Kent-Andre Mardal, Professor in Mechanics, Department of Mathematics,
University of Oslo
Adjunct Research Scientist,
Simula Research Laboratory
Since my PhD in 2003, I have been a Post Doctoral Fellow and later a Research Scientist at Simula Research Laboratory
with a 20% position at the University of Oslo until 2014 when I became an Associate Professor at the Mechanics
Division, Department of Mathematics and full Professor in 2015.
My research is computational mechanics with a strong focus on biomechanics, high-performance computing and scientific software.
From 2007-2017 I was the group leader of Biomedical flows and structures
in the center of Excellence "Center for Biomedical Computing"
- Biomechanics of the Brain
- Aging Brain, Dementia
- Interstitial fluid flow, glymphatic system
- Stroke caused by aneurysms
- The Chiari malformation and syringomyelia
- Partial Differential Equations
- Finite Element Methods
- Fluid and Solid mechanics
- Scientific Software and Scripting, in particular FEniCS
- Preconditioning, Multigrid and High-Performance Computing
A brief, noncomplete, and not completely up to date summary of my research:
For cerebrospinal fluid flow we have considered Chiari in idealized models
and patient-specific modelling in
[Plos One 2016],
transitional/turbulent effects in
[J Biomech 2014],
[J Numer Method Biomed Eng 2017]
and drug dispersion in
[Plos One 2017].
The interstitial fluid flow in the poro-elastic cord was
studied in [Comput Methods Biomech Biomed Engin 2016].
The glymphatic system
My research on the glymphatic system concerns the
insterstitial fluid flow which appears to be dominated by diffusion,
even though on a macroscale the clearance seem to happen faster
than diffusion, [JCI Insight 2018].
Furthermore, the traditional view of the 3. circulation where CSF is produced
in the Choroid Plexus is challenged by PC-MRI findings in [NeuroImage 2018]. Appropriate numerical methods are
proposed in [arXiv 2018] for multiple-network poroelasticity simulations.
Images taken from the PNAS 2017 and JCI Insight 2018 papers.
Stroke and aneurysms
I have been working
with blood flow in cerebral aneurysms, the flow of cerebrospinal fluid
that surrounds the central nervous system and the interstitial fluid
flow in the extracellular matrix. Crucial
for these applications is the development of personalized computational models.
For the cerebral aneurysms we
have considered nonlinear rheology in
[J Biomech 2013],
turbulence/transitional effects in
[J Biomech 2011],
[J Biomech 2013], with a proper DNS in
[Computers&Fluids 2016] ,
and the sensitivity of numerical resolution wrt common risk indicators in
[Plos One 2017],
comparison with 4D PC-MR in
[Med Phys 2011] and
[Med Phys 2016] and inverse modelling based on 4D PC-MR in
Images taken from the papers in Journal of Biomechanics 2011, 2013.
Already in my PhD, the concept of operator preconditioning was central. Operator preconditioning is a powerful and constructive framework for deriving efficient algorithms for systems of PDEs. My research on this topic was review and summarized
in the review paper [NLAA 2011] .
Order optimal preconditioners for Runge-Kutta schemes [SISC 2007],
time-dependent Stokes [Numer Math 2004],
[Numer Math 2013],
the Bidomain equations [NLAA 2006],
[Ann Biomed Eng 2006],
singular problems in linear elasticity
multiscale problems in terms of 2D-1D and 3D-1D couplings
Illustration of the operator preconditioning idea, illustration from the NLAA 2011 paper
Fractional Differential Equations and Multiphysics
Schemes for multi-physics and multi-scale problems can lead to fractional
differential equations. 2D-1D or 3D-2D couplings were considered in
and corressponding 3D-1D schemes in [NMPDE 2018]. Multilevel schemes are proposed in [arXiv 2018].
Numerical experiments suggesting that the trace of H^(1/2) functions are in H^(-0.14), taken from the NMPDE 2018 paper
My research on software was earlier related to Diffpack, but from
2007 and onwards I have been working with FEniCS". In the early days, I worked with several core components
and code generation, UFC, Trilinos, assembly and the Python interface, see the book. Nowadays, I work more with applications and a main topic
is now to interface FEniCS with FreeSurfer, a widely used software framework in neuroscience.
book chapter we considered the mathematics of zombies and
demonstrated that most zombie movies are not really realistic.
Images taken from a book chapter in book "Zombies in the academy".
we considered methods for assessing the
cosmic background radiation.
A full list of publications can be found in my CV.