardiac Microphysiological Systems for Evaluating Cardiac Drug Effects

S. Wall, K. H. Jæger, N. Huebsch, B. Charrez, K. Healy and A. Tveito

In Silico - Augmented Cardiac Microphysiological Systems for Evaluating Cardiac Drug Effects

#### Talks, contributed

S. Wall, A. Tveito, K. H. Jæger, A. G. Edwards, K. Healy, N. Huebsch and B. Charrez

In Silico Modeling of Cardiac Microphysiological Systems for Evaluating Drug Side Effects

Heart By Numbers Conference, Berlin, Germany

### 2017

#### Journal Articles

A. Tveito, K. H. Jæger, G. T. Lines, Ł. Paszkowski, J. Sundnes, A. G. Edwards, T. Mäki-Marttunen, G. Halnes and G. T. Einevoll

An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons

Frontiers in Computational Neuroscience

A. Tveito, K. H. Jæger, M. Kuchta, K. Mardal and M. E. Rognes

A cell-based framework for numerical modelling of electrical conduction in cardiac tissue

Frontiers in Physics, Computational Physics

T. Mäki-Marttunen, G. T. Lines, A. G. Edwards, A. Tveito, A. M. Dale, G. T. Einevoll and O. A. Andreassen

Pleiotropic effects of schizophrenia-associated genetic variants in neuron firing and cardiac pacemaking revealed by computational modeling

Translational Psychiatry

### 2016

#### Books

A. Tveito and G. T. Lines

Computing characterizations of drugs for ion channels and receptors using Markov models

#### Journal Articles

A. Tveito, G. T. Lines, A. G. Edwards and A. D. McCulloch

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states

Mathematical Biosciences

### 2015

#### Book Chapters

H. P. Langtangen, U. Rüde and A. Tveito

Scientific Computing

Encyclopedia of Applied and Computational Mathematics

A. Tveito, H. P. Langtangen and R. Winther

Computational Partial Differential Equations

Encyclopedia of Applied and Computational Mathematics

#### Edited books

Encyclopedia of Applied and Computational Mathematics

Encyclopedia of Applied and Computational Mathematics

#### Posters

J. Sundnes, S. Wall, V. Timmermann and A. Tveito

Mechano-electric feedback as a source of ectopic activity

Gordon Research Conference on Arrhythmia Mechanisms, Lucca, Italy

### 2013

#### Edited books

A. M. Bruaset and A. Tveito

Conversations About Challenges in Computing

#### Journal Articles

P. Li, G. T. Lines, M. Maleckar and A. Tveito

Mathematical Models of Cardiac Pacemaking Function

Frontiers in Physics

### 2012

#### Journal Articles

A. Tveito, G. T. Lines, M. E. Rognes and M. Maleckar

An Analysis of the Shock Strength Needed to Achieve Defibrillation in a Simplified Mathematical Model of Cardiac Tissue

International Journal of Numerical Analysis and Modeling

A. Tveito, G. T. Lines, A. G. Edwards, M. Maleckar, A. P. Michailova, J. E. Hake and A. D. McCulloch

Slow Calcium-Depolarization-Calcium Waves May Initiate Fast Local Depolarization Waves in Ventricular Tissue

Progress in Biophysics and Molecular Biology

A. Tveito, G. T. Lines, J. E. Hake and A. G. Edwards

Instabilities of the Resting State in a Mathematical Model of Calcium Handling in Cardiac Myocytes

Mathematical Biosciences

A. Tveito, G. T. Lines and M. Maleckar

A Note on a Possible Pro-Arrhythmic Property of Anti-Arrhythmic Drugs Aimed at Improving Gap-Junction Coupling

Biophysical Journal

### 2011

#### Journal Articles

A. Tveito, G. T. Lines, R. Artebrant, O. Skavhaug and M. Maleckar

Existence of Excitation Waves for a Collection of Cardiomyocytes Electrically Coupled to Fibroblasts

Mathematical Biosciences

A. Tveito, G. T. Lines, O. Skavhaug and M. Maleckar

Unstable Eigenmodes As Possible Drivers for Cardiac Arrhythmias

Journal of the Royal Society Interface

A. Tveito, O. Skavhaug, G. T. Lines and R. Artebrant

Computing the Stability of Steady-State Solutions of Mathematical Models of the Electrical Activity in the Heart

Mathematical Biosciences and Engineering

M. Hanslien, R. Artebrant, A. Tveito, G. T. Lines and X. Cai

Stability of Two Time-Integrators for the Aliev-Panfilov System

International Journal of Numerical Analysis and Modeling

A. Tveito, G. T. Lines, P. Li and A. D. McCulloch

On Defining Candidate Drug Characteristics for Long-QT

Mathematical Biosciences and Engineering

### 2010

#### Books

A. Tveito, H. P. Langtangen, B. F. Nielsen and X. Cai

Elements of Scientific Computing

#### Journal Articles

R. Artebrant, A. Tveito and G. T. Lines

A Method for Analyzing the Stability of the Resting State for a Model of Pacemaker Cells Surrounded by Stable Cells

Mathematical Biosciences and Engineering

### 2009

#### Books

A. Tveito and R. Winther

Introduction to Partial Differential Equations; a Computational Approach

#### Book Chapters

M. Jørgensen and S. Grimstad

Software Development Effort Estimation: Demystifying and Improving Expert Estimation

