Numerical analysis of adaptive UQ algorithms for PDEs with random inputs
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This is an EPSRC funded research project running from April 2018 to March 2020.

Research Team:  Alex Bespalov Arbaz Khan Catherine Powell David Silvester Feng Xu

Summary
Partial differential equations (PDEs) are key tools in the mathematical modelling of physical processes in science and engineering. Traditional deterministic PDE-based models assume precise knowledge of all inputs (material properties, initial conditions, external forces, etc.). There exist an abundance of numerical methods that can be used to compute a solution to such models to any required accuracy. In practical applications, however, a complete characterisation of all the inputs to a PDE model may not be available. Examples include the modulus of elasticity of a stressed body (in linear elasticity models)and wave characteristics of inhomogeneous media (in wave propagation models). In these cases, simulations based on deterministic models are unable to estimate probabilities of undesirable events (e.g., the fracture of a stressed plate) and, hence, to perform a reliable risk assessment. The emergent area of uncertainty quantification (UQ) deals with mathematical modelling at a different level. It involves the use of probabilistic techniques in order to (i) determine and quantify uncertainties in the inputs to PDE-based models, and (ii) analyse how these uncertainties propagate to the outputs (either the solution to the PDE, or a quantity of interest derived from the solution). The models are then described by PDEs with random data, where both inputs and outputs take the form of random fields ... more

The project builds on the research in the precursor project Analysis of Numerical Methods for Partial Differential Equations with Random Data

Research outputs to date
Research software
  • S-IFISS solves diffusion problems with uncertain coefficients (square domain, needs IFISS)
  • Stochastic T-IFISS solves diffusion problems with uncertain coefficients (aribtrary two-dimensional domains)
Link to  Manchester UQ group.

Page last modified: 21 September 2018