Numerical Analysis and Scientific Computing

Numerical Analysis and Scientific Computing

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

Ada Johanne Ellingsrud

Ada Johanne Ellingsrud

Research ScientistHead of Department

"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. 

Key partners

People in SCAN

Pietro Benedusi

Pietro Benedusi

Postdoctoral Fellow

Marius Causemann

Marius Causemann

PhD student

Cécile Daversin-Catty

Cécile Daversin-Catty

Research Scientist

Jørgen Dokken

Jørgen Dokken

Research Engineer

Ada Johanne Ellingsrud

Ada Johanne Ellingsrud

Research ScientistHead of Department

Marianne Fyhn

Marianne Fyhn

ProfessorAdjunct Chief Research Scientist

Ingeborg Gjerde

Ingeborg Gjerde

Research Engineer

Eirill Hauge

Eirill Hauge

PhD student

Ottar Hellan

Ottar Hellan

PhD student

Halvor Herlyng

Halvor Herlyng

PhD student

Martin Hornkjøl

Martin Hornkjøl

External PhD student

Adrian Kirkeby

Adrian Kirkeby

Postdoctoral Fellow

Miroslav Kuchta

Miroslav Kuchta

Senior Research Scientist

Mikkel Lepperød

Mikkel Lepperød

Research Scientist

Anders Malthe-Sørenssen

Anders Malthe-Sørenssen

ProfessorAdjunct Chief Research Scientist

Kent-Andre Mardal

Kent-Andre Mardal

ProfessorAdjunct Chief Research Scientist

Rami Masri

Rami Masri

Postdoctoral Fellow

Markus Pettersen

Markus Pettersen

PhD student

Sidney Pontes-Filho

Sidney Pontes-Filho

Postdoctoral Fellow

Benjamin Ragan-Kelley

Benjamin Ragan-Kelley

Senior Research Engineer

Jørgen Riseth

Jørgen Riseth

PhD student

Marie E. Rognes

Marie E. Rognes

Chief Research Scientist

Thomas Surowiec

Thomas Surowiec

Chief Research Scientist

Marte Julie Sætra

Marte Julie Sætra

Postdoctoral Fellow

Marius Zeinhofer

Marius Zeinhofer

Postdoctoral Fellow

Publications

Read simcardems: A FEniCS-based cardiac electro-mechanicssolver

H. Finsberg, I. G. M. van Herck, C. Daversin-Catty, H. Arevalo and S. Wall

simcardems: A FEniCS-based cardiac electro-mechanicssolver

Journal of Open Source Software

Read Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion

B. Gomez-Vargas, K. Mardal, R. Ruiz-Baier and V. Vinje

Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion

SIAM J. of Numerical Analysis

Read The role of clearance in neurodegenerative disease

G. S. Brennan, T. B. Thompson, H. Oliveri, M. E. Rognes and A. Goriely

The role of clearance in neurodegenerative disease

SIAM Journal on Applied Mathematics

Read The modelling error in multi-dimensional time-dependent solute transport models

R. Masri, M. Zeinhofer, M. Kuchta and M. E. Rognes

The modelling error in multi-dimensional time-dependent solute transport models

TBA

Read The distributed neocortex: How neuroscience can inspire distributed AI systems

M. Kvalsund, K. O. Ellefsen, K. Glette, S. Pontes-Filho and M. Lepperød

The distributed neocortex: How neuroscience can inspire distributed AI systems

Workshop "The Distributed Ghost Cellular Automata, Distributed Dynamical Systems, and Their Applications to Intelligence" at ALIFE 2023

Read The directional flow generated by peristalsis in perivascular networks - theoretical and numerical reduced-order description

I. Gjerde, M. E. Rognes and A. Sánchez

The directional flow generated by peristalsis in perivascular networks - theoretical and numerical reduced-order description

Journal of Applied Physics

Read SMART: Spatial Modeling Algorithms for Reaction and Transport

J. G. Laughlin, J. S. Dokken, H. Finsberg, E. A. Francis, C. T. Lee, M. E. Rognes and P. Rangamani

SMART: Spatial Modeling Algorithms for Reaction and Transport

Journal of Open Source Software

Read SMART: Spatial Modeling Algorithms for Reaction and Transport

J. G. Laughlin, J. S. Dokken, H. Finsberg, E. A. Francis, C. T. Lee, M. E. Rognes and P. Rangamani

SMART: Spatial Modeling Algorithms for Reaction and Transport

The Journal of Open Source Software

Read Rational approximation preconditioners for multiphysics problems

A. Budisa, X. Hu, M. Kuchta, K. Mardal and L. T. Zikatanov

Rational approximation preconditioners for multiphysics problems

Numerical Methods and Applications (NMA 2022)

Read Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints

B. Keith and T. M. Surowiec

Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints

Foundations of Computational Mathematics

Read Perivascular pathways and the dimension-2 gap

M. E. Rognes

Perivascular pathways and the dimension-2 gap

Scientific Computing Seminar, Brown University, Providence, Rhode Island, US

Read Perivascular pathways and the dimension-2 gap

M. E. Rognes

Perivascular pathways and the dimension-2 gap

Numerical Analysis and Scientific Computing Seminar, Courant Institute, NY, US