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Analysis of Stationary and Transient Boundary-Domain Integral Equations


Mathematics

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Prof S Mikhailov Applications accepted all year round Self-Funded PhD Students Only

About the Project

The project is aimed at formulation and mathematical analysis of boundary-domain integral equations of linear and nonlinear elliptic and parabolic partial differential equations with variable coefficients. The considered PDEs arise naturally in engineering and physics as mathematical models of stationary and transient processes in inhomogeneous media, e.g. heat transfer in inhomogeneous materials with thermo-conductivity coefficients depending on the point temperature and coordinate, materials with damage-induced inhomogeneity, elasto-plastic materials, potential and viscous compressible flows, fluid flows through porous media, electromagnetics and other areas. The formulation should be based on reducing a boundary value problem or an initial-boundary value problem for a PDE to a system of global or localised boundary-domain integral or integro-differential equations, by employing a parametrix (Levi function) and the Green identity. Analysis is supposed to be done in appropriate function spaces by implementing operator calculus, variational techniques, and other methods of functional analysis.

The project will contribute to a mathematical analysis framework for the emerging family of computational methods, for solving linear and nonlinear elliptic and parabolic partial differential equations, based on boundary-domain integral equations. A mesh-based or mesh-less discretisation of the latter equations lead to, respectively, linear or nonlinear systems of algebraic equations. In the case of localised boundary-domain integral equations, the matrices of the corresponding algebraic equations will be sparse. The mathematical analysis of the integral equations will give a basis for creating fast and stable algorithms for solution of their approximate discrete counterparts.

Funding Notes

Brunel offers a number of funding options to research students that help cover the cost of their tuition fees, contribute to living expenses or both. See more information here: https://www.brunel.ac.uk/research/Research-degrees/Research-degree-funding. Recently the UK Government made available the Doctoral Student Loans of up to £25,000 for UK and EU students and there is some funding available through the Research Councils. Many of our international students benefit from funding provided by their governments or employers. Brunel alumni enjoy tuition fee discounts of 15%.)

References

See some references available from http://people.brunel.ac.uk/~mastssm/publications.html
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