Achieving Scalable Parallel Molecular Dynamics Using Dynamic Spatial Domain Decomposition Techniques

To achieve scalable parallel performance in molecular dynamics simulations, we have modeled and implemented several dynamic spatial domain decomposition algorithms. The modeling is based upon the bulk synchronous parallel architecture model (BSP), which describes supersteps of computation, communication, and synchronization. Using this model, we have developed prototypes that explore the differing costs of several spatial decomposition algorithms and then use this data to drive implementation of our molecular dynamics simulator,Sigma. The parallel implementation is not bound to the limitations of the BSP model, allowing us to extend the spatial decomposition algorithm. For an initial decomposition, we use one of the successful decomposition strategies from the BSP study and then subsequently use performance data to adjust the decomposition, dynamically improving the load balance. The motivating reason to use historical performance data is that the computation to predict a better decomposition increases in cost with the quality of prediction, while the measurement of past work often has hardware support, requiring only a slight amount of work to modify the decomposition for future simulation steps. In this paper, we present our adaptive spatial decomposition algorithms, the results of modeling them with the BSP, the enhanced spatial decomposition algorithm, and its performance results on computers available locally and at the national supercomputer centers.     

Recent Advances on Topology Optimization of Multiscale Nonlinear Structures

Research on topology optimization mainly deals with the design of monoscale structures, which are usually made of homogeneous materials. Recent advances of multiscale structural modeling enables the consideration of microscale material heterogeneities and constituent nonlinearities when assessing the macroscale structural performance. However, due to the modeling complexity and the expensive computing requirement of multiscale modeling, there has been very limited research on topology optimization of multiscale nonlinear structures. This paper reviews firstly recent advances made by the authors on topology optimization of multiscale nonlinear structures, in particular techniques regarding to nonlinear topology optimization and computational homogenization (also known as FE²) are summarized. Then the conventional concurrent material and structure topology optimization design approaches are reviewed and compared with a recently proposed FE²-based design approach, which treats the microscale topology optimization process integrally as a generalized nonlinear constitutive behavior. In addition, discussions on the use of model reduction techniques is provided in regard to the prohibitive computational cost.     

Efficient Parallel Solution of Nonlinear Parabolic Partial Differential Equations by a Probabilistic Domain Decomposition

Initial- and initial-boundary value problems for nonlinear one-dimensional parabolic partial differential equations are solved numerically by a probabilistic domain decomposition method. This is based on a probabilistic representation of solutions by means of branching stochastic processes. Only few values of the solution inside the space-time domain are generated by a Monte Carlo method, and an interpolation is then made so to approximate suitable interfacial values of the solution inside the domain. In this way, a fully decoupled set of sub-problems is obtained. This method allows for an efficient massively parallel implementation, is scalable and fault tolerant. Numerical examples, including some for the KPP equation and beyond are given to show the performance of the algorithm.     

A Domain Decomposition Method Based on Natural Boundary Reduction for Nonlinear Time-Dependent Exterior Wave Problems

Received October 10, 2000; revised August 15, 2001 Published online February 18, 2002     

Degenerate Two-Phase Incompressible Flow IV: Local Refinement and Domain Decomposition

This is the fourth paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media. In this paper we describe a finite element approximation for this system on locally refined grids. This adaptive approximation is based on a mixed finite element method for the elliptic pressure equation and a Galerkin finite element method for the degenerate parabolic saturation equation. Both discrete stability and sharp a priori error estimates are established for this approximation. Iterative techniques of domain decomposition type for solving it are discussed, and numerical results are presented.     

基于物理信息的神经网络:最新进展与展望

基于物理信息的神经网络(Physics-informed Neural Networks,PINN),是一类用于解决有监督学习任务的神经网络,它不仅尽力遵循训练数据样本的分布规律,而且遵守由偏微分方程描述的物理定律.与纯数据驱动的神经网络学习相比,PINN在训练过程中施加了物理信息约束,因此能用更少的数据样本学习得到更...     

