Dr Alex Bespalov

• PhD in Computational Mathematics, Russian Academy of Sciences, 1999

Alex obtained his PhD in Computational Mathematics from the Russian Academy of Sciences in 1999.

Before joining the University of Birmingham, Alex held postdoctoral research positions at Universidad de Concepción (Chile), Brunel University, and the University of Manchester.

Teaching Programmes

• Computational Methods and Frontiers
• Computational Methods & Programming

Alex is happy to discuss potential supervision of PhD research projects in Numerical Analysis with motivated and suitably qualified candidates.

RESEARCH THEMES

• numerical solution of partial differential and boundary integral equations;
• numerical methods for uncertainty quantification;
• high order (p- and hp-) finite element and boundary element methods;
• error estimation, error control, and adaptivity;
• singularities and their numerical approximation;
• applications to electromagnetics, linear elasticity, and fluid dynamics

RESEARCH ACTIVITY

Alex specialises in Numerical Analysis. As a mathematician, he is interested to see how intrinsic properties of mathematical models (e.g., differential equations) influence their numerical approximations. He uses these insights together with advanced methods of applied analysis to provide mathematical justification of robust and accurate numerical algorithms tailored to specific problems of practical interest.

One direction of Alex’s research concerns numerical methods for problems with uncertain (or, random) data. Here, the focus is on developing efficient algorithms to deal with highly-dimensional discrete problems stemming from stochastic finite element approximations. This research is within a rapidly evolving area of uncertainty quantification, which is at the forefront of modern computational science. In this area, Alex has established research links with Dr Catherine Powell and Professor David Silvester at the University of Manchester.

Alex’s research in stochastic finite element method goes hand in hand with his expertise in and passion for high-order polynomial approximations. He also studies these in the context of finite element and boundary element methods for deterministic PDE problems posed over non-smooth (not necessarily bounded) domains. Here, non-smoothness of physical domain is one of key points when thinking of practical applications, e.g., in civil engineering (crack detection) and electromagnetics (radar design). In this area of research Alex has collaborative ties with Professor Norbert Heuer (Pontificia Universidad Católica de Chile), Professor Ralf Hiptmair (ETH Zurich, Switzerland), Dr Matthias Maischak (Brunel University, UK), and Professor Serge Nicaise (Université de Valenciennes, France).

• Alex is a reviewer for Mathematical Reviews (since 2008)