Curriculum Vitae Kent-Andre
Mardal
Personal information
Date of birth: 26.11.1974
Nationality: Norwegian
Education
Dr. Scient (PhD) in Applied Mathematics, Department of Informatics, University
of Oslo, 2003.
Thesis title: Software and Numerical Methods for the Incompressible Navier-Stokes Equations . My
PhD supervisors were Hans Petter Langtangen, Aslak Tveito and Ragnar Winther.
Employment and positions
Professor, Mechanics Division, Department of Mathematics, University of Oslo,
Norway, 2015–.
Associate Professor, Mechanics Division, Department of Mathematics, University
of Oslo, Norway, 2014-2015.
Adjunct Scientist (20%), Scientific Computing, Simula Research Lavoratory, Norway, 2014–.
Project Leader of Biomedical Flows and Structures group at Center for Biomedical Computing (CBC),
Simula Research Laboratory, Oslo, Norway
Senior Scientist, Scientific Computing, Simula Research Lavoratory, Norway, 2007–
2014.
Project Leader of Biomedical Flows and Structures group at Center for Biomedical Computing (CBC),
Simula Research Laboratory, Oslo, Norway
Associate Professor, Associate Professor, (20%) , Department of Informatics, University of Oslo 2003–2014.
Postdoctoral Fellow, Simula Research Laboratory, 2003-2007.
Grants
Research Grant.
2015–2016: ‘Improved intracranial pressure estimations using cloud-based simulations of the cerebral
blood flow‘. Fortissimo, EU-7th Framework Program, 200 000 euros, Mardal is partner.
Research Grant.
2011–2015: ‘Patient-specific mathematical modeling with applications to clinical medicine: Stroke and
syringomyelia’. Mardal is the PI. Grant ES209951 of about 0.8 million euros.
Research Grant.
2011–2012: ‘Magnitude of Turbulence in CSF Flow’. The Chiari & Syringomyelia Foundation funded a
grant of $30,000. Mardal was the PI.
Post Doctoral Grant .
2003–2006: ‘Mixed methods for the stress-displacement formulation of elasticity – A software framework
for advanced finite element methods’. Mardal was PI. Norwegian Research Council Postdoctoral Grant
no. ES254277.
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
Research Grant.
2009–2010: ‘Development of new technology for improving risk assessment of intracranial aneurysms
using computer simulation models’. Norwegian Research Council Grant no. ES439440. Mardal was
partner.
Teaching and supervision
Post doctoral supervisor, Simula Research Laboratory (2013–).
1. Erika Kristine Lindstrøm (2015– )
2. Simon Funke (2013– )
3. Martin Alnæs (2011-2015)
PhD supervisor, UiO.
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Lars Magnus Valnes, ongoing, 2015–
Magne Noraas, ongoing (with Bjørn Fredrik Nielsen), 2013–
Owais Khan, ongoing (with Kristian Valen-Sendstad and David Steinman), 2013–
Kartik Jain, ongoing (with main supervisor Sabine Roller), 2013–
Miroslav Kuchta, ongoing (with main supervisor Mikael Mortensen), 2013–
Øvind Evju, ongoing (with Kristian Valen-Sendstad, Martin Alnæs, Angelika Sorteberg), 2012–
Ole Elvetun - PDE-constrained optimization: Preconditioners and diffuse domain methods (with
main supervisor Bjørn Fredrik Nielsen), 2015
Karen Helene Støverud - Relation between the Chiari I malformation and syringomyelia from
a mechanical perspective, 2014 (with Hans Petter Langtangen, Mikael Mortensen, and Victor
Haughton)
Sigrid Dahl - Numerical simulations of blood flow in the left side of the heart, 2012 (with Bjørn
Skallerud, Leif Rune Hellevik, and Jan Vierendeels)
Kristian Valen-Sendstad - Computational Cerebral Hemodynamics, 2011 (with Anders Logg, Hans
Petter Langtangen and Bjørn A. Reif)
Martin Sandve Alnæs - A Compiler Framework for Automatic Linearization and Efficient Discretization of Nonlinear Partial Differential Equations, 2009 (with Joakim Sundnes)
Gunnar Andreas Staff - Numerical Computation of Initial Value Problems originated from Partial
Differential Equations, 2006 (with Hans Petter Langtangen)
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
MSc thesis supervisor, Department of Mathematics/Informatics, UiO (2011–).
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Vegard Vinje, ongoing
Imran Ali, ongoing
Jakob Schreiner, ongoing
Shifteh Sherafat, ongoing
Kristian Brox, ongoing
Per Thomas Haga, Numerical simulations of advection-dominated scalar mixing with applications to
spinal CSF flow and drug transport (with main supervisor Mikael Mortensen and Giulia Pizzichelli),
2015.
Ada Johanna Ellingsrud, Preconditioning unified mixed discretizations of coupled Darcy-Stokes flow
(with Marie Rognes), 2015.
Torbjørn Seland, Mathematical analysis of epidemic systems comparison of different models (with
Hans Petter Langtangen), 2014.
Tom Nærland Geometry decomposition algorithms for the Nitsche method on unfitted geometries
(with main supervisor Andre Massing), 2014.
Timo Koch Coupling a vascular graph model and the surrounding tissue to simulate flow processes
in vascular networks (with Natalie Schroder and Rainer Helmig, Stuttgart, Andre Massing, Simula),
2014.
Ingebort Sauge Torpe An in-depth study of one-shot optimization with applications to magnetic
resonance elastography, 2014 (with main supervisor Marie Rognes).
Nina Kristine Kylstad, Simulating the Viscoelastic Response of the Spinal Cord, 2014 (with main
supervisor Marie Rognes).
Jarle Sogn, Stabilized Finite Element Methods for the Brinkman Equation on Fitted and Fictitious
Domains (with Andre Massing), 2014.
Håkon Østerbø, The Effects of Heart Rate on Blood Flow in Intracranial Aneurysms (with Martin
Sandve Alnæs and Øvind Evju), 2013.
Mikkel Sanderud, Patient-Specific Modeling of Normal Pressure Hydrocephalus (with Karen Støverud
and Per Kristian Eide), 2012.
Adrian Hope, Analysis of a system of elliptic partial differential equations and its possible boundary
conditions when discretized with Hermite and Lagrange elements , 2012.
Sebastian Warmbrunn, Inspecting endovascular aneurysm treatments with porous medium flow
simulations and the use of a statistical framework, (with Katerina Baber and Rainer Helmig,
Stuttgart) 2012.
