Robust a priori and a posteriori error analysis for the approximation of Allen–Cahn and Ginzburg–Landau equations past topological changes

A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter and to the validity of the estimates in the presence of topological changes in the solution that represents singular points in the evolution. For typical singularities the estimates depend on the inverse of the parameter in a polynomial as opposed to exponential dependence of estimates resulting from a straightforward error analysis. The estimates naturally lead to adaptive mesh refinement and coarsening algorithms. Numerical experiments illustrate the reliability and efficiency of this approach for the evolution of interfaces and vortices that undergo topological changes

Look No Further: Adapting the Localization Sensory Window to the Temporal Characteristics of the Environment

Many localization algorithms use a spatiotemporal window of sensory information in order to recognize spatial locations, and the length of this window is often a sensitive parameter that must be tuned to the specifics of the application. This letter presents a general method for environment-driven variation of the length of the spatiotemporal window based on searching for the most significant localization hypothesis, to use as much context as is appropriate but not more. We evaluate this approach on benchmark datasets using visual and Wi-Fi sensor modalities and a variety of sensory comparison front-ends under in-order and out-of-order traversals of the environment. Our results show that the system greatly reduces the maximum distance traveled without localization compared to a fixed-length approach while achieving competitive localization accuracy, and our proposed method achieves this performance without deployment-time tuning.Comment: Pre-print of article appearing in 2017 IEEE Robotics and Automation Letters. v2: incorporated reviewer feedbac

Output feedback NN control for two classes of discrete-time systems with unknown control directions in a unified approach

10.1109/TNN.2008.2003290IEEE Transactions on Neural Networks19111873-1886ITNN

Fully-Coupled Simulation of Cosmic Reionization. I: Numerical Methods and Tests

We describe an extension of the Enzo code to enable fully-coupled radiation hydrodynamical simulation of inhomogeneous reionization in large $\sim (100 Mpc)^3$ cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. Radiation transport is done in the grey flux-limited diffusion (FLD) approximation, which is solved by implicit time integration split off from the gas energy and ionization equations, which are solved separately. This results in a faster and more robust scheme for cosmological applications compared to the earlier method. The FLD equation is solved using the hypre optimally scalable geometric multigrid solver from LLNL. By treating the ionizing radiation as a grid field as opposed to rays, our method is scalable with respect to the number of ionizing sources, limited only by the parallel scaling properties of the radiation solver. We test the speed and accuracy of our approach on a number of standard verification and validation tests. We show by direct comparison with Enzo's adaptive ray tracing method Moray that the well-known inability of FLD to cast a shadow behind opaque clouds has a minor effect on the evolution of ionized volume and mass fractions in a reionization simulation validation test. We illustrate an application of our method to the problem of inhomogeneous reionization in a 80 Mpc comoving box resolved with $3200^3$ Eulerian grid cells and dark matter particles.Comment: 32 pages, 23 figures. ApJ Supp accepted. New title and substantial revisions re. v

An exploration of the IGA method for efficient reservoir simulation

Novel numerical methods present exciting opportunities to improve the efficiency of reservoir simulators. Because potentially significant gains to computational speed and accuracy may be obtained, it is worthwhile explore alternative computational algorithms for both general and case-by-case application to the discretization of the equations of porous media flow, fluid-structure interaction, and/or production. In the present work, the fairly new concept of isogeometric analysis (IGA) is evaluated for its suitability to reservoir simulation via direct comparison with the industry standard finite difference (FD) method and 1st order standard finite element method (SFEM). To this end, two main studies are carried out to observe IGA’s performance with regards to geometrical modeling and ability to capture steep saturation fronts. The first study explores IGA’s ability to model complex reservoir geometries, observing L2 error convergence rates under a variety of refinement schemes. The numerical experimental setup includes an 'S' shaped line sink of varying curvature from which water is produced in a 2D homogenous domain. The accompanying study simplifies the domain to 1D, but adds in multiphase physics that traditionally introduce difficulties associated with modeling of a moving saturation front. Results overall demonstrate promise for the IGA method to be a particularly effective tool in handling geometrically difficult features while also managing typically challenging numerical phenomena.Petroleum and Geosystems Engineerin