A high dynamic range rendering pipeline for interactive applications

Realistic images can be computed at interactive frame rates for Computer Graphics applications. Meanwhile, High Dynamic Range (HDR) rendering has a growing success in video games and virtual reality applications, as it improves the image quality and the player’s immersion feeling. In this paper, we propose a new method, based on a physical lighting model, to compute in real time a HDR illumination in virtual environments. Our method allows to re-use existing virtual environments as input, and computes HDR images in photometric units. Then, from these HDR images, displayable 8-bit images are rendered with a tone mapping operator and displayed on a standard display device. The HDR computation and the tone mapping are implemented in OpenSceneGraph with pixel shaders. The lighting model, together with a perceptual tone mapping, improves the perceptual realism of the rendered images at low cost. The method is illustrated with a practical application where the dynamic range of the virtual environment is a key rendering issue: night-time driving simulation.     

Rejewski’s equations: Solving for the entry permutation

In 1932, Marian Rejewski, who was a young mathematician working at the Polish Cipher Bureau, brilliantly recovered the internal wiring of the military Enigma. His initial efforts were unsuccessful because he assumed that the entry permutation was the same as in the commercial machine. Luckily he tried the identity permutation as an alternative and that proved to be correct. This note describes how Rejewski’s equations may be used to deduce the entry permutation without any guesswork, a technique that was later rediscovered by Alan Turing and by Lieutenant Andrew Gleason.     

Performance and Comparison of Cell-Centered and Node-Centered Unstructured Finite Volume Discretizations for Shallow Water Free Surface Flows

Finite volume (FV) methods for solving the two-dimensional (2D) nonlinear shallow water equations (NSWE) with source terms on unstructured, mostly triangular, meshes are known for some time now. There are mainly two basic formulations of the FV method: node-centered (NCFV) and cell-centered (CCFV). In the NCFV formulation the finite volumes, used to satisfy the integral form of the equations, are elements of the mesh dual to the computational mesh, while for the CCFV approach the finite volumes are the mesh elements themselves. For both formulations, details are given of the development and application of a second-order well-balanced Godunov-type scheme, developed for the simulation of unsteady 2D flows over arbitrary topography with wetting and drying. The popular approximate Riemann solver of Roe is utilized to compute the numerical fluxes, while second-order spatial accuracy is achieved with a MUSCL-type reconstruction technique. The Green-Gauss (G-G) formulation for gradient computations is implemented for both formulations, in order to maintain a common framework. Two different stencils for the G-G gradient computations in the CCFV formulation are implemented and tested. An edge-based limiting procedure is applied for the control of the total variation of the reconstructed field. This limiting procedure is proved to be effective for the NCFV scheme but inadequate for the CCFV approach. As such, a simple but very effective modification to the reconstruction procedure is introduced that takes into account geometrical characteristics of the computational mesh. In addition, consistent well-balanced second-order discretizations for the topography source term treatment and the wet/dry front treatment are presented for both FV formulations, ensuring absolute mass conservation, along with a stable friction term treatment.     

A mixed formulation for the direct approximation of the control of minimal $$L^2$$-norm for linear type wave equations

This paper deals with the numerical computation of null controls for the wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. In [Cîndea, Fernández-Cara & Münch, Numerical controllability of the wave equation through primal methods and Carleman estimates, 2013], a so called primal method is described leading to a strongly convergent approximation of boundary controls: the controls minimize quadratic weighted functionals involving both the control and the state and are obtained by solving the corresponding optimality condition. In this work, we adapt the method to approximate the control of minimal square-integrable norm. The optimality conditions of the problem are reformulated as a mixed formulation involving both the state and its adjoint. We prove the well-posedeness of the mixed formulation (in particular the inf-sup condition) then discuss several numerical experiments. The approach covers both the boundary and the inner controllability. For simplicity, we present the approach in the one dimensional case.     

Positivity-Preserving Well-Balanced Arbitrary Lagrangian–Eulerian Discontinuous Galerkin Methods for the Shallow Water Equations

Journal of Scientific Computing - We present efficient numerical methods for solving a class of nonlinear Schrödinger equations involving a nonlocal potential. Such a nonlocal potential is...     

A conservative discontinuous Galerkin scheme for the 2D incompressible Navier–Stokes equations

In this paper we consider a conservative discretization of the two-dimensional incompressible Navier–Stokes equations. We propose an extension of Arakawa’s classical finite difference scheme for fluid flow in the vorticity–stream function formulation to a high order discontinuous Galerkin approximation. In addition, we show numerical simulations that demonstrate the accuracy of the scheme and verify the conservation properties, which are essential for long time integration. Furthermore, we discuss the massively parallel implementation on graphic processing units.     