Ida Norderhaug Drøsdal - Porous and Viscous Modeling of Cerebrospinal Fluid Flow in the Spinal
Canal Associated with Syringomyelia, 2012.
Øvind Evju - Sensitivity analysis of simulated blood flow in cerebral aneurysms, 2011 (with Kristian
Valen-Sendstad).
Gabriela Rutkowska - Computational Fluid Dynamics in Patient-Specific Models with Normal and
Chiari I Geometries, 2011.
Arne Jørgen Arnesen - Comparison of Finite Element Methods for the Navier-Stokes Equations,
2010.
Anna Blechingberg - On the Shaking Baby Syndrome, 2010 (with Arne Stray Pedersen and Joachim
Sundnes).
Susanne Hentschel - Modelling and Simulation of Blood Pressure in Rats, 2008 (with Hans Petter
Langtangen).
Robert Bauck Hamar - Kompilering av mindre Python moduler til C++, 2007.
Trygve Klovning Karper - Mixed finite element methods for coupled Darcy-Stokes flow, 2006 (with
Ragnar Winther).
Martin Sandve Alnæs - Finite element simulations of blood flow in the circle of Wills, 2006.
Didrik Lilja - On testing the optimum principles of Murray’s law, 2006 (with Hans Petter Langtangen).
Richard Magnor Stenbro - Python - Realizer, 2005
Erica Madeleine Linger - Solving the Unsteady Stokes Equations with the Parareal Algorithm, 2005
(with Gunnar Staff)
Nguyen Bao Anh - Visualisering av sammenhengen mellom krefter på et skrog og skrogets bevegelser
i sjø, 2005
Asbjørn Reglund Thorsen - Ruby-grensesnitt til Diffpack og analyse av kompilator-opsjoner ved
bruk av modifisert ACOVEA, 2005 (with Hans Petter Langtangen)
Master Westlie - Utvikling av et Python grensesnitt til Diffpacks C++ biblioteker, 2004.
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
BSc thesis supervisor, Department of Mathematics/Informatics, UiO (2011–).
1. Jan Helmig - A Numerical Investigation of the Stability of Different Schemes for a Simplified
Fluid-Structure Interaction Scheme with Application to Physiological Problems , (with Marek Behr
and Lutz Pauli, Aachen), 2013.
Lecturing at Department of Mathematics/Informatics, UiO (2002–).
{ "Mek3220 - Continuum Mechanics, H14, H15
{ "Mek4250 - Finite Element Methods in Compuational Mechanics, V15
{ "INF5660 - Advanced problem solving with high level languages", V04, V05, V06, V07 (with
Langtangen and Skavhaug)
{ "INF5600 - Iterative methods and multigrid", V02, V03, V04, V05, V07, and V10 (developed by me).
{ "INF5670 - Numerical methods for the Navier-Stokes equations", H04, H06, H07, and H09 (developed
by me)
{ "MAT-INF3360 - Introduction to Partial Differential Equations", V12 and V13
{ "INF5650 - Numerical methods for partial differential equations 2", V13 (with Logg) and V14 (alone)
Software Contributions
{ Dolfin, a problem solving environment for ordinary and partial differential equations, see
www.fenicsproject.org
{ Instant, a Python module for inlining of C/C++ code in Python, see www.fenicsproject.org
{ SyFi, a package for defining and using finite element methods, see www.fenicsproject.org
{ UFC, a unified form assembly code format, see www.fenicsproject.org
{ Finite Element Exterior Calculus, see www.fenicsproject.org
{ CBC.block: Block operators and algebra for DOLFIN, www.fenicsproject.org
{ Diffpack
Publications
Articles in International Journals
[1] K. Støverud, H. P. Langtangen, G. A. Ringstad, P. K. Eide and K.-A. Mardal.
Computational investigation of cerebrospinal fluid dynamics in the fourth ventricle and cranialcervical subarachnoid space in patients with Chiari I malformation. Submitted to PLOS ONE,
2015.
[2] K. Jain, S. Roller and K.-A. Mardal. Transitional flow in intracranial aneurysms – a
space and time refinement study below the Kolmogorov scales using Lattice Boltzmann Method.
Submitted to Computers and Fluids, 2015.
[3] Lee, J. J., K.-A. Mardal and a. R. Winther.. Parameter-robust discretization and
preconditioning of Biot’s consolidation model. Submitted to SISC, preprint arXiv:1507.03199,
2015.
[4] Mardal, Kent-André, B. F. Nielsen and M. Nordaas.. Robust preconditioners
for PDE-constrained optimization with limited observations. Submitted to BIT, preprint
arXiv:1506.06494, 2015.
[5] M. S. Alnæs, K.-A. Mardal, S. Bakke and A. Sorteberg. Computational fluid
dynamics evaluation of flow reversal treatment of giant basilar tip aneurysm. Interventional
Neuroradiology, 2015.
[6] Støverud, K. H. a. Alnæs, M. a. Langtangen, H. P. a. Haughton, V. a. Mardal
and K-A. Poro-elastic modeling of Syringomyelia–a systematic study of the effects of pia mater,
central canal, median fissure, white and gray matter on pressure wave propagation and fluid
movement within the cervical spinal cord. Computer Methods in Biomechanics and Biomedical
Engineering, 2015.
[7] V. Haughton and K.-A. Mardal. Spinal Fluid Biomechanics and Imaging: an Update for
Neuroradiologists. American Journal of Neuroradiology, vol. (appeared online), 2014.
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
[8] D. S. Seljebotn, K.-A. Mardal, J. Jewell, H. K. Eriksen and P. Bull. A Multilevel
Solver for Gaussian Constrained CMB Realizations. The Astrophysical Journal Supplement
Series, vol. 210(2), 2014.
[9] A. Helgeland, K.-A. Mardal, V. Haughton and B. A. P. Reif. Numerical Simulations
of the Pulsating Flow of Cerebrospinal Fluid Flow in the Cervical Spinal Canal of a Chiari
Patient. Journal of Biomechanics, vol. 21(47(5)), pp. 1082-90, 2014.
[10] S. Linge, K.-A. Mardal, A. Helgeland, J. Heiss and V. Haughton. Effect of CranioVertebral Decompression on CSF Dynamics in Chiari I Malformation Studied With Computational Fluid Dynamics. Journal of Neurosurgery, vol. (appeared online), 2014.