Simula Research Laboratory - by thinking constantly about it

L. Briand

Software Verification: a Scalable, Model-Driven, Empirically Grounded Approach

Simula Research Laboratory - by thinking constantly about it

E. Arisholm

A Series of Controlled Experiments on Software Maintenance

Simula Research Laboratory - by thinking constantly about it

D. I. K. Sjøberg

The Industry Is Our Lab - Organization and Conducting of Empirical Studies in Software Engineering at Simula

Simula Research Laboratory - by thinking constantly about it

D. I. K. Sjøberg and S. Grimstad

Software Engineering: Why - How - What - What's Next

Simula Research Laboratory - by thinking constantly about it

A. M. Bruaset and K. Vinje

Educating Researchers - a Virtue of Necessity

Simula Research Laboratory - by thinking constantly about it

A. M. Bruaset and M. M. Sundet

Bridging the Gap Between Industry and Research

Simula Research Laboratory - by thinking constantly about it

O. Lysne and A. M. Bruaset

Simula - the Language

Simula Research Laboratory - by thinking constantly about it

A. M. Bruaset, V. S. W. Eide, F. Eliassen, H. E. Gallis and C. Tarrou

Spinning Off From Simula

Simula Research Laboratory - by thinking constantly about it

C. Griwodz and O. Lysne

Networks and Distributed Systems - Why, What, How and What's Next

Simula Research Laboratory - by thinking constantly about it

A. Kvalbein and Y. Zhang

Providing Resilience in Communications Networks

Simula Research Laboratory - by thinking constantly about it

C. Griwodz and P. Halvorsen

RELAY - on the Performance and Resource Utilization of Time-Dependent Large-Scale Distributed Systems

Simula Research Laboratory - by thinking constantly about it

O. Lysne, T. Skeie, S. Reinemo, F. O. Sem-Jacobsen and N. A. Nordbotten

Scalable Interconnection Networks

Simula Research Laboratory - by thinking constantly about it

A. M. Bruaset

Turning Rocks Into Knowledge - Experiences and Results From an Industrial Collaboration in Computational Geosciences

Simula Research Laboratory - by thinking constantly about it

B. F. Nielsen, O. M. Lysaker, P. Grøttum, K. Mardal, A. Tveito, C. Tarrou, K. Haugaa, A. Abildgaard and J. G. Fjeld

Can ECG Recordings and Mathematics Tell the Condition of Your Heart?

Simula Research Laboratory - by thinking constantly about it

A. Logg, H. P. Langtangen and X. Cai

Past and Future Perspectives on Scientific Software

Simula Research Laboratory - by thinking constantly about it

H. P. Langtangen and J. Sundnes

Scientific Computing: Why - How - What - What's Next

Simula Research Laboratory - by thinking constantly about it

H. P. Langtangen and O. Lysne

The Hamming Experience

Simula Research Laboratory - by thinking constantly about it

G. T. Lines and J. Sundnes

Computer Simulations of the Heart

Simula Research Laboratory - by thinking constantly about it

#### Edited books

A. Tveito, A. M. Bruaset and O. Lysne

Simula Research Laboratory - by Thinking Constantly About It

#### Journal Articles

B. F. Nielsen, X. Cai, J. Sundnes and A. Tveito

Towards a Computational Method for Imaging the Extracellular Potassium Concentration During Regional Ischemia

Mathematical Biosciences

B. F. Nielsen, A. Tveito and W. Hackbusch

Preconditioning by Inverting the Laplacian; an Analysis of the Eigenvalues

IMA Journal of Numerical Analysis

G. T. Lines, S. Linge, M. C. MacLachlan and A. Tveito

Synchronizing Computer Simulations With Measurement Data for a Case of Atrial Flutter

Annals of Biomedical Engineering

M. Hanslien, R. Artebrant, J. Sundnes and A. Tveito

An Unconditionally Stable Second Order Method for the Luo-Rudy 1 Model Used in Simulations of Defibrillation

International Journal of Numerical Analysis and Modeling

J. Sundnes, R. Artebrant, O. Skavhaug and A. Tveito

A Second Order Algorithm for Solving Dynamic Cell Membrane Equations

IEEE Transactions on Biomedical Engineering

A. Tveito and G. T. Lines

A Note on a Method for Determining Advantageous Properties of an Anti-Arrhythmic Drug Based on a Mathematical Model of Cardiac Cells

Mathematical Biosciences

S. Linge, J. Sundnes, M. Hanslien, G. T. Lines and A. Tveito

Numerical Solution of the Bidomain Equations

Philosophical Transactions of the Royal Society A

#### Talks, contributed

B. F. Nielsen, O. M. Lysaker, P. Grøttum, A. Tveito, K. Haugaa, A. Abildgaard, J. G. Fjeld and M. Burger

Modelling, Mathematical Properties and Validation of the Inverse Ischemia Problem

Presented at the Bidomain Workshop, Graz, Austria

G. T. Lines, A. Tveito and P. Li

Antiarrhythmic Drug Identifaction

Presented at the Bidomain Workshop, Graz, Austria

### 2008

#### Journal Articles

B. F. Nielsen, O. Skavhaug and A. Tveito

Penalty Methods for the Numerical Solution of American Multi-Asset Option Problems