Passive micromixers for applications in the microreactor and μTAS fields

An overview is given of current developments in micromixing technology, where the emphasis is on liquid mixing in passive micromixers. The mixers presented are differentiated by the hydrodynamic principle employed, and four important principles are discussed in some detail: hydrodynamic focusing, flow separation, chaotic advection, and split-and-recombine flows. It is shown that these principles offer excellent mixing performance in various dynamical regimes. Hydrodynamic focusing is a concept working very much independently of the Reynolds number of the flow. Flow separation offers rich dynamical behavior over a Reynolds number scale of several hundred, with superior performance compared to purely diffusive mixing already found at low Reynolds numbers. For chaotic advection, different implementations tailor-made for low and comparatively high Reynolds numbers exist, both leading to an exponential increase of the interface between two fluids. Split-and-recombine flows can only be realized in a close-to-ideal form in the low Reynolds number regime. Corresponding mixers can be equipped with comparatively wide channels, enabling a favorable ratio of throughput to pressure drop. The overview given in this article should enable a potential user of micromixing technology to select the most favorable concept for the application envisaged, especially in the field of chemical process technology     

Global robust output regulation control for cascaded nonlinear systems using the internal model principle

This article considers the global robust output regulation problem via output feedback for a class of cascaded nonlinear systems with input-to-state stable inverse dynamics. The system uncertainties depend not only on the measured output but also all the unmeasurable states. By introducing an internal model, the output regulation problem is converted into a stabilisation problem for an appropriately augmented system. The designed dynamic controller could achieve the global asymptotic tracking control for a class of time-varying reference signals for the system output while keeping all other closed-loop signals bounded. It is of interest to note that the developed control approach can be applied to the speed tracking control of the fan speed control system. The simulation results demonstrate its effectiveness.     

An improved regularity criterion for the 3D Hall–MHD equations via the vorticity

In this paper, we consider the three-dimensional incompressible Hall–magnetohydrodynamic equations, and establish an improved regularity criterion of local in time classical solutions involving only the vorticity field. Consequently, this improves the previous result.     

LDG2: A Variant of the LDG Flux Formulation for the Spectral Volume Method

The local discontinuous Galerkin (LDG) viscous flux formulation was originally developed by Cockburn and Shu for the discontinuous Galerkin setting and later extended to the spectral volume setting by Wang and his collaborators. Unlike the penalty formulations like the interior penalty and the BR2 schemes, the LDG formulation requires no length based penalizing terms and is compact. However, computational results using LDG are dependant of the orientation of the faces especially for unstructured and non uniform grids. This results in lower solution accuracy and stiffer stability constraints as shown by Kannan and Wang. In this paper, we develop a variant of the LDG, which not only retains its attractive features, but also vastly reduces its unsymmetrical nature. This variant (aptly named LDG2), displayed higher accuracy than the LDG approach and has a milder stability constraint than the original LDG formulation. In general, the 1D and the 2D numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.     

JavaFit: A platform independent program for interactive nonlinear least-squares fitting using the Levenberg—Marquardt method

The JavaFit program is a package for carrying out interactive nonlinear least-squares fitting to determine the parameters of physical models from experimental data. It has been conceived as a platform independent package aimed at the relatively modest computational needs of spectroscopists, where it is often necessary to determine physical parameters from a variety of spectral lineshape models. The program is platform independent, provided that a Java runtime module is available for the host platform. The program is also designed to read a wide variety of data in ASCII column formats produced on DOS, Macintosh and UNIX platforms.     

Optimal vorticity accuracy in an efficient velocity–vorticity method for the 2D Navier–Stokes equations

We study a velocity–vorticity scheme for the 2D incompressible Navier–Stokes equations, which is based on a formulation that couples the rotation form of the momentum equation with the vorticity equation, and a temporal discretization that stably decouples the system at each time step and allows for simultaneous solving of the vorticity equation and velocity–pressure system (thus if special care is taken in its implementation, the method can have no extra cost compared to common velocity–pressure schemes). This scheme was recently shown to be unconditionally long-time \(H^1\) stable for both velocity and vorticity, which is a property not shared by any common velocity–pressure method. Herein, we analyze the scheme’s convergence, and prove that it yields unconditional optimal accuracy for both velocity and vorticity, thus making it advantageous over common velocity–pressure schemes if the vorticity variable is of interest. Numerical experiments are given that illustrate the theory and demonstrate the scheme’s usefulness on some benchmark problems.     