[11] I. N. Drøsdal, K.-A. Mardal, K.-H. Støverud and V. Haughton. Effect of the Central
Canal in the Spinal Cord on Fluid Movement Within the Cord. The Neuroradiology Journal,
vol. 26(5), pp. 585-590, 2013.
[12] K.-A. Mardal, J. Schoberl and R. Winther. A Uniformly Stable Fortin Operator for
the Taylor–Hood Element. Numerische Mathematik, vol. 123(3), pp. 537-551, 2013.
[13] Ø. Evju, K. Valen-Sendstad and K.-A. Mardal. A Study of Wall Shear Stress in 12
Aneurysms With Respect to Different Viscosity Models and Flow Conditions. Journal of
Biomechanics, vol. 46(16), pp. 2802-2808, 2013.
[14] K. Valen-Sendstad, K.-A. Mardal and D. A. Steinman. High-Resolution Computational
Fluid Dynamics Detects High-Frequency Velocity Fluctuations in Bifurcation, But Not Sidewall,
Aneurysms of the Middle Cerebral Artery. Journal of Biomechanics, vol. 18(46(2)), pp. 402-407,
2013.
[15] K.-A. Mardal, G. Rutkowska, S. Linge and V. Haughton. Estimation of CSF Flow
Resistance in the Upper Cervical Spine. The Neuroradiology Journal, vol. 3(2), pp. 49-53,
2013.
[16] K.-H. Støverud, H. P. Langtangen, V. Haughton and K.-A. Mardal. CSF Pressure
and Velocity in Obstructions of the Subarachnoid Spaces. The Neuroradiology Journal, vol.
26(2), 2013.
[17] S. Linge, K.-A. Mardal, V. Haughton and A. Helgeland. Simulating CSF Flow
Dynamics in the Normal and the Chiari I Subarachnoid Space During Rest and Exertion.
American Journal of Neuroradiology, vol. 34(1), 2013.
[18] B. F. Nielsen and K.-A. Mardal. Analysis of the Minimal Residual Method Applied to
Ill-Posed Optimality Systems. SIAM Journal on Scientific Computing, vol. 35(2), 2013.
[19] G. Rutkowska, V. Haughton, S. Linge and K.-A. Mardal. Patient-Specific 3D Simulation of Cyclic CSF Flow at the Cranio-Cervical Region. American Journal of Neuroradiology,
vol. 33(9), pp. 1756-1762, 2012.
[20] K.-A. Mardal and R. Winther. Preconditioning Discretizations of Systems of Partial
Differential Equations. Numerical Linear Algebra with Applications, vol. 18(1), pp. 1-40, 2011.
[21] J. Jiang, K. Johnson, K. Valen-Sendstad, K.-A. Mardal, O. Wieben and C.
Strother. Flow Characteristics in a Canine Aneurysm Model: a Comparison of 4-D Accelerated Phase-Contrast MR Measurements and Computational Fluid Dynamics Simulations.
Medical Physics, vol. 38(11), pp. 6300-6313, 2011.
[22] K.-H. Støverud, K.-A. Mardal, V. Haughton and H. P. Langtangen. CSF Flow
in Chiari I and Syringomyelia From the Perspective of Computational Fluid Dynamics. The
Neuroradiology Journal, vol. 24(1), pp. 20-23, 2011.
[23] T. K. Nilssen, G. A. Staff and K.-A. Mardal. Order Optimal Preconditioners for Fully
Implicit Runge-Kutta Schemes Applied to the Bidomain Equations. Numer. Methods Partial
Differential Equations, vol. 27(5), pp. 1290-1312, 2011.
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
[24] S. Linge, V. Haughton, A. E. Løvgren, K.-A. Mardal, A. Helgeland and H. P.
Langtangen. Effect of Tonsilar Herniation on Cyclic CSF Flow Studied With Computational
Flow Analysis. American Journal of Neuroradiology, vol. 32(5), pp. 1474-1481, 2011.
[25] K. Valen-Sendstad, K.-A. Mardal, M. Mortensen, B. A. P. Reif and H. P. Langtangen. Direct Numerical Simulation of Transitional Flow in a Patient–Specific Intracranial
Aneurysm. Journal of Biomechanics, vol. 44(16), pp. 2826-2832, 2011.
[26] T. K. Nilssen, G. A. Staff and K.-A. Mardal. Order Optimal Preconditioners for Fully
Implicit Runge-Kutta Schemes Applied to the Bidomain Equations. Numerical Methods for
Partial Differential Equations, vol. 27(5), pp. 1290-1312, 2011.
[27] S. Hentschel, K.-A. Mardal, A. E. Løvgren, S. Linge and V. Haughton. Characterization of Cyclical CSF Flow in the Foramen Magnum and Upper Cervical Spinal Canal With
MR Flow Imaging and Computational Fluid Dynamics. American Journal of Neuroradiology,
vol. 31(6), pp. 997-1002, 2010.
[28] M. S. Alnæs and K.-A. Mardal. On the Efficiency of Symbolic Computations Combined
With Code Generation for Finite Element Methods. ACM Transactions on Mathematical
Software, vol. 37(1), 2010.
[29] M. Burger, K.-A. Mardal and B. F. Nielsen. Stability Analysis of the Inverse Transmembrane Potential Problem in Electrocardiography. Inverse Problems, vol. 26(10), 2010.
[30] B. F. Nielsen and K.-A. Mardal. Efficient Preconditioners for Optimality Systems Arising
in Connection With Inverse Problems. SIAM Journal on Control and Optimization, vol. 48(8),
2010.
[31] H. Lindekleiv, K. Valen-Sendstad, M. K. Morgan, K.-A. Mardal, K. Faulder, J.
Magnus, K. Waterloo, B. Romner and T. Ingebrigtsen. Sex Differences in Intracranial
Arterial Bifurcations. Gender Medicine, vol. 7(2), 2010.
[32] M. S. Alnæs, A. Logg, K.-A. Mardal, O. Skavhaug and H. P. Langtangen. Unified
Framework for Finite Element Assembly. International Journal of Computational Science and
Engineering, vol. 4(4), pp. 231-244, 2009.
[33] S. Linge, V. Haughton, A. E. Løvgren, K.-A. Mardal and H. P. Langtangen. CSF
Flow Dynamics at the Cranio-Vertebral Junction Studied With an Idealized Model of the
Subarachnoid Space and Computational Flow Analysis. American Journal of Neuroradiology,
vol. 31(1), pp. 185-192, 2009.
