The Applied and Numerical Analysis (ANA) group is focused on the analysis of mathematical models of biological, chemical or physical processes described by differential, integral and integro-differential equations, and in the development, analysis and implementation of numerical methods for their approximate solutions.
The diverse applications considered by the group include rigorous analysis and computational modelling of problems in acoustic, elastic and electromagnetic wave propagation, modelling of fluid flows, biological processes, viscoelasticity and fracture in solids. Novel finite element and boundary element methods are developed and analysed for these applications, leading to robust algorithms and specialised software. A related research topic is approximation of orthogonal polynomials and special functions with explicit error terms.
The group research also includes analysis of nonlinear problems, like Navier-Stokes system, Gierer-Meinhardt system, and abstract bifurcation problems.
The ANA group is home of a major international collaboration on analytical and numerical methods for boundary-domain integral equations, aimed at creating a new method for analysis and solution of variable-coefficient and nonlinear PDEs.
Specific research expertise
- Analysis of partial differential equations, including nonlinear PDEs of fluid mechanics and mathematical biology (S. Mikhailov, M. Winter)
- Analysis and numerical implementation of boundary-domain integral and integro-differential equations (S. Mikhailov)
- Computational modelling of problems in solid mechanics, as well as acoustic, elastic and electromagnetic wave propagation, by Finite Element and Boundary Element methods (S. Langdon, M. Maischak, S. Shaw, M. Warby, J. Whiteman)
- Approximation of orthogonal polynomials and special functions (I. Krasikov)
- Abstract bifurcation and singularity theory (J. Furter)
- Fast solvers and preconditioners, error estimators and adaptive algorithms, high performance and scientific computing, software development (S. Langdon, M. Maischak, S. Shaw)
- Theoretical and computational modelling of fatigue, damage, durability, and fracture (S. Mikhailov)
For more detailed descriptions of research and list of individual publications, please follow the links to the web pages of individual group members.
Major external collaborators
- Prof. I. Babuska, University of Texas at Austin, USA
- Prof. O. Chkadua, Mathematical Institute, Tbilisi State University, Tbilisi, Georgia
- Prof. M. Kohr, Babeş-Bolyai University, Cluj-Napoca, Romania
- Prof. M. Lanza de Cristoforis, University of Padua, Padua, Italy
- Prof. D. Natroshvili, Georgian Institute of Technology, Tbilisi, Georgia
- Prof. S. Rjasanow, University of Saarland, Saarbrucken, Germany
- Prof. E. Stephan, University of Hannover, Hannover, Germany
- Prof. J. Wei, University of British Columbia, Vancouver, Canada
- Prof. W.L. Wendland, University of Stuttgart, Stuttgart, Germany
- Dr. T.G. Ayele, Addis Ababa University, Addis Ababa, Ethiopia
- Dr. T.T. Dufera, Adama Science and Technology University, Adama, Ethiopia
Externally funded projects
- MARM programme grant supporting collaboration with Adama University of Science and Technology, Ethiopia (London Mathematical Society, 2020-2021, S. Mikhailov)
- Mathematical Analysis of Boundary-Domain Integral Equations for Nonlinear PDEs (EPSRC, 2015-2018, S. Mikhailov).
- Acoustic Localisation of Coronary Artery Stenosis (EPSRC, 2010-2014, S. Shaw, J. Whiteman)
- Mathematical Analysis of Localised Boundary-Domain Integral Equations for BVPs with Variable Coefficients (EPSRC, 2010-2013, S. Mikhailov).
- Boundary-Domain Integral and Integro-Differential Equations: Formulation, Analysis, Localisation (Royal Society, 2006-2009, S. Mikhailov).
- Analysis of Boundary-Domain Integral and Integro-Differential Equations (LMS–IMU–AMMSI Initiative “Mentoring African Research in Mathematics” funded by the Nuffield Foundation, 2006-2008, S. Mikhailov).