Kent-Andre Mardal, Professor in Mechanics, Department of Mathematics, University of Oslo and
Adjunct Research Scientist, Simula Research Laboratory
E-mail: kent-and@math.uio.no, kent-and@simula.no

News   Research   Teaching/Students/Available master projects   Software   CV   Conferences/Traveling

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" at Simula.

Interests:
A brief, noncomplete summary of my research:
Computational biomechamics

For cerebrospinal fluid flow we have considered Chiari in idealized models in [AJNR 2010], [AJNR 2010], [AJNR 2011], craniovertebral decompression [J Neurosurgery], exercise [AJNR 2013], and patient-specific modelling in [AJNR 2012], [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, [PNAS 2017] 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.
interstitial fluid flow
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 [arXiv 2016].
nonlinear viscosity transition to turbulence
Images taken from the papers in Journal of Biomechanics 2011, 2013.

Preconditioning
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], inverse problems [SICON 2010], [SISC 2013], [BIT 2017], singular problems in linear elasticity [arXiv 2016], multiscale problems in terms of 2D-1D and 3D-1D couplings [SISC 2016], [arXiv 2016], poroelasticity [SISC 2017], [arXiv 2017].

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 [SISC 2016] 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

Scientific Software
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 Symbolic computations 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.

Other
In the 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".
Finally, in the paper we considered methods for assessing the cosmic background radiation.

A full list of publications can be found in my CV.