Journal of Computational and Applied Mathematics

S. Linge, G. T. Lines, J. Sundnes and A. Tveito

On the Frequency of Automaticity During Ischemia in Simulations Based on Stochastic Perturbations of the Luo-Rudy 1 Model

Computers in Biology and Medicine

A. Tveito and G. T. Lines

A Condition for Setting Off Ectopic Waves in Computational Models of Excitable Cells

Mathematical Biosciences

#### Talks, contributed

B. F. Nielsen, O. M. Lysaker, P. Grøttum, A. Tveito, A. Abildgaard, J. G. Fjeld and K. Haugaa

On the Use of Computer Simulations for Identifying Ischemic Heart Disease; Theoretical and Practical Aspects

Presented at the workshop Mathematics in Medicine/Biology, Centre of Mathematics for Applications, Department of Mathematics, University of Oslo

B. F. Nielsen, O. M. Lysaker, P. Grøttum, A. Tveito, A. Abildgaard, J. G. Fjeld and K. Haugaa

Theoretical and Practical Aspects of the Inverse Problem of Electrocardiography

Presented at Institut für Mathematik und Wissenschaftliches Rechnen, Karl Franzes Universität in Graz, Austria. Also presented at Institut für Numerische und Angewandte Mathematik, Westfälische Wilhelms-Universität Münster, Germany

B. F. Nielsen, O. M. Lysaker, P. Grøttum, A. Tveito, A. Abildgaard, J. G. Fjeld and K. Haugaa

The Inverse Problem of Identifying Ischemic Heart Disease

Presented at the annual meeting of European Cardiac Simulation Group, Bologna, Italy

### 2007

#### Journal Articles

A. Schroll, G. T. Lines and A. Tveito

On the Accuracy of Operator Splitting As Applied to Discretized Reaction Diffusion Systems

International Journal of Computer Mathematics

B. F. Nielsen, T. S. Ruud, G. T. Lines and A. Tveito

Optimal Monodomain Approximations of the Bidomain Equations

Applied Mathematics and Computation

K. Mardal, B. F. Nielsen, X. Cai and A. Tveito

An Order Optimal Solver for the Discretized Bidomain Equations

Numerical Linear Algebra with Applications

M. C. MacLachlan, J. Sundnes, O. Skavhaug, O. M. Lysaker, B. F. Nielsen and A. Tveito

A Linear System of Partial Differential Equations Modeling the Resting Potential of a Heart With Regional Ischemia

Mathematical Biosciences

M. Hanslien, J. Sundnes and A. Tveito

An Unconditionally Stable Numerical Method for the Luo-Rudy 1 Model Used in Simulations of Defibrillation

Mathematical Biosciences

X. Cai, B. F. Nielsen and A. Tveito

A Note on the Efficiency of the Conjugate Gradient Method for a Class of Time-Dependent Problems

Numerical Linear Algebra with Applications

B. F. Nielsen, O. M. Lysaker and A. Tveito

On the Use of the Resting Potential and Level Set Methods for Identifying Ischemic Heart Disease; an Inverse Problem

Journal of Computational Physics

### 2006

#### Books

J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, K. Mardal and A. Tveito

Computing the Electrical Activity in the Heart

#### Book Chapters

X. Cai and H. P. Langtangen

Parallelizing PDE Solvers Using the Python Programming Language

Numerical Solution of Partial Differential Equations on Parallel Computers

X. Cai and G. T. Lines

Full-Scale Simulation of Cardiac Electrophysiology on Parallel Computers

Numerical Solution of Partial Differential Equations on Parallel Computers

#### Proceedings, non-refereed

C. Tarrou, O. M. Lysaker, X. Cai, K. Mardal, C. Tarrou, T. S. Ruud, M. C. MacLachlan and A. Tveito

Identifying Ischemic Heart Disease in Terms of ECG Recordings and an Inverse Problem for the Bidomain Equations; Modeling and Experiments

The Third International Conference "Inverse Problems: Modeling and Simulation"

#### Edited books

A. M. Bruaset and A. Tveito

Numerical Solution of Partial Differential Equations on Parallel Computers

#### Journal Articles

M. Hanslien, K. H. Karlsen and A. Tveito

On a Finite Difference Scheme for a Beeler-Reuter Based Model of Cardiac Electrical Activity

International Journal of Numerical Analysis and Modeling

J. Sundnes, B. F. Nielsen, K. Mardal, X. Cai, G. T. Lines and A. Tveito

On the Computational Complexity of the Bidomain and the Monodomain Models of Electrophysiology

Annals of Biomedical Engineering

M. C. MacLachlan, B. F. Nielsen, O. M. Lysaker and A. Tveito

Computing the Size and Location of Myocardial Ischemia Using Measurements of ST-Segment Shift

IEEE Transactions on Biomedical Engineering

#### Talks, contributed

B. F. Nielsen, O. M. Lysaker, X. Cai, K. Mardal, C. Tarrou, M. C. MacLachlan, J. Sundnes, G. T. Lines and A. Tveito

Computational Issues in Heart Modeling

Presented at the Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria

M. Hanslien, J. Sundnes, G. T. Lines and A. Tveito

Simulating Electrical Activity in the Heart

Presented at St Jude Medical, Stockholm, Sweeden

M. Hanslien, J. Sundnes and A. Tveito

Simulations of Reentrant Arrhythmias in the Heart, and Defibrillation As a Treatment

Presented at NADA, KTH, Sweeden

### 2005

#### Journal Articles

J. Sundnes, G. T. Lines and A. Tveito

An Operator Splitting Method for Solving the Bidomain Equations Coupled to a Volume Conductor Model for the Torso

Mathematical Biosciences

M. Hanslien, K. H. Karlsen and A. Tveito

A Maximum Principle for an Explicit Finite Difference Scheme Approximating the Hodgkin-Huxley Model

BIT

#### Talks, contributed

O. M. Lysaker, B. F. Nielsen, A. Tveito, G. T. Lines, J. Sundnes and C. Tarrou

Kan Man Simulere Et Hjerteslag?

