Enhanced goal-oriented error assessment and computational strategies in adaptive reduced basis solver for stochastic problems

This work focuses on providing accurate low-cost approximations of stochastic ¿nite elements simulations in the framework of linear elasticity. In a previous work, an adaptive strategy was introduced as an improved Monte-Carlo method for multi-dimensional large stochastic problems. We provide here a complete analysis of the method including a new enhanced goal-oriented error estimator and estimates of CPU (computational processing unit) cost gain. Technical insights of these two topics are presented in details, and numerical examples show the interest of these new developments.Postprint (author's final draft

Feedback control of inertial microfluidics using axial control forces

Inertial microfluidics is a promising tool for many lab-on-a-chip applications. Particles in channel flows with Reynolds numbers above one undergo cross-streamline migration to a discrete set of equilibrium positions in square and rectangular channel cross sections. This effect has been used extensively for particle sorting and the analysis of particle properties. Using the lattice Boltzmann method, we determine equilibrium positions in square and rectangular cross sections and classify their types of stability for different Reynolds numbers, particle sizes, and channel aspect ratios. Our findings thereby help to design microfluidic channels for particle sorting. Furthermore, we demonstrate how an axial control force, which slows down the particles, shifts the stable equilibrium position towards the channel center. Ultimately, the particles then stay on the centerline for forces exceeding a threshold value. This effect is sensitive to particle size and channel Reynolds number and therefore suggests an efficient method for particle separation. In combination with a hysteretic feedback scheme, we can even increase particle throughput

One machine, one minute, three billion tetrahedra

This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A simple dedicated data structure, an efficient sorting of the points and the optimization of the insertion algorithm have permitted to accelerate reference implementations by a factor three. Our second contribution is a multi-threaded version of the Delaunay kernel that is able to concurrently insert vertices. Moore curve coordinates are used to partition the point set, avoiding heavy synchronization overheads. Conflicts are managed by modifying the partitions with a simple rescaling of the space-filling curve. The performances of our implementation have been measured on three different processors, an Intel core-i7, an Intel Xeon Phi and an AMD EPYC, on which we have been able to compute 3 billion tetrahedra in 53 seconds. This corresponds to a generation rate of over 55 million tetrahedra per second. We finally show how this very efficient parallel Delaunay triangulation can be integrated in a Delaunay refinement mesh generator which takes as input the triangulated surface boundary of the volume to mesh