University of Birmingham > Talks@bham > Optimisation and Numerical Analysis Seminars > Fast iterative solvers for PDE with random coefficients

Fast iterative solvers for PDE with random coefficients

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  • UserDaniel Loghin (University of Birmingham)
  • ClockThursday 29 November 2018, 12:00-13:00
  • HouseNuffield G13.

If you have a question about this talk, please contact Sergey Sergeev.

Over the last two decades several standard models in science and engineering have been refined to allow for uncertainty in the coefficients or input data arising in the modelling process. A common reformulation is to represent these coefficients as random fields. The resulting models are PDE with random coefficients, with solutions or other quantities of interest being also random fields. Consequently, the aim is to evaluate or approximate various relevant statistics associated with the PDE , such as the expected value of the solution. This is in general achieved numerically using methods such as Monte Carlo or the stochastic Galerkin finite element method. The latter is the focus of the talk.

The stochastic Galerkin finite element method uses approximation of both physical and probability space simultaneously. This results in a deterministic parametric PDE set in a high-dimensional space. One of the significant challenges associated with this approach is known as ‘the curse of dimensionality’: the resulting linear system is huge, with the size growing exponentially with the size of the approximating probability space. Such systems can only be solved iteratively, also using preconditioners to accelerate the convergence of the iterative solver. In the talk we will discuss various approaches to preconditioning, including existing analysis and numerical experiments which confirm or investigate independence of discretisation parameters of the proposed solvers. The motivating model is a scalar diffusion problem with random diffusivity arising as a reformulation of the Darcy equations.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

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