LAMIS - SOMMERKURS Matematikk - med røtter og vinger, Asker

J. Sundnes, M. Hanslien and A. Tveito

An Unconditionally Stable Numerical Method for the Luo-Rudy I Model Used in Defibrillation

Presented at Tulane University, New Orleans

K. Mardal, B. F. Nielsen and A. Tveito

Preconditioners for Elliptic Problems With Variable Coefficients

Presented at the SIAM Conference on Mathematical and Computational Issues in the Geosciences, Avignon, France

B. F. Nielsen, O. M. Lysaker, M. C. MacLachlan and A. Tveito

On the Use of Level Set Techniques for Identifying Heart Infarctions

Presented at the Level Set Methods for Direct and Inverse Problems workshop in Linz, Austria

B. F. Nielsen, O. M. Lysaker, C. Tarrou, M. C. MacLachlan, A. Abildgaard and A. Tveito

On the Use of ST-Segment Shifts and Mathematical Models for Identifying Ischemic Heart Disease

Presented at the Computers in Cardiology conference in Lyon, France

B. F. Nielsen, O. M. Lysaker, C. Tarrou, M. C. MacLachlan, A. Abildgaard and A. Tveito

Kan Vi Identifisere Hjerteinfarkt Ved Hjelp Av Datamaskiner?

Presented at the BeMatA seminar (Norwegian Research Council), Hurdal

#### Proceedings, refereed

B. F. Nielsen, O. M. Lysaker, C. Tarrou, A. Abildgaard, M. C. MacLachlan and A. Tveito

On the Use of ST-Segment Shifts and Mathematical Models for Identifying Ischemic Heart Disease

Computers in Cardiology 2005, Lyon, France, September 25-28

#### Technical reports

B. F. Nielsen, T. S. Ruud, G. T. Lines and A. Tveito

Optimal Monodomain Approximations of the Bidomain Equations

K. Mardal, B. F. Nielsen, X. Cai and A. Tveito

An Order Optimal Solver for the Discretized Bidomain Equations

### 2004

#### Book Chapters

X. Cai, G. T. Lines and A. Tveito

Parallel Solution of the Bidomain Equations With High Resolutions

Parallel Computing: Software Technology, Algorithms, Architectures & Applications

#### Talks, contributed

K. Mardal and A. Tveito

Block Preconditioners for PDEs Arising From the Bi-Domain Model of the Electrical Activity in the Heart

Talk at the Copper Mountain Conference, Colorado, USA

B. F. Nielsen, O. M. Lysaker, G. T. Lines and A. Tveito

Parameter Identification Problems for Infarction Modelling

Presented at the 2004 SIAM Conference on the Life Sciences, Portland, Oregon, USA

J. Sundnes, G. T. Lines and A. Tveito

Challenges in Mathematical Models of the Heart

Presented at the SIAM Annual meeting, Portland, Oregon

#### Technical reports

K. Lie and A. Tveito

Development of a Staggered Central Difference Scheme That Does Not Use a Spatial Reconstruction

T. K. Nilssen, L. Ingebrigtsen, M. Hanslien, G. T. Lines and A. Tveito

Resolution Requirements for a 1D Monodomain Model for Simulating

M. C. MacLachlan, B. F. Nielsen and A. Tveito

On the Use of ST Shifts to Identify Ischemic Heart Disease: Towards a Computational Approach

### 2003

#### Book Chapters

X. Cai, E. Acklam, H. P. Langtangen and A. Tveito

Parallel Computing

Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming

X. Cai

Overlapping Domain Decomposition Methods

Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming

A. Kjeldstad, H. P. Langtangen, J. Skogseid and K. Bjørlykke

Simulation of Sedimentary Basins

Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming

H. P. Langtangen and K. Mardal

Using Diffpack From Python Scripts

K. Mardal, G. Zumbusch and H. P. Langtangen

Multigrid Methods in Diffpack

K. Mardal and H. P. Langtangen

Mixed Elements in Diffpack

O. Skavhaug, B. F. Nielsen and A. Tveito

Mathematical Models of Financial Derivatives

Advanced Topics in Computational Partial Differential Equations -Numerical Methods and Diffpack Programming

O. Skavhaug, B. F. Nielsen and A. Tveito

Numerical Methods for Financial Derivatives

Advanced Topics in Computational Partial Differential Equations -Numerical Methods and Diffpack Programming