[34] T. Karper, K.-A. Mardal and R. Winther. Unified Finite Element Discretizations of
Coupled Darcy-Stokes Flow. Numer. Methods Partial Differential Equations, vol. 25(2), pp.
311-326, 2008.
[35] K.-A. Mardal, B. F. Nielsen, X. Cai and A. Tveito. An Order Optimal Solver for the
Discretized Bidomain Equations. Numerical Linear Algebra with Applications, vol. 14(2), pp.
83–98, 2007.
[36] M. S. Alnæs, J. G. Isaksen, K.-A. Mardal, B. Romner, M. Morgan and T. Ingebrigtsen. Computation of Hemodynamics in the Circle of Willis. Stroke, vol. 38(9), pp.
2500–2505, 2007.
[37] K.-A. Mardal, T. K. Nilssen and G. A. Staff. Order Optimal Preconditioners for Implicit
Runge-Kutta Schemes Applied to Parabolic PDE’s. SIAM Journal on Scientific Computing,
vol. 29(1), pp. 361-375, 2007.
[38] K.-A. Mardal, O. Skavhaug, G. T. Lines, G. A. Staff and Å. Ødegård. Using Python
to Solve Partial Differential Equations. Computing in Science & Engineering, vol. 9(3), pp.
48-51, 2007.
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
[39] K.-A. Mardal and R. Winther. An Observation on Korn’s Inequality for Nonconforming
Finite Element Methods. Math. Comp., vol. 75(253), pp. 1-6, 2006.
[40] K.-A. Mardal and T. K. Nilssen. Reuse of Standard Preconditioners for Higher-Order
Time Discretizations of Parabolic PDEs. Journal of Numerical Mathematics, vol. 14(2), pp.
103-122, 2006.
[41] G. A. Staff, K.-A. Mardal and T. K. Nilssen. Preconditioning of Fully Implicit RungeKutta Schemes for Parabolic PDEs. Modeling, Identification and Control, vol. 27(2), pp.
109-123, 2006.
[42] J. Sundnes, B. F. Nielsen, K.-A. 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, vol. 34(7), pp. 1088-1097, 2006.
[43] K. -A. Mardal and R. Winther. Uniform Preconditioners for the Time Dependent Stokes
Problem. Numerische Mathematik, vol. 98(2), pp. 305–327, 2004.
[44] H. P. Langtangen, K. -A. Mardal and R. Winther. Numerical Methods for Incompressible Viscous Flow. Advances in Water Resources, vol. 25(8), pp. 1125-1146, 2002.
[45] K. -A. Mardal, X. -C. Tai and R. Winther. A Robust Finite Element Method for
Darcy-Stokes Flow. SIAM Journal on Numerical Analysis, vol. 40, pp. 1605-1631, 2002.
[46] J. Sundnes, G. Lines, K. -A. 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, vol. 5(6), 2002.
Books
[1] J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, K.-A. Mardal and A. Tveito.
Computing the Electrical Activity in the Heart, Springer, 2006.
Edited Books
[1] A. Logg, K.-A. Mardal and A. Massing. Proceedings of the 26th Nordic Seminar on
Computational Mechanics, Published Electronically (http://www.nscm26.org), 2013.
[2] A. Logg, K.-A. Mardal and G. N. Wells. Automated Solution of Differential Equations
by the Finite Element Method, Springer, 2012.
Chapters in Books
[1] W. J. Bradley, V. Haughton and K.-A. Mardal. Cerebrospinal fluid circulation disorders.
Accepted for publication in Handbook of Clinical Neurology, edited by missing, missing, 2015.
[2] Ø. Evju and K.-A. Mardal. On the Assumption of Laminar Flow in Physiological Flows:
Cerebral Aneurysms As an Illustrative Example. Accepted for publication in The Cardiocirculatory System: from Modeling to Clinical Applications, edited by A. Quarteroni, Springer,
2014.
[3] H. P. Langtangen, K.-A. Mardal and P. Røtnes. Escaping the Zombie Threat by
Mathematics. In Zombies in the Academy: living death in higher education, edited by C. M. A.
Whelan and R. Walker, University of Chicago Press, 2013.
[4] R. C. Kirby and K.-A. Mardal. Constructing General Reference Finite Elements. In
Automated Solution of Differential Equations by the Finite Element Method, edited by A. Logg,
K.-A. Mardal and G. N. Wells, Springer, 2012.
[5] I. Wilbers, K.-A. Mardal and M. S. Alnæs. Instant: Just-in-Time Compilation of C/C++
in Python. In Automated Solution of Differential Equations by the Finite Element Method,
edited by A. Logg, K.-A. Mardal and G. N. Wells, Springer, 2012.
[6] M. S. Alnæs, A. Logg and K.-A. Mardal. UFC: a Finite Element Code Generation
Interface. In Automated Solution of Differential Equations by the Finite Element Method, edited
by A. Logg, K.-A. Mardal and G. N. Wells, Springer, 2012.
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
[7] S. Støle-Hentschel, S. Linge, A. E. Løvgren and K.-A. Mardal. Cerebrospinal Fluid
Flow. In Automated Solution of Differential Equations by the Finite Element Method, edited by
A. Logg, K.-A. Mardal and G. N. Wells, Springer, 2012.
[8] J. E. Hake and K.-A. Mardal. Lessons Learned in Mixed Language Programming. In
Automated Solution of Differential Equations by the Finite Element Method, edited by A. Logg,
K.-A. Mardal and G. N. Wells, Springer, 2012.
[9] A. Logg, K.-A. Mardal and G. N. Wells. Finite Element Assembly. In Automated
Solution of Differential Equations by the Finite Element Method, edited by A. Logg, K.-A.
Mardal and G. N. Wells, Springer, 2012.
[10] M. S. Alnæs and K.-A. Mardal. SyFi and SFC: Symbolic Finite Elements and Form
Compilation. In Automated Solution of Differential Equations by the Finite Element Method,
edited by A. Logg, K.-A. Mardal and G. N. Wells, Springer, 2012.
[11] M. Mortensen, K.-A. Mardal and H. P. Langtangen. Simulation of Transitional Flows.
In Automated Solution of Differential Equations by the Finite Element Method, edited by A.
Logg, K.-A. Mardal and G. N. Wells, Springer, 2012.
