Over the last decade, deep learning (DL), a branch of machine learning, has experienced
rapid progress. Powerful tools for tasks that have been traditionally complex to automate …

Mathematical and numerical modelling of the cardiovascular system is a research topic that
has attracted remarkable interest from the mathematical community because of its intrinsic …

In the last 50 years there has been a tremendous progress in solving numerically the Navier-
Stokes equations using finite differences, finite elements, spectral, and even meshless …

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 …

The benchmarking case of flow past a circular cylinder at the Reynolds number (Re) of 3900
is computed with two open-source codes, OpenFOAM and Nektar++, which are based on …

Completely revised text focuses on use of spectral methods to solve boundary value,
eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational …

Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

In this paper, we review the recent development of phase-field models and their numerical
methods for multi-component fluid flows with interfacial phenomena. The models consist of a …

Spectral methods have long been popular in direct and large eddy simulation of turbulent
flows, but their use in areas with complex-geometry computational domains has historically …

Implicit-explicit (IMEX) linear multistep time-discretization schemes for partial differential
equations have proved useful in many applications. However, they tend to have undesirable …