J. Sundnes, G. T. Lines, P. Grøttum and A. Tveito

Electrical Activity in the Human Heart

T. Thorvaldsen, H. P. Langtangen and H. Osnes

Finite Element Modeling of Elastic Structures

X. Cai, A. M. Bruaset, H. P. Langtangen, G. T. Lines, K. Samuelsson, W. Shen, A. Tveito and G. Zumbusch

Performance Modeling of PDE Solvers

K. Mardal, J. Sundnes, H. P. Langtangen and A. Tveito

Block Preconditioning and Systems of PDEs

#### Edited books

H. P. Langtangen and A. Tveito

Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

#### Journal Articles

L. Ingebrigtsen, T. K. Nilssen, H. P. Langtangen and A. Tveito

On the Accuracy of Operator Splitting for a Fluid-Structure Interaction Problem

International Journal of Nonlinear Sciences and Numerical Simulation

G. T. Lines, P. Grøttum and A. Tveito

Modeling the Electrical Activity of the Heart -A Bidomain Model of the Ventricles Embedded in a Torso

Computing and Visualization in Science

G. T. Lines, M. L. Buist, P. Grøttum, A. J. Pullan, J. Sundnes and A. Tveito

Mathematical Models and Numerical Methods for the Forward Problem in Cardiac Electrophysiology

Computing and Visualization in Science

#### Talks, contributed

X. Cai, G. T. Lines and A. Tveito

Toward Extremely High-Resolution Simulation of Human Heart

Talk at the ParCo 2003 Conference, 2 - 5 September 2003, Dresden, Germany

W. Chen, A. Bounaim, X. Cai, S. Holm, A. Tveito and Å. Ødegård

Mathematical and Numerical Modeling of Medical Ultrasound Wave Propagation

Invited talk to MACSI-Workshop for Numerical Simulations for Ultrasound Imaging and Inversion, St. Georgen, Austria, pages 8-13

B. F. Nielsen, G. T. Lines and A. Tveito

Determining the Size and Location of a Myocardial Infarction; a Scientific Computing Framework

Presented at the European Conference on Numerical Mathematics and Advanced Applications, Prague, Czech Republic

G. T. Lines, B. F. Nielsen, A. Tveito, J. Sundnes, P. Grøttum, X. Cai and K. Mardal

Computing the Electrical Activity in the Human Heart

Presented at the Centre of Mathematics for Applications, Oslo

A. Tveito, G. T. Lines, J. Sundnes, B. F. Nielsen, P. Grøttum, X. Cai and K. Mardal

Computing the Electrical Activity in the Human Heart

Presented at the European Conference on Numerical Mathematics and Advanced Applications, Prague, Czech Republic

A. Tveito, G. T. Lines, B. F. Nielsen, J. Sundnes, P. Grøttum, X. Cai and K. Mardal

Computing the Heart

Presented at the 21st CAD-FEM users' meeting 2003 - International congress on FEM technology, Potsdam, Germany

#### Proceedings, refereed

A. Bounaim, S. Holm, W. Chen, Å. Ødegård, A. Tveito and K. Thomenius

FETD Simulation of Wave Propagation Modeling the CARI Breast Sonography

Proceedings of ICCSA2003, International Conference on Computational Science and its Applications

H. P. Langtangen and H. Osnes

Stochastic Partial Differential Equations

Å. Ødegård, H. P. Langtangen and A. Tveito

Fully Implicit Methods for Systems of PDEs

### 2002

#### Books

A. Tveito and R. Winther

Einführung in Die Theorie Der Partiellen Differentialgleichungen; Ein Numerischer Zugang

#### Journal Articles

G. T. Lines, J. Sundnes and A. Tveito

A Domain Embedding Strategy for Solving the Bidomain Equations on Complicated Geometries

International Journal of Bioelectromagnetism

B. F. Nielsen, O. Skavhaug and A. Tveito

Penalty and Front-Fixing Methods for the Numerical Solution of American Option Problems

Journal of Computational Finance

J. Sundnes, G. T. Lines, K. Mardal and A. Tveito

Multigrid Block Preconditioning for a Coupled System of Partial Differential Equations Modeling the Electrical Activity in the Heart

Computer Methods in Biomechanics and Biomedical Engineering

J. Sundnes, G. T. Lines and A. Tveito

A Second Order Scheme for Solving the Bidomain and Forward Problem

International Journal of Bioelectromagnetism

J. Sundnes, G. T. Lines and A. Tveito

ODE Solvers for a Stiff System Arising in the Modeling of the Electrical Activity of the Heart

International Journal of Nonlinear Sciences and Numerical Simulation

#### Talks, contributed

H. P. Langtangen and A. Tveito

How Should We Prepare the Students of Science and Technology for a Life in the Computer Age?

Invited talk at the Department of Mathematics, University of Coimbra, Portugal

G. T. Lines, J. Sundnes, A. Tveito, X. Cai, K. Mardal and A. M. Bruaset

Diffpack Simulation of the Electrical Activity in the Heart

Invited minisymposium talk at the 20th CAD-FEM User's Meeting, Friedrichshafen, Germany

#### Proceedings, refereed

W. Chen, S. Holm, A. Bounaim, Å. Ødegård and A. Tveito

Frequency Decomposition Time-Domain Model of Broadband Frequency-Dependent Absorption

The 9th Workshop of the Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields

B. F. Nielsen, O. Skavhaug and A. Tveito

A Penalty Scheme for Solving American Option Problems

Progress in industrial mathematics at ECMI 2000

#### Technical reports

A. Bounaim, S. Holm, W. Chen, Å. Ødegård and A. Tveito

Simulation of the CARI Technique for Breast Tumor Detection Using Ultrasound Wave Propagation