[12] K. Valen-Sendstad, A. Logg, K.-A. Mardal, H. Narayanan and M. Mortensen. A
Comparison of Some Common Finite Element Schemes for the Incompressible Navier-Stokes
Equations. In Automated Solution of Differential Equations by the Finite Element Method,
edited by A. Logg, K.-A. Mardal and G. N. Wells, Springer, 2012.
[13] K. Valen-Sendstad, K.-A. Mardal and A. Logg. Computational Hemodynamics. In
Automated Solution of Differential Equations by the Finite Element Method, edited by A. Logg,
K.-A. Mardal and G. N. Wells, Springer, 2012.
[14] K.-A. Mardal and J. B. Haga. Block Preconditioning of Systems of PDEs. In Automated
Solution of Differential Equations by the Finite Element Method, edited by A. Logg, K.-A.
Mardal and G. N. Wells, Springer, 2012.
[15] K.-A. Mardal and R. Winther. Construction of Preconditioners by Mapping Properties for
Systems of Partial Differential Equations. In Efficient preconditioning methods for elliptic partial
differential equations, edited by O. Axelsson and J. Karatson, Bentham Science Publishers,
2011.
[16] B. F. Nielsen, O. M. Lysaker, P. Grøttum, K.-A. Mardal, A. Tveito, C. Tarrou,
K. Haugaa, A. Abildgaard and J. G. Fjeld. Can ECG Recordings and Mathematics Tell
the Condition of Your Heart?. In Simula Research Laboratory - by thinking constantly about it,
edited by T. Tveito, A. M. Bruaset and O. Lysne, Springer, 2009.
[17] A. Logg, K.-A. Mardal, M. S. Alnæs, H. P. Langtangen and O. Skavhaug. A Hybrid
Approach to Efficient Finite Element Code Development. In Petascale Computing – Algorithms
and Applications, edited by D. A. Bader, Chapman and Hall, 2007.
[18] H. P. Langtangen and K. -A. Mardal. Using Diffpack From Python Scripts. In Advanced
Topics in Computational Partial, edited by H. Langtangen and A. Tveito, Springer, 2003.
[19] K. -A. Mardal, G. Zumbusch and H. P. Langtangen. Multigrid Methods in Diffpack. In
Advanced Topics in Computational Partial, edited by H. Langtangen and A. Tveito, Springer,
2003.
[20] K. -A. Mardal, J. Sundnes, H. P. Langtangen and A. Tveito. Block Preconditioning
and Systems of PDEs. In Advanced Topics in Computational Partial, edited by H. Langtangen
and A. Tveito, Springer, 2003.
[21] K. -A. Mardal and H. P. Langtangen. Mixed Elements in Diffpack. In Advanced Topics
in Computational Partial, edited by H. Langtangen and A. Tveito, Springer, 2003.
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
Conference Proceedings
[1] M. Mortensen, K.-A. Mardal, B. Martin and S. Pahlavian. Preliminary Study of
the Impact of Spinal Cord Nerve Roots and Denticulate Ligaments on Drug Movement in the
Cervical Spinal Subarachnoid Space. In The Nordic Seminar on Computational Mechanics,
2013
[2] K.-H. Støverud, K.-A. Mardal and H. P. Langtangen. Effect of Oscillatory Cerebrospinal Fluid Pressure on Fluid Movement in the Spinal Cord. In Seven’th National Conference
on Computational Mechanics (MekIT’13), 2013
[3] K. Valen-Sendstad, K.-A. Mardal, M. Mortensen, B. A. P. Reif and H. P. Langtangen. On the Complexity of Stationary Flow in Patient–Specific Aneurysms. In MekIT’11
Sixth national conference on Computational Mechanics, 2011
[4] K. Valen-Sendstad, K.-A. Mardal, M. Mortensen, B. A. P. Reif and H. P. Langtangen. Direct Numerical Simulation of Transitional Flow in a Patient-Specific MCA Aneurysm.
In Proceedings of the ASME 2011 Summer Bioengineering Conference, 2011
[5] K. Valen-Sendstad, M. Mortensen, K.-A. Mardal, B. A. P. Reif and H. P. Langtangen. Investigations of Transistional Flows Using Image Based Hemodynamics. In 8th
International Conference on CFD in Oil & Gas, Metallurgical and Process Industries, 2011
[6] I. N. Drøsdal, V. Haughton, K.-A. Mardal and K.-H. Støverud. Porous and
Viscous Flow Modeling on the Study of Cyst Development in the Human Spinal Cord. In 8th
International Conference on CFD in Oil & Gas, Metallurgical and Process Industries, 2011
[7] K.-H. Støverud, K.-A. Mardal, H. P. Langtangen and V. Haughton. The Effect of
Varying Cross-Sectional Areas on Cerebrospinal Fluid Flow and Pressure in the Cervical Spine.
In MekIT’11, 2011
[8] S. Linge, V. Haughton, A. E. Løvgren, K.-A. Mardal, A. Helgeland, H. P. Langtangen and K.-H. Støverud. Cyclic Cerebrospinal Fluid Flow (I): Towards the Understanding
of Cerebrospinal Fluid Flow Dynamics in Chiari I Malformation. In ASNR 49th Annual Meeting
& the Foundation of the ASNR Symposium, June 4 - 9, 2011., 2011
[9] S. Linge, K.-A. Mardal, V. Haughton and A. Helgeland. Cerebrospinal Fluid Flow
Characteristics at Double Heart Rate. In Neuroradiology, 53 (Suppl. 1), S33, 35th European
Soc of Neuroradiology ann. meeting, Antwerpen, Belgium, 2011
[10] K.-H. Støverud, K.-A. Mardal, V. Haughton and H. P. Langtangen. CSF Flow in
Chiari I and Syringomyelia - From the Perspective of Fluid Dynamics. In Proceedings of the
XIX Symposium Neuroradiologicum, Bologna, Italy, 2010
[11] J. Jiang, K. Johnson, K. Valen-Sendstad, K.-A. Mardal, D. Consigny, O. Wieben
and C. Strother. Comparison of Aneurismal Hemodynamics Between 4D Accelerated PhaseContrast MR Angiography and Computational Fluid Dynamics Simulations: Initial Experience
in a Canine Aneurysm Model. In Proceedings of the ASME 2010 Summer Bioengineering
Conference, 2010
[12] K. Valen-Sendstad, M. Mortensen, H. P. Langtangen, B. A. P. Reif and K.-A.
