a b s t r a c tNektar++ is an open-source software framework designed to support the development of highperformance scalable solvers for partial differential equations using the spectral/hp element method. High-order methods are gaining prominence in several engineering and biomedical applications due to their improved accuracy over low-order techniques at reduced computational cost for a given number of degrees of freedom. However, their proliferation is often limited by their complexity, which makes these methods challenging to implement and use. Nektar++ is an initiative to overcome this limitation by encapsulating the mathematical complexities of the underlying method within an efficient C++ framework, making the techniques more accessible to the broader scientific and industrial communities. The software supports a variety of discretisation techniques and implementation strategies, supporting methods research as well as application-focused computation, and the multi-layered structure of the framework allows the user to embrace as much or as little of the complexity as they need. The libraries capture the mathematical constructs of spectral/hp element methods, while the associated collection of pre-written PDE solvers provides out-of-the-box application-level functionality and a template for users who wish to develop solutions for addressing questions in their own scientific domains.
Program summaryProgram title: Nektar++
Catalogue identifier: AEVV_v1_0Program summary URL:
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. However, the sparsity, distribution and uncertainty of recorded data make accurate conduction velocity calculation difficult. A wide range of mathematical approaches have been proposed for addressing this challenge, often targeted towards specific data modalities, species or recording environments. Many of these algorithms require identification of activation times from electrogram recordings which themselves may have complex morphology or low signal-to-noise ratio. This paper surveys algorithms designed for identifying local activation times and computing conduction direction and speed. Their suitability for use in different recording contexts and applications is assessed.
Results are presented from a numerical study of transient growth experienced by infinitesimal perturbations to flow in an axisymmetric pipe with a sudden 1-2 diametral expansion. First, the downstream reattachment point of the steady laminar flow is accurately determined as a function of Reynolds number and it is established that the flow is linearly stable at least up to Re=1400. A direct method is used to calculate the optimal transient energy growth for specified time horizon tau, Re up to 1200, and low-order azimuthal wavenumber m. The critical Re for the onset of growth with different m is determined. At each Re the maximum growth is found in azimuthal mode m=1 and this maximum is found to increase exponentially with Re. The time evolution of optimal perturbations is presented and shown to correspond to sinuous oscillations of the shear layer. Suboptimal perturbations are presented and discussed. Finally, direct numerical simulation in which the inflow is perturbed by Gaussian white noise confirms the presence of the structures determined by the transient growth analysis. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3313931
Patient-specific cardiac models are now being used to guide therapies. The increased use of patient-specific cardiac simulations in clinical care will give rise to the development of virtual cohorts of cardiac models. These cohorts will allow cardiac simulations to capture and quantify inter-patient variability. However, the development of virtual cohorts of cardiac models will require the transformation of cardiac modelling from small numbers of bespoke models to robust and rapid workflows that can create large numbers of models. In this review, we describe the state of the art in virtual cohorts of cardiac models, the process of creating virtual cohorts of cardiac models, and how to generate the individual cohort member models, followed by a discussion of the potential and future applications of virtual cohorts of cardiac models.This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.