A study on boundary force model used in multiscale simulations with non-periodic boundary condition

This paper presents an investigation of the non-periodic boundary condition (NPBC) which is often used in multiscale atomistic–continuum simulations. The relationship between the boundary force exerted by the imaginary atoms outside the atomistic domain and the fluid state parameters including density and temperature at the boundary is studied. A fitting formula of the boundary force as a function of the fluid state has been proposed based on the relationship. The accuracy of the fitting formula is verified by the equilibrium molecular dynamics (MD) simulations. Poiseuille flow with viscous dissipation and unsteady heat transfer between two walls is then simulated using the proposed fitting formula. The elimination of density oscillation near the boundary of atomistic region and good agreement of velocity and temperature evolutions with time from pure MD and the multiscale simulations adopting NPBC further confirm the correctness of our fitting formula.     

A mixed interface finite element for cohesive zone models

The phenomena of crack initiation, propagation and ultimate fracture are studied here under the following assumptions: (i) the crack law is modelled by means of a cohesive zone model and (ii) the crack paths are postulated a priori. In this context, a variational formulation is proposed which relies on an augmented Lagrangian. A mixed interface finite element is introduced to discretise the crack paths, the degrees of freedom of which consist in the displacement on both crack lips and the density of cohesive forces. This enables an exact treatment of multi-valued cohesive laws (e.g. initial adhesion, contact conditions, possible rigid unloading, etc.), without penalty regularisation.A special attention is paid to the convergence with mesh-refinement, i.e. the well-posedness of the problem, on the basis of theoretical results of contact mechanics and some complementary numerical investigations. Fulfilment of the LBB condition is the key factor to gain the desired properties. Moreover, it is shown that the integration of the constitutive law admits a unique solution as soon as some condition on the augmented Lagrangian is enforced. Finally, a 3D simulation shows the applicability to practical engineer problems, including in particular the robustness of the formulation and its compatibility with classical solution algorithms (Newton method, line-search, path-following techniques).     

An examination of stability in cohesive zone modeling

Stable crack propagation hinges on the driving force and the resistance. In the context of a cohesive approach to fracture, properly resolving the cohesive zone ensures that the resistance is in equilibrium with the driving force. Additional restrictions on the mesh size can stem from crack stability. For high strength, low toughness (brittle) materials, the requirements for stability can exceed those for cohesive zone resolution. Examples in 1-D and 2-D reveal that decrements in the mesh size transition the system from indefinite to positive definite. Moreover, small decreases in the mesh size beyond the transition provide substantial reductions in the condition number. We contrast a physical instability resulting from material properties, geometry, or boundary conditions from a numerical instability resulting from the mesh size and propose that the selected discretization should ensure that the cohesive zone is both resolved and stabilized.     

An artificial neural network-based multiscale method for hybrid atomistic-continuum simulations

This paper presents an artificial neural network-based multiscale method for coupling continuum and molecular simulations. Molecular dynamics modelling is employed as a local “high resolution” refinement of computational data required by the continuum computational fluid dynamics solver. The coupling between atomistic and continuum simulations is obtained by an artificial neural network (ANN) methodology. The ANN aims to optimise the transfer of information through minimisation of (1) the computational cost by avoiding repetitive atomistic simulations of nearly identical states, and (2) the fluctuation strength of the atomistic outputs that are fed back to the continuum solver. Results are presented for prototype flows such as the isothermal Couette flow with slip boundary conditions and the slip Couette flow with heat transfer.     

A wavelet-based multiscale vector-ANN model to predict comovement of econophysical systems

The paper proposes a parsimonious nonlinear framework for modeling bivariate stochastic processes. The method is a vector autoregressive-like approach equipped with a wavelet-based feedforward neural network, allowing practitioners dealing with extremely random two-dimensional information to make predictions and plan their future more and more precisely. Artificial Neural Networks (ANN) are recognized as powerful computing devices and universal approximators that proved valuable for a wide range of univariate time series problems. We expand their coverage to handle nonlinear bivariate data. Wavelet techniques are used to strengthen the procedure, since they allow to break up processes information into a finite number of sub-signals, and subsequently extract microscopic patterns in both time and frequency fields. The proposed model can be very valuable especially when modeling nonlinear econophysical systems with high extent of volatility.     