The local discontinuous Galerkin method for 2D nonlinear time-fractional advection–diffusion equations

This paper presents a numerical solution of time-fractional nonlinear advection–diffusion equations (TFADEs) based on the local discontinuous Galerkin method. The trapezoidal quadrature scheme (TQS) for the fractional order part of TFADEs is investigated. In TQS, the fractional derivative is replaced by the Volterra integral equation which is computed by the trapezoidal quadrature formula. Then the local discontinuous Galerkin method has been applied for space-discretization in this scheme. Additionally, the stability and convergence analysis of the proposed method has been discussed. Finally some test problems have been investigated to confirm the validity and convergence of the proposed method.

     

A path reflectance correction for improved cloud detection using the VIIRS 412 nm band

Satellite data collected in the ultraviolet region of the electromagnetic spectrum have proven useful in the detection of clouds over desert backgrounds and in the discrimination between clouds and heavy aerosols over ocean surfaces. However, both of these applications within the Visible Infrared Imager Radiometer Suite (VIIRS) cloud mask (VCM) algorithm exploiting data collected in the 412 nm band were found to demonstrate a scan angle dependence that corresponds to variations in path reflectance caused by Rayleigh (i.e. molecular) scattering in this bandpass. As a consequence, it became necessary to correct the calibrated VIIRS 412 nm reflectances for molecular path reflectance prior to applying the logic previously described in earlier publications. The new procedures developed to make this path reflectance correction are presented in this article, along with results created using the VCM algorithm with and without those corrections being applied to the VIIRS observations. VCM performance is based upon comparisons to manually generated cloud masks created from VIIRS imagery. It is concluded that a correction for path reflectance variations is needed to fully exploit the cloud detection and typing algorithms within the VCM algorithm that exploit data collected in this 412 nm VIIRS band.     

Operator-splitting methods for the 2D convective Cahn–Hilliard equation

In this work, we present operator-splitting methods for the two-dimensional nonlinear fourth-order convective Cahn–Hilliard equation with specified initial condition and periodic boundary conditions. The full problem is split into hyperbolic, nonlinear diffusion and linear fourth-order problems. We prove that the semi-discrete approximate solution obtained from the operator-splitting method converges to the weak solution. Numerical methods are then constructed to solve each sub equations sequentially. The hyperbolic conservation law is solved by efficient finite volume methods and dimensional splitting method, while the one-dimensional hyperbolic conservation laws are solved using front tracking algorithm. The front tracking method is based on the exact solution and hence has no stability restriction on the size of the time step. The nonlinear diffusion problem is solved by a linearized implicit finite volume method, which is unconditionally stable. The linear fourth-order equation is solved using a pseudo-spectral method, which is based on an exact solution. Finally, some numerical experiments are carried out to test the performance of the proposed numerical methods.     

SENFIS: a Sensor Node File System for increasing the scalability and reliability of Wireless Sensor Networks applications

In the last years the Wireless Sensor Networks’ (WSN) technology has been increasingly employed in various application domains. The extensive use of WSN posed new challenges in terms of both scalability and reliability. This paper proposes Sensor Node File System (SENFIS), a novel file system for sensor nodes, which addresses both scalability and reliability concerns. SENFIS can be mainly used in two broad scenarios. First, it can transparently be employed as a permanent storage for distributed TinyDB queries, in order to increase the reliability and scalability. Second, it can be directly used by a WSN application for permanent storage of data on the WSN nodes. The experimental section shows that SENFIS implementation makes an efficient use of resources in terms of energy consumption, memory footprint, flash wear levelling, while achieving execution times similarly with existing WSN file systems.     

Unconditional convergence and optimal L2 error estimates of the Crank–Nicolson extrapolation FEM for the nonstationary Navier–Stokes equations

In this paper, we study stability and convergence of fully discrete finite element method on large timestep which used Crank–Nicolson extrapolation scheme for the nonstationary Navier–Stokes equations. This approach bases on a finite element approximation for the space discretization and the Crank–Nicolson extrapolation scheme for the time discretization. It reduces nonlinear equations to linear equations, thus can greatly increase the computational efficiency. We prove that this method is unconditionally stable and unconditionally convergent. Moreover, taking the negative norm technique, we derive the $L^2$, $H^1$-unconditionally optimal error estimates for the velocity, and the $L^2$-unconditionally optimal error estimate for the pressure. Also, numerical simulations on unconditional$L^2$-stability and convergent rates of this method are shown.