### 2001

#### Journal Articles

J. Sundnes, G. T. Lines and A. Tveito

Efficient Solution of Ordinary Differential Equations Modeling Electrical Activity in Cardiac Cells

Mathematical Biosciences

#### Talks, contributed

J. Sundnes, G. T. Lines, K. Mardal and A. Tveito

On Numerical Techniques for the Bidomain Model

Presented at the SIAM Annual meeting, San Diego, California

B. F. Nielsen, O. Skavhaug and A. Tveito

Numerical Solution of American Option Problems Using Penalty Methods

Presented at the SIAM Annual Meeting in San Diego, USA

#### Proceedings, refereed

L. Ingebrigtsen, A. Bounaim, H. P. Langtangen and A. Tveito

Moving Mesh Techniques for Fluid Flow Simulations

Proceedings from the First SIAM-EMS Conference on Applied Mathematics in our Changing World

#### Technical reports

G. T. Lines, X. Cai and A. Tveito

A Parallel Solution of the Bidomain Equations Modeling the Electrical Activity of the Heart

### 2000

#### Book Chapters

H. P. Langtangen and A. Tveito

How Should We Prepare the Students of Science and Technology for a Life in the Computer Age?

Mathematics Unlimited - 2001 and Beyond

#### Journal Articles

H. J. Schroll and A. Tveito

Local Existence and Stability for a Hyperbolic-Elliptic System Moeling Two-Phase Reservoir Flow

Electronical Journal of Partial Differential Equations

#### Talks, contributed

B. F. Nielsen, O. Skavhaug and A. Tveito

Penalty Methods for the Numerical Solution of American Option Problems

Presented at the Department of Mathematics, University of Oslo, Norway

J. Sundnes, G. T. Lines and A. Tveito

Efficient Solution of ODEs Modeling Electrical Activity in Cardiac Cells

DIFTA seminar, Norwegian University of Science and Technology

#### Proceedings, refereed

Å. Ødegård, P. D. Fox, S. Holm and A. Tveito

Finite Element Modeling of Pulsed Bessel Beams and X-Waves Using Diffpack

Proceedings of 25th International Acoustical Imaging Symposium

Å. Ødegård, P. D. Fox, S. Holm and A. Tveito

Finite Element Simulation of Acoustic Fields With Diffpack

Proceeding of 23rd Scandinavian Symposium on Physical Acoustics

#### Technical reports

J. Sundnes, G. T. Lines and A. Tveito

An Investigation of Different Solvers for Stiff ODE Systems

### 1999

#### Journal Articles

W. Shen, A. Tveito and R. Winther

On the Zero Relaxation Limit for a System Modeling the Motions of a Viscoelastic Solid

Siam J. of Math. Anal.

X. Cai, B. F. Nielsen and A. Tveito

An Analysis of a Preconditioner for the Discretized Pressure Equation Arising in Reservoir Simulation

IMA Journal of Numerical Analysis

### 1998

#### Journal Articles

B. F. Nielsen and A. Tveito

An Upscaling Method for One-Phase Flow in Heterogeneous Reservoirs; a Weighted Output Least Squares (WOLS) Approach

Computational Geosciences

X. Cai, H. P. Langtangen, B. F. Nielsen and A. Tveito

A Finite Element Method for Fully Nonlinear Water Waves

J. Comput. Phys.

#### Proceedings, refereed

G. T. Lines, P. Grøttum and A. Tveito

A Coupled Torso and Myocardium Simulator Using the Luo-Rudy Cell Model - Implementation and Results

Proceedings of the XXVth International Congress on Electrocardiology

W. Shen, A. Tveito and R. Winther

Rate of Convergence for the Zero Relaxation Limit

Proceedings of the seventh international conference on hyperbolic problems

#### Technical reports

X. Cai, A. M. Bruaset, H. P. Langtangen, G. T. Lines, K. Samuelsson, W. Shen, A. Tveito and G. Zumbusch

Performance Modeling of PDE Solvers

### 1997

#### Book Chapters

E. Andreassen, E. Gundersen, E. Hinrichsen and H. P. Langtangen

A Mathematical Model for the Melt Spinning of Polymer Fibers

Numerical Methods and Software Tools in Industrial Mathematics

E. Arge and M. Dæhlen

Data Reduction for Piecewise Linear Curves

Numerical methods and Software Tools in Industrial Mathematics

J. G. Bjaalie, M. Dæhlen and T. V. Stensby

Surface Modelling From Biomedical Data

Numerical Methods and Software Tools in Industrial Mathematics

A. M. Bruaset and H. P. Langtangen

Basic Tools for Linear Algebra

Numerical methods and Software Tools in Industrial Mathematics

E. Gundersen and H. P. Langtangen

Finite Element Methods for Two-Phase Flow in Heterogeneous Porous Media

Numerical Methods and Software Tools in Industrial Mathematics

E. Haug and H. P. Langtangen

The Basic Equations in Eulerian Continuum Mechanics

Numerical Methods and Software Tools in Industrial Mathematics

N. P. Fremming, Ø. Hjelle and C. Tarrou

Surface Modelling From Scattered Geological Data

Numerical Methods and Software Tools in Industrial Mathematics

E. Arge and Ø. Hjelle

Software Tools for Modelling Scattered Data

Numerical Methods and Software Tools in Industrial Mathematics

#### Edited books

M. Dæhlen and A. Tveito

Numerical Methods and Software Tools in Industrial Mathematics

#### Journal Articles

B. F. Nielsen and A. Tveito

On the Approximation of the Solution of the Pressure Equation by Changing the Domain

SIAM J. Appl. Math.