Mardal. Implementing a K-E Turbulence Model in the FEniCS Finite Element Programming
Environment. In MekIT’09, 2009
[13] S. Linge, A. E. Løvgren, K.-A. Mardal, V. Haughton and H. P. Langtangen. Effect
of Tonsilar Position on Cerebrospinal Fluid Flow in the Spinal Subarachnoid Space Studied
With Computational Fluid Dynamics. In Proceedings of the ASNR 47th annual meeting, May
16-21, Vancouver, BC, Canada, 2009
[14] A. E. Løvgren, S. Linge, K.-A. Mardal, V. Haughton and H. P. Langtangen. CFD
Analysis of Cerebrospinal Fluid Flow in the Cranio-Cervical Region. In 21st Nordic Seminar
on Computational Mechanics, 2008
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
[15] O. C. Myklebust, S. Hentschel and K.-A. Mardal. Patient-Specific Computational
Fluid Dynamic Simulations in the Circle of Willis. In 21st Nordic Seminar on Computational
Mechanics, 2008
[16] M. S. Alnæs, K.-A. Mardal and J. Sundnes. Application of Symbolic Finite Element
Tools to Nonlinear Hyperelasticity. In Fourth national conference on Computational Mechanics
(MekIT’07), 2007
[17] B. F. Nielsen, O. M. Lysaker, C. Tarrou, J. Sundnes, X. Cai and K.-A. Mardal. On
the Use of the Bidomain Equations for Computing the Transmembrane Potential Throughout
the Heart Wall: an Inverse Problem. In Computers in Cardiology 2006, 2006
[18] K.-A. Mardal. SyFi - an Element Matrix Factory, With Emphasis on the Incompressible
Navier-Stokes Equations. In Para’06, 2006
[19] C. Tarrou, O. M. Lysaker, X. Cai, K.-A. Mardal, C. Tarrou, T. S. Ruud, M.
MacLachlan and A. Tveito. Identifying Ischemic Heart Disease in Terms of ECG Recordings
and an Inverse Problem for the Bidomain Equations; Modeling and Experiments. In The Third
International Conference "Inverse Problems: Modeling and Simulation", 2006
[20] G. A. Staff, K.-A. Mardal and T. K. Nilssen. Block Preconditioners for Fully Implicit
Runge-Kutta Schemes Applied to the Bidomain Equations. In ECCOMAS CFD 06, 2006
[21] G. A. Staff, K.-A. Mardal and T. K. Nilssen. Preconditioning of Fully Implicit RungeKutta Schemes for Parabolic PDEs. In SIMS05. 46th Conference on Simulation and Modeling,
Trondheim, October 13-14, 2005
[22] G. A. Staff and K.-A. Mardal. The Accuracy of the Velocity Approximation With Respect
to the Pressure Approximation for Incompressible Fluid Flow. In Third National Conference
on Computational Mechanics (MekIT 05), 2005
[23] G. A. Staff, K.-A. Mardal and T. K. Nilssen. Preconditioning of Fully Implicit RungeKutta Schemes for Parabolic PDEs. In SIMS05. 46th Conference on Simulation and Modeling,
Trondheim, October 13-14, 2005
[24] A. Kristoffersen and K. -A. Mardal. Solving Heat Distribution in Room Using Mixed
Finite Element for Coupling the Navier-Stokes Equations and the Heat Equation. In Proceedings
of the Second National Conference on Computational Mechanics (MekIT’03), 2003
[25] K. -A. Mardal, H. P. Langtangen and R. Winter. Error Estimates for the Linear
Navier-Stokes Equations. In Proceedings of the Second National Conference on Computational
Mechanics (MekIT’03), 2003
[26] H. P. Langtangen and K. -A. Mardal. A Software Framework for Mixed Finite Element
Programming. In Proceedings of the 2nd International Conference, 2002
[27] K. -A. Mardal and H. P. Langtangen. An Efficient Parallel Iterative Approach to a Fully
Implicit Mixed Finite Element Formulation for the Navier-Stokes Equations. In ECCOMAS
CFD 2001, Computational Fluid Dynamics, 2001
[28] K. -A. Mardal, H. P. Langtangen and R. Winter. An Optimal Iterative Method for
the Time-Dependent Stokes Problem. In Tenth Conference Virtual Proceedings, Copper, 2001
[29] K.-A. Mardal and H. P. Langtangen. An Effective Iterative Approach to a Fully Implicit
Mixed Finite Element Formulation for the Navier-Stokes Equations. In 13th Nordic Seminar
on Computational Mechanics (NSCM-13), 2000
Technical Reports
[1] O. Skavhaug, K.-A. Mardal and H. P. Langtangen. A Python Framework for Verifying
Codes for Numerical Solutions of Partial Differential Equations, Simula Research Laboratory,
2005
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
[2] P. Böhm, A. M. Bruaset, H. P. P. Langtangen, K.-A. Mardal and G. Wachutka.
Diffpack Implementation of Edge-Based Non-Standard Finite Element Methods, Simula Research Laboratory, 2004
[3] K. -A. Mardal, E. Acklam and D. Calhoun. How to Use MATLAB in C++ Programs,
Simula Research Laboratory, 2002
Manuals
[1] K.-A. Mardal and H. P. Langtangen. Combining FEniCS With Your Favorite Software
in C, C++, Fortran, Or MATLAB, 2013
[2] M. S. Alnæs, A. Logg, K.-A. Mardal, O. Skavhaug and H. P. Langtangen. UFC
Specification and User Manual 1.0, 2007
[3] M. S. Alnæs and K.-A. Mardal. SyFi User Manual, 2006
Theses
[1] K. -A. Mardal. Software and Numerical Methods for the Incompressible Navier-Stokes
Equations, Ph.D. Thesis, Faculty of Mathematics and Natural Sciences, University of Oslo,
2003.
Preprints
[1] K.-A. Mardal, J. Schöberl and R. Winther. A Uniform Inf-Sup Condition With
Applications to Preconditioning, 2012
Other Publications
[1] Kylstad, Nina, K.-A. Mardal, V. Haughton and a. M. E. Rognes., Effect of Spinal
Cord Viscoelasticity on Its Response to CSF Pressure Waves: a Computational Study., 2015.,
Talk at ASNR, 2015.
[2] V. Haughton and K.-A. Mardal, Role of CSF flow in the pathogenesis of Syringomyelia,
Plenary Talk at ASNR, Chicago, 2015.
