Numerical experiments of some Krylov subspace methods for black oil model

This paper discusses preconditioned Krylov subspace methods for solving large scale linear systems that originate from oil reservoir numerical simulations. Two types of preconditioners, one being based on an incomplete LU decomposition and the other being based on iterative algorithms, are used together in a combination strategy in order to achieve an adaptive and efficient preconditioner. Numerical tests show that different Krylov subspace methods combining with appropriate preconditioners are able to achieve optimal performance.

Fostering 'habits of reflection, independent study and free inquiry': an analysis of the short-lived phenomenon of General/Liberal Studies in English vocational education and training

In 1957, 12 years after the end of World War II, the Ministry of Education issued Circular 323 to promote the development of an element of ‘liberal studies’ in courses offered by technical and further education (FE) colleges in England. This was perceived to be in some ways a peculiar or uncharacteristic development. However, it lasted over 20 years, during which time most students on courses in FE colleges participated in what were termed General or Liberal Studies classes that complemented and/or contrasted with the technical content of their vocational programmes. By the end of the 1970s, these classes had changed in character, moving away from the concept of a ‘liberal education’ towards a prescribed diet of ‘communication studies’. The steady decline in apprenticeship numbers from the late 1960s onwards accelerated in the late 1970s, resulting in a new type of student (the state-funded ‘trainee’) into colleges whose curriculum would be prescribed by the Manpower Services Commission. This paper examines the Ministry’s thinking and charts the rise and fall of a curriculum phenomenon that became immortalised in the ‘Wilt’ novels of Tom Sharpe. The paper argues that the Ministry of Education’s concerns half a century ago are still relevant now, particularly as fresh calls are being made to raise the leaving age from compulsory education to 18, and in light of attempts in England to develop new vocational diplomas for full-time students in schools and colleges.