H. J. Schroll, A. Tveito and R. Winther

An L^1-Error Bound for a Finite Difference Scheme Applied to a Stiff System of Conservation Laws

SIAM J. Numer. Anal.

A. Tveito and R. Winther

On the Rate of Convergence to Equilibrium for a System of Conservation Laws Including a Relaxation Term

SIAM Journal on Mathematical Analysis

#### Talks, contributed

A. M. Bruaset, X. Cai, H. P. Langtangen, A. Tveito and G. W. Zumbusch

Design Issues and Recent Developments in Diffpack

Invited minisymposium talk at the SIAM Annual meeting, Stanford University, California, USA

A. M. Bruaset, X. Cai, H. P. Langtangen and A. Tveito

Diffpack: an Object-Oriented Software Environment for Scientific Computing

Invited minisymposium talk at the Fourth US National Congress on Computational Mechanics, San Fransisco

A. M. Bruaset, X. Cai, H. P. Langtangen and A. Tveito

Numerical Solution of PDEs on Parallel Computers Utilizing Sequential Simulators

Talk at the ISCOPE Conference 1997, California

B. F. Nielsen and A. Tveito

A Weighted Output Least Squares Approach to Upscaling of One-Phase Flow in Heterogeneous Reservoirs

Presented at Fourth SIAM Conference on Mathematical and Computational Issues in the Geosciences in New Mexico, USA

#### Proceedings, refereed

E. Arge, A. M. Bruaset and H. P. Langtangen

Object-Oriented Numerics

Numerical Methods and Software Tools in Industrial Mathematics

E. Arge, A. M. Bruaset, P. B. Calvin, J. F. Kanney and H. P. Langtangen

On the Numerical Efficiency of C++ in Scientific Computing

Numerical Methods and Software Tools in Industrial Mathematics

A. M. Bruaset

Krylov Subspace Iterations for Sparse Linear Systems

Numerical Methods and Software Tools in Industrial Mathematics

A. M. Bruaset and H. P. Langtangen

A Comprehensive Set of Tools for Solving Partial Differential Equations; Diffpack

Numerical Methods and Software Tools in Industrial Mathematics

A. M. Bruaset, X. Cai, H. P. Langtangen and A. Tveito

Numerical Solution of PDEs on Parallel Computers Utilizing Sequential Simulators

Scientific Computing in Object-Oriented Parallel Environments

### 1996

#### Journal Articles

W. Shen, A. Tveito and R. Winther

A System of Conservation Laws Including a Stiff Relaxation Term; the 2D Case

BIT

J. O. Langseth, A. Tveito and R. Winther

On the Convergence of Operator Splitting Applied to Conservation Laws With Source Terms

SIAM J. Numer. Anal.

#### Proceedings, refereed

A. M. Bruaset, B. F. Nielsen and A. Tveito

On the Stability of Solutions of the Pressure Equation With Respect to Perturbations in the Mobility Tensor

Proceedings of the Third International Congress on Industrial and Applied Mathematics

### 1995

#### Journal Articles

A. Tveito and R. Winther

The Solution of Nonstrictly Hyperbolic Systems of Conservation Laws May Be Hard to Compute

SIAM J. Sci. Comput.

E. Arge, M. Dæhlen and A. Tveito

Approximation of Scattered Data Using Smooth Grid Functions

J. Comput. Appl. Math.

H. Holden, N. H. Risebro and A. Tveito

Maximum Principles for a Class of Conservation Laws

SIAM J. Appl. Math.

#### Talks, contributed

B. F. Nielsen, X. Cai and A. Tveito

A Preconditioner for the Pressure Equation in Reservoir Simulation

Presented at Institut für Mathematik, Johannes Kepler Universität in Linz, Austria

A. M. Bruaset, B. F. Nielsen and A. Tveito

On the Stability of Solutions of the Pressure Equation With Respect to Perturbations in the Mobility Tensor

Talk at ICIAM 95, Hamburg, Germany

B. F. Nielsen, X. Cai and A. Tveito

A Preconditioner for the Pressure Equation in Reservoir Simulation

Presented at Institut für Mathematik, Johannes Kepler Universität in Linz, Austria

### 1994

#### Journal Articles

A. M. Bruaset and A. Tveito

A Numerical Study of Optimized Sparse Preconditioners

BIT

#### Talks, contributed

A. M. Bruaset and A. Tveito

On the Application of Fourier-Based Techniques for Investigating the Performance of Preconditioners

Talk at Second Hellenic Conference on Mathematics and Informatics (HERMIS'94), Athens, Greece

#### Proceedings, refereed

A. Tveito and R. Winther

A System of Conservation Laws With a Relaxation Term

Proceedings of the fifth international conference on hyperbolic problems

A. Tveito

A Computational Study of the Fluid Dynamic Limit of the Broadwell Model

HERMIS '94, Proceedings of the 2nd Hellenic-European Confernece on Mathematics and Informatics

A. M. Bruaset and A. Tveito

On the Application of Fourier-Based Techniques for Investigating the Performance of Preconditioners

Proceedings of the Second Hellenic Conference on Mathematics and Informatics (HERMIS'94)

### 1993

#### Journal Articles

A. Tveito and R. Winther

An Error Estimate for a Finite Difference Scheme Approximating a Hyperbolic System of Conservation Laws

SIAM J. Numer. Anal.