Numerical studies of finite element variational multiscale methods for turbulent flow simulations

Different realizations of variational multiscale (VMS) methods within the framework of finite element methods are studied in turbulent channel flow simulations. One class of VMS methods uses bubble functions to model resolved small scales whereas the other class contains the definition of the resolved small scales by an explicit projection in its set of equations. All methods are employed with eddy viscosity models of Smagorinsky type. The simulations are performed on grids for which a Direct Numerical Simulation blows up in finite time.     

A parallel computational model for GATE simulations

GATE/Geant4 Monte Carlo simulations are computationally demanding applications, requiring thousands of processor hours to produce realistic results. The classical strategy of distributing the simulation of individual events does not apply efficiently for Positron Emission Tomography (PET) experiments, because it requires a centralized coincidence processing and large communication overheads. We propose a parallel computational model for GATE that handles event generation and coincidence processing in a simple and efficient way by decentralizing event generation and processing but maintaining a centralized event and time coordinator. The model is implemented with the inclusion of a new set of factory classes that can run the same executable in sequential or parallel mode. A Mann–Whitney test shows that the output produced by this parallel model in terms of number of tallies is equivalent (but not equal) to its sequential counterpart. Computational performance evaluation shows that the software is scalable and well balanced.     

Improving stability of stabilized and multiscale formulations in flow simulations at small time steps

The objective of this paper is to show that use of the element-vector-based definition of stabilization parameters, introduced in [T.E. Tezduyar, Computation of moving boundaries and interfaces and stabilization parameters, Int. J. Numer. Methods Fluids 43 (2003) 555–575; T.E. Tezduyar, Y. Osawa, Finite element stabilization parameters computed from element matrices and vectors, Comput. Methods Appl. Mech. Engrg. 190 (2000) 411–430], circumvents the well-known instability associated with conventional stabilized formulations at small time steps. We describe formulations for linear advection–diffusion and incompressible Navier–Stokes equations and test them on three benchmark problems: advection of an L-shaped discontinuity, laminar flow in a square domain at low Reynolds number, and turbulent channel flow at friction-velocity Reynolds number of 395.     

Digital marbling: a multiscale fluid model

This paper presents a multiscale fluid model based on mesoscale dynamics and viscous fluid equations as a generic tool for digital marbling purposes. The model uses an averaging technique on the adaptation of a stochastic mesoscale model to obtain the effect of fluctuations at different levels. It allows various user controls to simulate complex flow behaviors as in traditional marbling techniques, as well as laminar and turbulent flows. Material transport is based on an improved advection solution to be able to match the highly detailed, sharp fluid interfaces in marbling patterns. In the transport model, two reaction models are introduced to create different effects and to simulate density fluctuations.     

A GPU-assisted hybrid model for real-time crowd simulations

In this paper, we propose two new techniques for real-time crowd simulations; the first one is the clustering of agents on the GPU and the second one is incorporating the global cluster information into the existing microscopic navigation technique. The proposed model combines the agent-based models with macroscopic information (agent clusters) into a single framework. The global cluster information is determined on the GPU, and based on the agents' positions and velocities. Then, this information is used as input for the existing agent-based models (velocity obstacles, rule-based steering and social forces). The proposed hybrid model not only considers the nearby agents but also the distant agent configurations. Our test scenarios indicate that, in very dense circumstances, agents that use the proposed hybrid model navigate the environment with actual speeds closer to their intended speeds (less stuck) than the agents that are using only the agent-based models.     

EULAG, a computational model for multiscale flows

EULAG (Eulerian/semi-Lagrangian fluid solver) is an established computational model for simulating thermo-fluid flows across a wide range of scales and physical scenarios. It is noteworthy for its nonoscillatory integration algorithms, robust elliptic solver, and generalized coordinate formulation enabling grid adaptivity technology. In this paper we highlight the key model ingredients, demonstrate its capabilities with a select subset of recent applications, and show its performance both in terms of accuracy and scalability on massively parallel processor architectures. A comprehensive list of references is provided to facilitate more detailed study.     

