Numerical Analysis Community

Introduction

 

Numerical analysis is the science of methods for computer simulation of complex physical processes. It includes development and implementation of algorithms, and analysis of their complexity, stability and convergence properties - that is, how fast, robust and accurate they are. The subject is interdisciplinary and has interfaces to mathematics, computer science and various applications.

 

Development of better numerical algorithms is an important component in successful e-Science based research, often matching the improvement of hardware in terms of speed gains. This is particularly true in problem areas at the forefront of research that have only recently become amenable to computer simulations. One such challenging area is multiscale modeling, where algorithmic progress will be essential and it is insufficient to wait for the next generation of computer hardware. Problems involving multiple scales in time and space are abundant in science and engineering, and at the core of several of the e-Science communities, from fluids and climate modeling to atomistic and ab initio simulations. The fine scales often have a strong effect on the coarse scale dynamics and must be taken into account in a numerical simulation, but representing all scales is computationally too expensive. A special difficulty concerns stochastic micro or macro models, which are often necessary for complex systems. High-frequency wave propagation is a particular multiscale problem where the computational difficulty lies in the need to resolve a short wavelength over a large domain. Another application area of interest is multiphase and complex flow where processes on the microscale influence the macroscopic flow.

 

The area of Numerical Analysis bridges the simulation demands in applications and the theoretical understanding of algorithms in Mathematics and Computer Science. Within SeRC, Numerical Analysis is a core e-Science area. The members actively interact with application groups via the e-Science communities. Numerical Analysis is therefore a key link between many parts of SeRC.

 

 

Research environment

 

Research in the Numerical Analysis community in SeRC is focused on the numerical solution of differential equations modeling the interaction of phenomena on widely different spatial and temporal scales. The classical example concerns models in fluid mechanics and the description of turbulence, which still harbors deep unanswered questions. Materials science and biophysics are characterized by models with large-scale separation, high complexity and stochastic elements. The treatment of these models demands new depth and precision from the techniques used, as well as a combination of knowledge from different disciplines. Realistic models demand large-scale numerical computations and research is also geared towards algorithm development and program construction in scalable (distributed) computer environments. This subject is central to the advancement of science and engineering, and to the development of engineering tools for industry and government.

The group is centered at the Department of Numerical Analysis, KTH and the current members are:

 

  • Professors (full/associate): Björn Engquist, Katarina Gustavsson, Michael Hanke, Johan Hoffman, Elias Jarlebring, Jesper Oppelstrup, Olof Runborg, Mattias Sandberg, Anders Szepessy and Anna-Karin Tornberg.
  • Assistant professors: Sara Zahedi.

 

Currently SeRC finances directly Olof Runborg (SeRC faculty, 50%) and the PhD students Doghonay Arjmand, Ashraful Kadir and Davoud Saffar Shamshirgar.

 

 

Overall research goals

 

Numerical Analysis is one of the core e-Science areas in SeRC. The overall goal of the area is to promote more efficient and robust simulation algorithms within SeRC as a whole. To achieve this Numerical Analysis focuses on:

 

  • Basic research in numerical analysis with relevance to the e-Science communities. This is typically conducted as PhD projects led by an advisor from Numerical Analysis, but in collaboration with scientists from other e-Science communities.
  • Directed research as parts of projects led by other e-Science communities. In PhD projects a researcher from Numerical Analysis is co-advisor for the student.