#### Technical reports

E. Arge, M. Dæhlen and A. Tveito

A Strategy for the Approximation of Large Scattered Data Sets

M. Larsen, E. Mehlum, B. Spjelkavik and A. Tveito

A Numerical Comparison of Two Methods for Solving the Waterwave System

### 1992

#### Journal Articles

N. H. Risebro and A. Tveito

A Front-Tracking Method for Conservation Laws in One Dimension

J. Comput. Phys.

E. Arge, M. Dæhlen and A. Tveito

Box-Splines; a Computational Study

J. Comput. Appl. Math.

A. M. Bruaset and A. Tveito

RILU Preconditioning; a Computational Study

J. Comput. Appl. Math.

O. Dahl, T. Johansen, A. Tveito and R. Winther

Multicomponent Chromatography in a Two-Phase Environment

SIAM J. Appl. Math.

H. P. Langtangen, A. Tveito and R. Winther

Instability of Buckley-Leverett Flow in a Heterogeneous Medium

Transport in Porous Media

#### Talks, contributed

P. G. Holm, A. Tveito and M. Dæhlen

Bruk Av Splines for Kompakt Og Griduavhengig Lagring Av Reservoardata

Misc

#### Proceedings, refereed

J. O. Langseth, N. H. Risebro and A. Tveito

A Conservative Front Tracking Scheme for 1D Hyperbolic Conservation Laws

Proceeedings of the fourth international conference on hyperbolic problems

A. Tveito, R. Winther and T. Løvereide

Hyperbolic Conservation Laws, Finite Difference Schemes and Error Estimates

Proceedings of the fourth international conference on hyperbolic problems

#### Technical reports

M. Dæhlen, T. Dokken, P. Evensen, P. G. Holm, H. P. Langtangen, A. Mo and A. Tveito

Industriell Matematikk

A. Tveito

Higher Order Godunov Methods for Spatial Dependent Flux-Functions

### 1991

#### Journal Articles

A. Tveito and R. Winther

Existence, Uniqueness and Continuous Dependence for a System of Hyberbolic Conservation Laws Modeling Polymer Flooding

Siam J. of Math. Anal.

N. H. Risebro and A. Tveito

Front-Tracking Applied to a Non-Strictly Hyperbolic System of Conservation

SIAM Journal on Scientific and Statistical Computing

#### Talks, contributed

M. Dæhlen and A. Tveito

Verktøy I Industriell Matematikk

Proc. IT i industrien

A. M. Bruaset and A. Tveito

MILU-Like Preconditioners for Elliptic Problems

Talk at the Third Seminar on Mathematical Models and Methods in Reservoir Simulation, Ustaoset, Norway

A. M. Bruaset and A. Tveito

A Simplified MILU-Like Preconditioner for Elliptic Problems

Talk at the IMACS International Symposium on Iterative Methods in Linear Algera, Brussels, Belgium

A. M. Bruaset and A. Tveito

Is MILU Optimal?

Talk at the Fifth Annual Meeting of the Nordic Society for Applied Mathematics (NORTIM)

M. Dæhlen and A. Tveito

Matematikk Kan Brukes

Ingeniørnytt, kronikk

#### Technical reports

A. M. Bruaset and A. Tveito

A Simplified MILU-Like Preconditioner for Elliptic Problems

E. Arge, M. Dæhlen and A. Tveito

Computing Smooth Box Spline Approximations to Regularly Scattered Data

M. Dæhlen, H. P. Langtangen and A. Tveito

Some Research Projects in Industrial Mathematics

### 1990

#### Journal Articles

A. Tveito and R. Winther

Convergence of a Non-Conservative Finite Difference Scheme for a System of Hyperbolic Conservation Laws

J. of Diff. and Integ. Eq.

A. Tveito

Convergence and Stability of the Lax-Friedrichs Scheme for a Nonlinear Parabolic Polymer Flooding Problem

Adv. in Appl. Math.

A. M. Bruaset, A. Tveito and R. Winther

On the Stability of Relaxed Incomplete LU Factorizations

Math. Comp.

### 1989

#### Journal Articles

T. Johansen, A. Tveito and R. Winther

A Riemann Solver for a Two-Phase Multicomponent Process

SIAM Journal on Scientific and Statistical Computing

### 1988

#### Journal Articles

H. P. Langtangen and A. Tveito

A Numerical Comparison of Conjugate Gradient-Like Methods

Communications in Applied Numerical Methods

### 1986

#### Talks, contributed

H. P. Langtangen, T. Rusten, A. Tveito and S. Ø. Wille

An Element by Element Preconditioner for Iterative Equation Solvers

Talk at the 2nd International Conference on Finite Element Methods in Water Resources, Lisboa, Portugal

#### Proceedings, refereed

H. P. Langtangen, T. Rusten, A. Tveito and S. Ø. Wille

An Element by Element Preconditioner for Iterative Equation Solvers

Proceedings of the 2nd international conference on Finite Element Methods in Water Resources, Lisboa, Portugal