The multiscale veto model: A two-stage analog network for edge detection and image reconstruction

This article presents the theory behind a model for a two-stage analog network for edge detection and image reconstruction to be implemented in analog VLSI. Edges are detected in the first stage using the multiscale veto rule, which states that an edge exists only if it can pass a threshold test for each of a set of smoothing filters of decreasing bandwidth. The image is reconstructed in the second stage from the brightness values at the pixels between which edges occur. The effect of the multiscale veto rule is that noise is removed with the efficiency of the narrowest-band smoothing filter, while edges are well-localized to feature boundaries without having to identify maxima in the magnitude of the gradient. Unlike previous analog models for edge detection and reconstruction, there are no problems of local minima, and for any given set of parameters, there is a unique solution. The reconstructed images appear natural and are very similar visually to the originals.     

Variational multiscale large-eddy simulations of the flow past a circular cylinder: Reynolds number effects

Variational multiscale large-eddy simulations (VMS–LES) of the flow around a circular cylinder are carried out at different Reynolds numbers in the subcritical regime, viz. Re = 3900, 10,000 and 20,000, based on the cylinder diameter. A mixed finite-element/finite-volume discretization on unstructured grids is used. The separation between the largest and the smallest resolved scales is obtained through a variational projection operator and finite-volume cell agglomeration. The WALE subgrid scale model is used to account for the effects of the unresolved scales; in the VMS approach, it is only added to the smallest resolved ones. The capability of this methodology to accurately predict the aerodynamic forces acting on the cylinder and in capturing the flow features are evaluated for the different Reynolds numbers considered. The sensitivity of the results to different simulation parameters, viz. agglomeration level and numerical viscosity, is also investigated at Re = 20,000.     

A multiscale assembly inspection algorithm

An important aspect of robust automated assembly is an accurate and efficient method for the inspection of finished assemblies. This novel algorithm is trained on synthetic images generated using the CAD model of the different components of the assembly. Once trained on synthetic images, the algorithm can detect assembly errors by examining real images of the assembled product     

A method for computation of surface roughness of digital elevation model terrains via multiscale analysis

In this paper, an algorithm to compute surface roughness of digital elevation model (DEM) terrains via multiscale analysis is proposed. The algorithm employs the lifting scheme to generate multiscale DEMs. At each scale, the areas of pixels that are modified are computed. Granulometric analysis is employed to compute the average area of curvature regions in the terrain, and the average roughness of the terrain due the distribution of curvature regions. The selected case studies of the algorithm implementation demonstrated that the proposed algorithm provides a surface roughness parameter that is realistic with respect to the amplitudes and frequencies of the terrain, invariant with respect to rotation and translation, and has intuitive meaning. The algorithm allows for a good quantification of a region’s convexity/concavity over varying scales, distinguishing between shallow and deep incisions of valleys and ridges of the terrain, and hence, provides an accurate surface roughness parameter.     

A new grid-associated algorithm in the distributed hydrological model simulations

This paper presents a new grid-associated algorithm to improve the performance of a D8 algorithm based distributed hydrological model computation.The algorithm is based on the well known single-flow D8 algorithm of grid flow.This algorithm allocates calculation priorities according to the distance between the units and the outlet,then carries out the ergodic computations of the hydrological units according to the priority division.For the parallelized algorithm,a standard thread-level shared memory system f...     

A multiscale edge detection algorithm based on wavelet domain vector hidden Markov tree model

The wavelet analysis is an efficient tool for the detection of image edges. Based on the wavelet analysis, we present an unsupervised learning algorithm to detect image edges in this paper. A wavelet domain vector hidden Markov tree (WD-VHMT) is employed in our algorithm to model the statistical properties of multiscale and multidirectional (subband) wavelet coefficients of an image. With this model, each wavelet coefficient is viewed as an observation of its hidden state and the hidden state indicates if the wavelet coefficient belongs to an edge. The WD-VHMT model can be learned by an expectation-maximization algorithm. After the model is learned, we employ an extended Viterbi algorithm to uncover the hidden state sequences according to the maximum a posterior estimation. The experiment results of the edge detection for several images are provided to evaluate our algorithm.