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• PhD in Computational Mathematics, Russian Academy of Sciences, 1999.
• BSc in Mathematics, 1994.

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

Before joining the University Â鶹¾«Ñ¡, Alex held postdoctoral research positions at Universidad de Concepción (Chile), Brunel University, and the University of Manchester.

Semester 1

LH/LM Financial Mathematics

LH/LM Numerical Methods and Numerical Linear Algebra

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
• Software development

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) inputs. Here, the focus is on the development and analysis of efficient, accurate and practical numerical methods for solving high-dimensional parameter-dependent partial differential equations (PDEs). This research is within a rapidly evolving area of uncertainty quantification, which is at the forefront of modern computational science.

Alex's research in numerical methods for uncertainty quantification 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 the key points when thinking of practical applications, e.g., in civil engineering (crack detection) and electromagnetics (radar design).

Alex has been collaborating with many colleagues across the world, notably with Professor Norbert Heuer (Pontificia Universidad Católica de Chile), Professor Ralf Hiptmair (ETH Zurich, Switzerland), Professor Serge Nicaise (Université de Valenciennes, France), Professor Dirk Praetorius (Technical University of Vienna), and Professor David Silvester (University of Manchester).

• Reviewer for Mathematical Reviews (2008-2013)

• SIAM member (since 2018)