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Keywords: High-order finite elements Spectral/hp elements Continuous Galerkin method Discontinuous Galerkin method FEM a b s t r a c t Nektar++ is an open-source software framework designed to support the development of high-performance scalable solvers for partial differential equations using the spectral/hp element method. High-order methods are gaining(More)
OBJECTIVES The aim was to measure changes in walking patterns and self rated fatigue in people with multiple sclerosis (MS) compared with age matched control subjects, from the morning to the afternoon within a single day. METHODS Fourteen patients with MS and the same number of matched control subjects performed four 10 m gait trials at their preferred(More)
SUMMARY We demonstrate that radically differing implementations of finite element methods are needed on multi-core (CPU) and many-core (GPU) architectures, if their respective performance potential is to be realised. Our experimental investigations using a finite element advection-diffusion solver show that increased performance on each architecture can(More)
A spectral/hp element discretisation permits both geometric flexibility and beneficial convergence properties to be attained simultaneously. The choice of elemental polynomial order has a profound effect on the efficiency of different implementation strategies with their performance varying substantially for low and high order spectral/hp discretisations.(More)
From h to p efficiently: selecting the optimal spectral/hp discretisation in three dimensions Abstract. There is a growing interest in high-order finite and spectral/hp element methods using Continuous and Discontinuous Galerkin formulations. In this paper we investigate the effect of hand P-type refinement on the relationship between runtime performance(More)
There is a growing interest in high-order finite and spectral/ℎℎ element methods using continuous and discontinuous Galerkin formulations. In this paper we investigate the effect of ℎ-and-type refinement on the relationship between runtime performance and solution accuracy. The broad spectrum of possible domain discretisations makes establishing a(More)
We present a numerical discretisation of an embedded two-dimensional manifold using high-order continuous Galerkin spectral/hp elements, which provide exponential convergence of the solution with increasing polynomial order, while retaining geometric flexibility in the representation of the domain. Our work is motivated by applications in cardiac(More)
—As the capabilities of computational platforms continue to grow, scientific software is becoming ever more complex in order to target these platforms effectively. When using large-scale distributed infrastructure such as clusters and clouds it can be difficult for end-users to make efficient use of these platforms. In the libhpc project we are developing a(More)
Developing software to undertake complex, compute-intensive scientific processes requires a challenging combination of both specialist domain knowledge and software development skills to convert this knowledge into efficient code. As computational platforms become increasingly heterogeneous and newer types of platform such as Infrastructure-as-a-Service(More)
Measurements of cardiac conduction velocity provide valuable functional and structural insight into the initiation and perpetuation of cardiac arrhythmias, in both a clinical and laboratory context. The interpretation of activation wavefronts and their propagation can identify mechanistic properties of a broad range of electrophysiological pathologies.(More)