Thinking out of the box – skills for work

Since the Dearing Report .1 there has been an increased emphasis on the development of employability and transferable (‘soft’) skills in undergraduate programmes. Within STEM subject areas, recent reports concluded that universities should offer ‘greater and more sustainable variety in modes of study to meet the changing demands of industry and students’.2 At the same time, higher education (HE) institutions are increasingly conscious of the sensitivity of league table positions on employment statistics and graduate destinations. Modules that are either credit or non-credit bearing are finding their way into the core curriculum at HE. While the UK government and other educational bodies argue the way forward over A-level reform, universities must also meet the needs of their first year cohorts in terms of the secondary to tertiary transition and developing independence in learning.

Implementation of an interior point source in the ultra weak variational formulation through source extraction

The Ultra Weak Variational Formulation (UWVF) is a powerful numerical method for the approximation of acoustic, elastic and electromagnetic waves in the time-harmonic regime. The use of Trefftz-type basis functions incorporates the known wave-like behaviour of the solution in the discrete space, allowing large reductions in the required number of degrees of freedom for a given accuracy, when compared to standard finite element methods. However, the UWVF is not well disposed to the accurate approximation of singular sources in the interior of the computational domain. We propose an adjustment to the UWVF for seismic imaging applications, which we call the Source Extraction UWVF. Differing fields are solved for in subdomains around the source, and matched on the inter-domain boundaries. Numerical results are presented for a domain of constant wavenumber and for a domain of varying sound speed in a model used for seismic imaging.

Variational data assimilation for very large environmental problems

Variational data assimilation is commonly used in environmental forecasting to estimate the current state of the system from a model forecast and observational data. The assimilation problem can be written simply in the form of a nonlinear least squares optimization problem. However the practical solution of the problem in large systems requires many careful choices to be made in the implementation. In this article we present the theory of variational data assimilation and then discuss in detail how it is implemented in practice. Current solutions and open questions are discussed.

Only connect: an annotated bibliography reflecting the breadth and diversity of systems thinking

The field of systems thinking is both broad and diverse. This paper tries to provide assistance to outsiders wishing to find out what systems thinking is and also to insiders interested in exploring areas of the systems movement other than their own. A selection of books, papers and articles is given. Each has a full reference and a brief annotation, this being an account of, and a critical comment on, its content. The selection does not aim to be definitive or authoritative and obviously displays the predilections of the authors. However, the hope is that it will convey a sense of the intellectual and practical endeavours that, to the authors, constitute systems thinking and that it may aid the exploration of the range of holistic ideas that people have found useful in thinking about and acting in the world.

Trying to think systematically about 'systems thinking'

I noticed with interest that Peter Checkland has now contributed' to the debate on the use of the term 'systems thinking' in a paper by Eric Wolstenholme2. However, due to the self-confessed lag in his reading schedule, Peter is responding to the original piece and not to any of the subsequent observations on it3'4 (although he is kind enough to reference some of my other work on the matter).

Whole life thinking and engineering the future

Whole-life thinking for engineers working on the built environment has become more important in a fast changing world.Engineers are increasingly concerned with complex systems, in which the parts interact with each other and with the outside world in many ways – the relationships between the parts determine how the system behaves. Systems thinking provides one approach to developing a more robust whole life approach. Systems thinking is a process of understanding how things influence one another within a wider perspective. Complexity, chaos, and risk are endemic in all major projects. New approaches are needed to produce more reliable whole life predictions. Best value, rather than lowest cost can be achieved by using whole-life appraisal as part of the design and delivery strategy.

A variational approach to retrieve rain rate by combining information from rain gauges, radars, and microwave links

Accurate and reliable rain rate estimates are important for various hydrometeorological applications. Consequently, rain sensors of different types have been deployed in many regions. In this work, measurements from different instruments, namely, rain gauge, weather radar, and microwave link, are combined for the first time to estimate with greater accuracy the spatial distribution and intensity of rainfall. The objective is to retrieve the rain rate that is consistent with all these measurements while incorporating the uncertainty associated with the different sources of information. Assuming the problem is not strongly nonlinear, a variational approach is implemented and the Gauss–Newton method is used to minimize the cost function containing proper error estimates from all sensors. Furthermore, the method can be flexibly adapted to additional data sources. The proposed approach is tested using data from 14 rain gauges and 14 operational microwave links located in the Zürich area (Switzerland) to correct the prior rain rate provided by the operational radar rain product from the Swiss meteorological service (MeteoSwiss). A cross-validation approach demonstrates the improvement of rain rate estimates when assimilating rain gauge and microwave link information.

Discontinuous Galerkin methods for the p-biharmonic equation from a discrete variational perspective

We study discontinuous Galerkin approximations of the p-biharmonic equation for p∈(1,∞) from a variational perspective. We propose a discrete variational formulation of the problem based on an appropriate definition of a finite element Hessian and study convergence of the method (without rates) using a semicontinuity argument. We also present numerical experiments aimed at testing the robustness of the method.

Blending systems thinking approaches for organisational analysis: reviewing child protection in England

This paper concerns the innovative use of a blend of systems thinking ideas in the ‘Munro Review of Child Protection’, a high-profile examination of child protection activities in England, conducted for the Department for Education. We go ‘behind the scenes’ to describe the OR methodologies and processes employed. The circumstances that led to the Review are outlined. Three specific contributions that systems thinking made to the Review are then described. First, the systems-based analysis and visualisation of how a ‘compliance culture’ had grown up. Second the creation of a large, complex systems map of current operations and the effects of past policies on them. Third, how the map gave shape to the range of issues the Review addressed and acted as an organising framework for the systemically coherent set of recommendations made. The paper closes with an outline of the main implementation steps taken so far to create a child protection system with the critically reflective properties of a learning organisation, and methodological reflections on the benefits of systems thinking to support organisational analysis.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.