From Longinus to Tolkien: A Theory of the Fantastic Sublime

As concepts, the fantastic and the sublime share much in common. Both have the power to take a reader outside the scope of his or her own worldview and experience, and both share the paradoxical power to both elevate and humble the human spirit. So it is surprising that few scholars have explored the intersection between these two constructs, and none has attempted to systematically explore how this intersection operates in the context of literary theory. This thesis endeavors to build a theoretical framework for the fantastic sublime by exploring its constituent parts. First, I examine the contribution of the ancient literary critic Longinus, whose basis of the sublime within language informs and infuses the entire concept of the fantastic sublime. Second, I undertake a close reading of J. R. R. Tolkien’s essay “On Fairy-Stories” to illustrate how Tolkien’s higher-order ideas about fantasy complement Longinus’s linguistic building blocks. Finally, I make the case that Romanticism, specifically the work and thought of Samuel Taylor Coleridge, is the ideological glue that binds the fantastic sublime together

Self-adaptive isogeometric spatial discretisations of the first and second-order forms of the neutron transport equation with dual-weighted residual error measures and diffusion acceleration

As implemented in a new modern-Fortran code, NURBS-based isogeometric analysis (IGA) spatial discretisations and self-adaptive mesh refinement (AMR) algorithms are developed in the application to the first-order and second-order forms of the neutron transport equation (NTE). These AMR algorithms are shown to be computationally efficient and numerically accurate when compared to standard approaches. IGA methods are very competitive and offer certain unique advantages over standard finite element methods (FEM), not least of all because the numerical analysis is performed over an exact representation of the underlying geometry, which is generally available in some computer-aided design (CAD) software description. Furthermore, mesh refinement can be performed within the analysis program at run-time, without the need to revisit any ancillary mesh generator. Two error measures are described for the IGA-based AMR algorithms, both of which can be employed in conjunction with energy-dependent meshes. The first heuristically minimises any local contributions to the global discretisation error, as per some appropriate user-prescribed norm. The second employs duality arguments to minimise important local contributions to the error as measured in some quantity of interest; this is commonly known as a dual-weighted residual (DWR) error measure and it demands the solution to both the forward (primal) and the adjoint (dual) NTE. Finally, convergent and stable diffusion acceleration and generalised minimal residual (GMRes) algorithms, compatible with the aforementioned AMR algorithms, are introduced to accelerate the convergence of the within-group self-scattering sources for scattering-dominated problems for the first and second-order forms of the NTE. A variety of verification benchmark problems are analysed to demonstrate the computational performance and efficiency of these acceleration techniques.Open Acces