[3] K.-A. Mardal, Poroelastic modeling of Syringomyelia - the effects of pia mater, central
canal, median fissure, white and grey matter on pressure wave propagation and fluid movement
within the cervical spinal, Invited Talk at International Hydrocephalus Imaging Working Group,
Chicago, 2015.
[4] K.-A. Mardal, K. Jain, K. H. Støverud, G. Ringstad and P. K. Eide, On the
complexity of the Cerebrospinal fluid flow in the upper spinal column – is the assumption of
laminar flow appropriate?, Invited Talk at Cerebrospinal Fluid Dynamics Society Meeting,
Amiens, 2015.
[5] K.-A. Mardal, Computational modelling of the biomechanics in the central nervous system
– Chiari and syringomyelia, Invited Talk at Complex materials; Mathematical models and
numerical methods, Oslo, 2015.
[6] K.-A. Mardal, Computational modelling of the biomechanics in the central nervous system –
Chiari and syringomyelia, Invited Talk at Simpla meeting, Oslo, 2015.
[7] K.-A. Mardal, Flows in complex geometries such as blood vessels and the central nervous
system, Invited Talk at EarthFlows kick-off meeting, Oslo, 2015.
[8] K.-A. Mardal, On the Modeling of the Central Nervous System in Chiari Patients - Transitional Flow, Poroelasticity and Porous-Viscus Flow Couplings, Keynote talk at Gordon
Conference on Flow & Transport in Permeable Media, Portland, US, 2014.
[9] K.-A. Mardal, T. Seland, H. P. Langtangen and P. Røtnes, Er Zombier En Trussel
Mot Menneskeheten?, Invitert Foredrag ved Upop aften - Det norske student samfund, UiO,
2014.
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
[10] K.-A. Mardal, A. Helgeland, V. Haughton, A. Reif and K.-H. Støverud, On the
Assumption of Laminar Flow of CSF in Chiari Patients, Invited Talk at international Chiari
Research Group, 2014.
[11] K.-A. Mardal, K.-H. Støverud, G. Ringstad and P. K. Eide, CSF Flow at Foramen
Magnum, International Hydrocephalus Imaging Working Group, Montreal, Canada, 2014.
[12] K.-A. Mardal, O. M. Khan, K. Valen-Sendstad and D. Steinman, On Numerical
Methods for Transitional Flow – Application to Blood Flow in Aneurysms, Quality and Validation
of Computational Cardio-vascular Biomechanics, WCCM-ECCM-ECCOM, Barcelona, Spain,
2014.
[13] K.-A. Mardal, K.-H. Støverud, M. Mortensen, K. Jain, B. Martin and S. Pahlavian,
Cerebrospinal Fluid Flow in Association With the Central Nervous System - Chiari and Drug
Delivery, MS on Computational Biomechanics, WCCM-ECCM-ECCOM, Barcelona, Spain,
2014.
[14] K.-A. Mardal, Operator Preconditioning for Well-Posed and Ill-Posed Problems, Keynote
Talk Preconditioning 2013 Conference, Oxford, UK, 2013.
[15] K.-A. Mardal and B. F. Nielsen, Efficient Preconditioning of Optimality Systems With
Non-Self-Adjoint State Operators, Invited talk at IFIP 2013, minisymposia Preconditioning for
PDE-Constrained Optimization, Linz, Austria, 2013.
[16] K.-A. Mardal, On the Assumption of Laminar Flow in the Modeling of Physiological Flow,
Keynote Talk at Modelling of physiological flows (MPF 2013) conference, Sardinia, Italy, 2013.
[17] K.-A. Mardal and H. P. Langtangen, Will FEniCS Fly?, Talk at FEniCS 12 workshop,
Simula, Oslo, Norway, 2012.
[18] K.-A. Mardal, Blood Flow in Cerebral Aneurysms – Can Turbulence Be a Risk Indicator?,
Invited talk at SDU workshop, Odense, Denmark, 2012.
[19] K.-A. Mardal, The Finite Element Library FEniCS + Blood Flow Simulations in Cerebral
Aneurysms, Invited talk in Marsden’s lab at UCSD, 2012.
[20] K.-A. Mardal, The Finite Element Library FEniCS, Invited talk in Steinman’s lab, University
of Toronto, 2012.
[21] K.-A. Mardal, H. P. Langtangen and P. Røtnes, Are Zombies a Threat to Mankind?,
Invited talk for the opening of "RF kjelleren" at the University of Oslo, 2012.
[22] K.-A. Mardal, B. F. Nielsen and M. S. Alnæs, Efficient Preconditioning of Optimality
Systems, Talk at EMG 2012, Schwitzingen, Germany, 2012.
[23] K.-A. Mardal, On Well-Posedness and Stability, Talk at CBC Seminar series, Simula, Oslo,
2012.
[24] K.-A. Mardal, On the Construction of Preconditioners for Systems of PDEs, Invited talk at
SIAM Conference on Computational Science and Engineering, MS2, Reno, US, 2011.
[25] K.-A. Mardal, A. Logg, H. P. Langtangen and G. Wells, FEniCS: an Attempt to
Combine Simplicity, Generality, Efficiency and Reliability, Invited talk at a Minisymposium at
SIAM Conference on Computational Science and Engineering, Reno, US, 2011.
[26] K.-A. Mardal, K. Valen-Sendstad and Ø. Evju, Simulating Blood Flow in Cerebral
Aneurysm, Invited talk at Minisymposium "Numerical Methods for Biomedical Problems" on
Enumath, Leicester, UK, 2011.
[27] K.-A. Mardal and B. F. Nielsen, Efficient Preconditioning of Optimality Systems, Talk at
Precond 11 Conference, Bordeaux, France, 2011.
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
[28] K.-A. Mardal and G. Wells, Domain-Specific Languages and Code Generation for PDE
Problems, Minisymposium at Enumath, Leicester, UK, 2011.
[29] K.-A. Mardal, A. Logg and G. Wells, FEniCS: Automated Solution of Differential
Equations, Talk at SIAM Conference on Computational Science and Engineering, Reno, US,
2011.
[30] K.-A. Mardal, K. Valen-Sendstad, M. S. Alnæs, M. Mortensen, H. P. Langtangen
and B. A. P. Reif, The Finite Element Library FEniCS and Simulation of Blood Flow in
Cerebral Aneurysms, Talk at CSB Seminar, University of Stuttgart, 2011.
[31] K.-A. Mardal, K.-H. Støverud, V. Haughton, S. Linge, H. P. Langtangen, G.
