The Numerical Analysis and Scientific Computing (SCAN) department's mission is to develop mathematical methods and scientific tools to better understand complex physical processes – with a particular focus on fundamental problems in physiology. The department team creates numerical simulation technology that is accessible to the research community, with a core part of our mission being to develop software tools to help facilitate open and reproducible research practices.
SCAN hosts research projects with multi-disciplinary teams consisting of experts in mathematics, numerical methods, physical modelling and optimization, and scientific software development.
Department Head
"SCAN addresses challenges across all stages in scientific computing – from the theoretical foundations to implementation and open-access numerical software, and in-silico studies providing insight into fundamental physiological processes."
Dr. Ada Ellingsrud, head of the SCAN department
Focus areas
Numerical modelling of multiphysics problems
Many physiological processes involve multiple simultaneous physical phenomena – such as blood flow in pulsating vessels or water circulation through porous brain tissue. These processes, which relate to fluid flow, waste clearance and volume control are crucial for the wellbeing of the brain.
The dynamics of such multiphysics systems can be modelled via coupled systems of partial differential equations (PDEs). Although the models provide a powerful tool for better understanding the phenomena at hand, the complexity of the systems makes them challenging to approximate, both numerically and computationally.
We develop and analyse new mathematical models for multiphysics problems and associated property-preserving numerical schemes based on finite element methods. Further, we develop robust and scalable iterative methods for solving the arising large-scale linear systems.
In collaboration with medical doctors and experimentalists, we apply computational models to conduct in-silico studies providing sorely needed insight into fundamental processes related to fluid flow and circulation in brain tissue across scales - from the cellular to the organ level.
Hybrid modelling combining data with physics
With advances in technology and the huge amounts of data now available, machine learning techniques, such as deep neural networks (DNNs), are becoming increasingly valuable for studying physiological problems. The drawback of these techniques, however, is that they do not have underlying knowledge about the physical laws governing the system they are modelling. Traditional physics-based computational methods can help to bridge this gap.
We combine the strengths of both approaches by incorporating machine learning with physics-based computational methods to create models that can learn. Further, we take advantage of well-established theoretical foundations developed for solving PDEs, such as multigrid methods, to develop more reliable and robust machine learning techniques.
Scientific software development
An important aspect of our work is to make our developments accessible to researchers and engineers through open-source software. In addition, we develop software tools that support reproducible and interactive science. Our tools aim to support the full research lifecycle – from exploration through to proof and publication, to archiving and sharing of data and code.
People in SCAN
Publications
simcardems: A FEniCS-based cardiac electro-mechanicssolver
Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion
The role of clearance in neurodegenerative disease
The modelling error in multi-dimensional time-dependent solute transport models
The distributed neocortex: How neuroscience can inspire distributed AI systems
The directional flow generated by peristalsis in perivascular networks - theoretical and numerical reduced-order description
SMART: Spatial Modeling Algorithms for Reaction and Transport
SMART: Spatial Modeling Algorithms for Reaction and Transport
Rational approximation preconditioners for multiphysics problems
Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints
Perivascular pathways and the dimension-2 gap
Perivascular pathways and the dimension-2 gap