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Dr Alex Bespalov
Applications accepted all year round
Competition Funded PhD Project (European/UK Students Only)
About the Project
PhD Studentship in Numerical Analysis and Scientific Computing
The project concerns numerical solution of partial differential equations (PDEs) with uncertainty in input data. It will focus on developing adaptive algorithms for efficient solution of such problems. This will involve both rigorous mathematical analysis and extensive numerical experimentation. The algorithms will be designed, analysed, and implemented (in a MATLAB environment).
PDEs are key tools in the mathematical modelling of processes in science and engineering. In practical PDE-based models, precise knowledge of inputs (e.g., material properties, initial conditions, external forces) may not be available, or there might be uncertainty about the inputs. In these cases the models are described by PDEs with random data. Such problems arise in many scientific and industrial contexts when it is essential to accurately model complex processes and perform a reliable risk assessment. One of the major challenges in numerical solution of PDEs with random data is the high dimensionality of the resulting discretisations. Therefore, the development of robust and effective numerical methods which make best use of available computational resources is a very active research area.
The project will provide training in modern numerical analysis and uncertainty quantification techniques, thus equipping the student with highly desirable skills for working in either industry or academia.
Entry requirements:
We are looking for an enthusiastic and motivated graduate with
- a 1st class degree in Mathematics, preferably at the MMath/MSc level, or equivalent;
- a solid background in numerical analysis of PDEs;
- good programming skills;
- good communication skills (oral and written).
Good knowledge of probability theory will be beneficial.
Informal inquiries should be directed to Dr Alex Bespalov, e-mail: [Email Address Removed]
The project concerns numerical solution of partial differential equations (PDEs) with uncertainty in input data. It will focus on developing adaptive algorithms for efficient solution of such problems. This will involve both rigorous mathematical analysis and extensive numerical experimentation. The algorithms will be designed, analysed, and implemented (in a MATLAB environment).
PDEs are key tools in the mathematical modelling of processes in science and engineering. In practical PDE-based models, precise knowledge of inputs (e.g., material properties, initial conditions, external forces) may not be available, or there might be uncertainty about the inputs. In these cases the models are described by PDEs with random data. Such problems arise in many scientific and industrial contexts when it is essential to accurately model complex processes and perform a reliable risk assessment. One of the major challenges in numerical solution of PDEs with random data is the high dimensionality of the resulting discretisations. Therefore, the development of robust and effective numerical methods which make best use of available computational resources is a very active research area.
The project will provide training in modern numerical analysis and uncertainty quantification techniques, thus equipping the student with highly desirable skills for working in either industry or academia.
Entry requirements:
We are looking for an enthusiastic and motivated graduate with
- a 1st class degree in Mathematics, preferably at the MMath/MSc level, or equivalent;
- a solid background in numerical analysis of PDEs;
- good programming skills;
- good communication skills (oral and written).
Good knowledge of probability theory will be beneficial.
Informal inquiries should be directed to Dr Alex Bespalov, e-mail: [Email Address Removed]
Funding Notes
For UK and EU candidates:
funding may be available through a college or EPSRC scholarship in competition with all other PhD applications;
the scholarship will cover tuition fees, training support, and a stipend at standard rates for 3-3.5 years;
early application is strongly recommended;
the application procedure and deadlines are advertised at https://www.birmingham.ac.uk/schools/mathematics/phd/phd-programme.aspx;
strong UK/EU candidates are encouraged to make an informal inquiry.
For non-UK/non-EU candidates:
strong self-funded applicants will be considered;
exceptionally strong candidates in this category may be awarded a tuition fee waiver (for up to 3 years) in competition with all other PhD applications.
funding may be available through a college or EPSRC scholarship in competition with all other PhD applications;
the scholarship will cover tuition fees, training support, and a stipend at standard rates for 3-3.5 years;
early application is strongly recommended;
the application procedure and deadlines are advertised at https://www.birmingham.ac.uk/schools/mathematics/phd/phd-programme.aspx;
strong UK/EU candidates are encouraged to make an informal inquiry.
For non-UK/non-EU candidates:
strong self-funded applicants will be considered;
exceptionally strong candidates in this category may be awarded a tuition fee waiver (for up to 3 years) in competition with all other PhD applications.
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Career overview
Dr Alex Bespalov obtained a BSc in Mathematics in 1994 and a PhD in Computational Mathematics from the Russian Academy of Sciences in 1999. He has held postdoctoral research positions at Universidad de Concepción in Chile, Brunel University, and the University of Manchester before joining the University of Birmingham. Dr Bespalov is currently an Associate Professor in Numerical Analysis and a member of the Applied Mathematics group within the School of Mathematics. His research focuses on the design, analysis, and implementation of robust and accurate numerical algorithms for solving mathematical problems arising from real-life applications. His work has been supported by the Engineering and Physical Sciences Research Council (EPSRC) and The Alan Turing Institute. Dr Bespalov has collaborated with several international colleagues and has been actively involved in the development of numerical methods for uncertainty quantification and high-order finite element methods.
Research interests
Dr Alex Bespalov''s research focuses on Numerical Analysis, specifically the design, analysis, and implementation of robust and accurate numerical algorithms for solving mathematical problems arising from real-life applications. His areas of interest include the numerical solution of partial differential and boundary integral equations, numerical methods for uncertainty quantification, high-order finite element and boundary element methods, error estimation, error control, and adaptivity. He studies singularities and their numerical approximation, with applications to electromagnetics, linear elasticity, and fluid dynamics. Dr Bespalov is particularly interested in developing efficient numerical methods for high-dimensional parameter-dependent partial differential equations, which is a key area in uncertainty quantification. He also explores high-order polynomial approximations within finite element and boundary element methods for deterministic PDE problems, considering practical applications such as civil engineering and radar design. His research has been supported by EPSRC and The Alan Turing Institute, and he collaborates with various international colleagues in the field.
Numerical Analysis
Computational Mathematics
Numerical Algorithms
Partial Differential Equations
Boundary Integral Equations
Uncertainty Quantification
Finite Element Methods
Boundary Element Methods
Error Estimation
Error Control
Adaptivity
High-Order Approximations
Software Development
Electromagnetics
Linear Elasticity
Fluid Dynamics
Stochastic Galerkin Methods
Robust Numerical Methods
Practical Applications
Mathematical Modelling
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