Rutkowska and I. N. Drøsdal, Cerebrospinal Fluid Flow in the Upper Cervical Canal in
Patients With the Chiari I Malformation, Invited talk at 1ST CSF Hydrodynamics Symposium,
2011.
[32] K.-A. Mardal, CSF Strømning I Forbindelse Med Chiari Malformasjon Og Syringomyelia,
CBC Workshop on Clinical Issues Related to the Cerebrospinal Fluid, Simula, Oslo, Norway,
2010.
[33] K.-A. Mardal and B. F. Nielsen, An Operator Theoretical Approach to Preconditioning
Optimality Systems, Talk at European Multi-Grid Conference, EMG, Isola d’Ischia, Italy, 2010.
[34] K.-A. Mardal, H. P. Langtangen and P. Røtnes, Is Zombies a Threat to Mankind?,
Talk presented at FEniCS 2010, 2010.
[35] K.-A. Mardal, S. Hentschel, A. Logg and K. Valen-Sendstad, Cerebral Blood Flow,
Invited talk at Telemark College, Engineering Faculty, Porsgrunn, Norway, 2009, 2009.
[36] K.-A. Mardal, S. Hentschel, A. Helgeland, H. P. Langtangen, S. Linge, A. E.
Løvgren, A. Logg and K. Valen-Sendstad, Patient-Specific Simulations of Stroke and
Syringomyelia, Talk at Advisory commitee meeting FFI project P1112 Aerosols: Dispersion,
Transport and Consequences, Nov 03, 2009.
[37] K.-A. Mardal, V. Haughton, S. Hentschel, H. P. Langtangen, S. Linge, A. E.
Løvgren and K. Valen-Sendstad, CSF Flow Modelling, Invited talk at CSR Flow Research
Conference at University of Wisconsin, Nov 9, 2009.
[38] K.-A. Mardal, A. Logg, S. Hentschel, O. C. Myklebust and K. Valen-Sendstad,
Patient-Specific Hemodynamics in FEniCS, Presentation at the FEniCS 09 Workshop, Simula,
Oslo, Norway, 2009.
[39] K.-A. Mardal, A. Helgeland, S. Hentschel, H. P. Langtangen, A. Logg, S. Linge,
A. E. Løvgren and K. Valen-Sendstad, Some Biomedical Applications at Simula, Talk at
the CBC Workshop on Computational Biology with UMB, 2009.
[40] K.-A. Mardal, S. Hentschel, A. Logg and K. Valen-Sendstad, Patient-Specific
Hemodynamics in FEniCS, Invited talk at the minisymposium on Computational Vascular and
Cardiovascular Mechanics at USNCCM 2009, Colombus, Ohio, US, 2009.
[41] K.-A. Mardal, K. Valen-Sendstad, O. C. Myklebust and S. Hentschel, Scientific
Computing at Simula, Invited Talk at Workshop on Cerebral Aneurysms and Subarachnoidal
Hemorrhage, Tromsø Jan 24-26, 2008.
[42] K.-A. Mardal, B. F. Nielsen and M. S. Alnæs, Two Steps Towards Automating Efficient
Solution of Inverse Problems, Invited Talk at the FEniCS 08 Workshop, March 5-7,Baton
Rouge, Louisiana, US, 2008.
[43] K.-A. Mardal, K. Valen-Sendstad, O. C. Myklebust and S. Hentschel, Blood Flow
Computations at Simula, Invited talk at Medical Physics, University of Wisconsin, US, 2008.
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/
[44] K.-A. Mardal, Hemodynamics in the Circle of Willis, Invited talk at Institute for Computational and Applied Mathematics, Muenster, Germany, November 18, 2008.
[45] K.-A. Mardal and M. S. Alnæs, Finite Elements With Symbolic Computations and Code
Generation, Talk at Software Issues in Computational Science and Engineering (SCSE 2007),
Uppsala, 2007-08-11, 2007.
[46] K.-A. Mardal, Computation of Hemodynamics in the Circle of Willis, Talk at Workshop:
Modelling and Computation of Biomedical Processes - June 7-14, 2007, 2007.
[47] K.-A. Mardal, Computation of Hemodynamics in the Circle of Willis, Talk at Workshop:
Modelling and Computation of Biomedical Processes - June 7-14, 2007, 2007.
[48] M. S. Alnæs, A. M. Bruaset, X. Cai, H. P. Langtangen, K.-A. Mardal, H. Moe,
O. Skavhaug and Å. Ødegård, Python in High Performance Computing, 1 Day Tutorial
presented at the Para06 Workshop, Umeå, Sweden, 2006.
[49] K.-A. Mardal, SyFi - a Package for Symbolic Finite Element Computations, Presented at
the Fenics06 workshop in Delft, Netherlands, 2006.
[50] O. Skavhaug, K.-A. Mardal and Å. Ødegård, The Tallinn PyCC Tutorial, Tutorial at
the Simula Scientific Computing Seminar - Tallinn Estonia - November 20-21, 2006, 2006.
[51] K.-A. Mardal, SyFi - an Element Matrix Factory, With Emphasis on the Incompressible
Navier-Stokes Equations, Presentation held at the Para06 workshop, Umeå, 2006.
[52] H. P. Langtangen and K.-A. Mardal, Mathematical Modeling of Blood Flow, Lectures
given at European Mathematical Society Summer School for Mathematical Modeling of the
Heart, Svalbard, 2006.
[53] K.-A. 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, 2005.
[54] A. M. Bruaset, M. S. Alnæs, H. P. Langtangen, K.-A. Mardal, H. Moe, O. Skavhaug
and Å. Ødegård, Scientific Computing in Python, 1 Day Tutorial ASIM 2005, 2005.
[55] Å. Ødegård, K. -A. Mardal, P. Miller, H. Moe, O. Skavhaug, A. -M. Bruaset and
H. P. Langtangen, High Performance Computing in Python, 1 day Tutorial, SC2004, 2004.
[56] K. -A. 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„ 2004.
[57] K.-A. Mardal, A. Huerta, H. P. Langtangen and D. Harry, Numerical Modeling
of Crust and Mantle Movement, Talk presented at SIAM Conference on Mathematical and
Computational Issues in the Geosciences (GS0), Austin, Texas, US, 2003.
Department of Mathematics, University of Oslo – Postboks 1053 Blindern 0316 OSLO
H (+47) 9361 0854 • B kent-and@math.uio.no • http://folk.uio.no/∼kent-and/