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A multilevel preconditioner for data assimilation with 4D-Var

The department of Mathematics and Statistics at the University of Limerick invites you to a seminar by Dr Alison Ramage (University of Strathclyde).

Title: A multilevel preconditioner for data assimilation with 4D-Var

Abstract: Large-scale variational data assimilation problems are commonly found in applications like numerical weather prediction and oceanographic modelling. The 4D-Var method is frequently used to calculate a forecast model trajectory that best fits the available

observations to within the observational error over a period of time. One key challenge is that the state vectors used in realistic applications could contain billions or trillions of unknowns so, due to memory limitations, in practice it is often impossible to assemble, store or manipulate the matrices involved explicitly. In this talk we present a limited memory approximation to the Hessian of the linearised quadratic minimisation subproblems, computed using the Lanczos method, based on a multilevel approach.

We then use this approximation as a preconditioner within 4D-Var and show that it can reduce memory requirements and increase computational efficiency.

This seminar will take place on Friday, November 18, at 4pm, in A2-002.

If you have any questions regarding this seminar, please direct them to Iain Moyles (061 233726,  A full list of upcoming seminars can be found at

Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (, centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.