Research My research area is the study of novel computational algorithms for the numerical solution of partial differential equations (p.d.e.s). This area is part of the emerging discipline of Scientific Computing, and is, perhaps, one of its most challenging components. The physical problems that are modelled by p.d.e.s are of great importance to a wide range of both industrial and academic research groups. Examples range from being able to design better harbours to understanding environmental pollution or modelling the behaviour of lubricants in a car engine. The focus of my research has been on two important classes of p.d.e.s - parabolic and hyperbolic systems of equations, the solutions to which depend on both space and time. The new algorithms and the associated software have resulted have then been used as part of successful interdisciplinary academic collaborations and, through the Computational PDEs Unit at Leeds (CPDE Unit), with industry, most notably Shell Research (now Shell Global Solutions). The approach I have taken in this research has been to derive numerical methods and develop software on both serial and parallel computers for a broad, mathematically-defined problem class using the Method of Lines in which the equations are decoupled in space and time. This has made it possible for users from different physical applications areas to solve their problems by creating a mathematical model which fits inside the general problem class. The key aspects of my work have been to:
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