A finite element method with mesh adaptivity for computing vortex states in fast-rotating Bose-Einstein condensates

Numerical computations of stationary states of fast-rotating Bose-Einstein condensates require high spatial resolution due to the presence of a large number of quantized vortices. In this paper we propose a low-order finite element method with mesh adaptivity by metric control, as an alternative approach to the commonly used high order (finite difference or spectral) approximation methods. The mesh adaptivity is used with two different numerical algorithms to compute stationary vortex states: an imaginary time propagation method and a Sobolev gradient descent method. We first address the basic issue of the choice of the variable used to compute new metrics for the mesh adaptivity and show that simultaneously refinement using the real and imaginary part of the solution is successful. Mesh refinement using only the modulus of the solution as adaptivity variable fails for complicated test cases. Then we suggest an optimized algorithm for adapting the mesh during the evolution of the solution towards the equilibrium state. Considerable computational time saving is obtained compared to uniform mesh computations. The new method is applied to compute difficult cases relevant for physical experiments (large nonlinear interaction constant and high rotation rates).Comment: to appear in J. Computational Physic

Functional adaptivity for digital library services in e-infrastructures: the gCube approach

We consider the problem of e-Infrastructures that wish to reconcile the generality of their services with the bespoke requirements of diverse user communities. We motivate the requirement of functional adaptivity in the context of gCube, a service-based system that integrates Grid and Digital Library technologies to deploy, operate, and monitor Virtual Research Environments defined over infrastructural resources. We argue that adaptivity requires mapping service interfaces onto multiple implementations, truly alternative interpretations of the same functionality. We then analyse two design solutions in which the alternative implementations are, respectively, full-fledged services and local components of a single service. We associate the latter with lower development costs and increased binding flexibility, and outline a strategy to deploy them dynamically as the payload of service plugins. The result is an infrastructure in which services exhibit multiple behaviours, know how to select the most appropriate behaviour, and can seamlessly learn new behaviours

Parameterization adaption for 3D shape optimization in aerodynamics

When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an explicit geometrical representation, it is natural to seek for an analogous concept of parameterization adaptivity. We propose here an adaptive parameterization for three-dimensional optimum design in aerodynamics by using the so-called "Free-Form Deformation" approach based on 3D tensorial B\'ezier parameterization. The proposed procedure leads to efficient numerical simulations with highly reduced computational costs