Crowd Simulation and Its Applications: Recent Advances

This article surveys the state-of-the-art crowd simulation techniques and their selected applications, with its focus on our recent research advances in this rapidly growing research field. We first give a categorized overview on the mainstream methodologies of crowd simulation. Then, we describe our recent research advances on crowd evacuation,pedestrian crowds, crowd formation, traffic simulation, and swarm simulation. Finally, we offer our viewpoints on open crowd simulation research challenges and point out potential future directions in this field.     

Guest Editorial: Road Pricing Problems: Recent Methodological Advances

Networks and Spatial Economics -     

The approximate Dirichlet Domain Decomposition method. Part I: An algebraic approach

We present a new approach to the construction of Domain Decomposition (DD) preconditioners for the conjugate gradient method applied to the solution of symmetric and positive definite finite element equations. The DD technique is based on a non-overlapping decomposition of the domain Ω intop subdomains connected later with thep processors of a MIMD computer. The DD preconditioner derived contains three block matrices which must be specified for the specific problem considered. One of the matrices is used for the transformation of the nodal finite element basis into the approximate discrete harmonic basis. The other two matrices are block preconditioners for the Dirichlet problems arising on the subdomains and for a modified Schur complement defined over all nodes on the coupling boundaries between the subdomains. The relative spectral condition number is estimated. Relations to the additive Schwarz method are discussed. In the second part of this paper, we will apply the results of this paper to two-dimensional, symmetric, second-order, elliptic boundary value problems and present numerical results performed on a transputer-network.     

神经形态视觉传感器的研究进展及应用综述

神经形态视觉传感器具有高时域分辨率、高动态范围、低数据冗余和低功耗等优势,近年来在自动驾驶、无人机视觉导航、工业检测及视觉监控等领域(尤其在涉及高速运动和极端光照等条件下)产生了巨大的应用前景.神经形态视觉是一个包含硬件、软件、生物神经模型等的视觉感知系统,终极目标是模拟生物视觉感知结构与机理,以硅视网膜达到、扩展或超...     

Spectral Element Methods on Unstructured Meshes: Comparisons and Recent Advances

Spectral element approximations for triangles are not yet as mature as for quadrilaterals. Here we compare different algorithms and show that using an integration rule based on Gauss-points for simplices is of interest. We point out that this can be handled efficiently and allows to recover the convergence rate theoretically expected, even with curved elements.     

Computational Logic in Multi-Agent Systems: Recent Advances and Future Directions

Starting from the early days of multi-agent systems research, considerable effort has been devoted to giving formal foundations to agent technologies. Work done in this direction, based on computational logic, is an attempt to bridge an existing gap, between theoretical frameworks and their practical implementations. In the last two editions of the workshop on Computational Logic in Multi-Agent Systems, CLIMA'01 and CLIMA'02, two discussion panels have been organized, aimed at bringing researchers together and exchanging ideas on a number of topics. In this article, we elaborate on the outcome of such panels, to draw some considerations about the recent advances and future directions of Computational Logic in Multi-Agent Systems.     

产品协同设计的任务分解与耦合机制研究

在产品协同设计的初始阶段,合理的任务分解有利于协同设计的顺利进行,从而提高设计效率与质量。文章研究了任务的分解与耦合策略,采用按功能划分和按结构划分相结合的方式,并根据设计组的满意度对产品协同设计的任务进行了分解,用设计结构矩阵描述设计任务的耦合关系,提出了利用图论中基于邻接矩阵的深度优先搜索算法求出耦合任务集的原理与方法,并通过具体实例验证了该方法。     

Numerical Integrations and Unit Resolution Multipliers for Domain Decomposition Methods with Nonmatching Grids

In this paper, we are concerned with the non-overlapping domain decomposition method (DDM) with nonmatching grids for three-dimensional problems. The weak continuity of the DDM solution on the interface is imposed by some Lagrange multiplier. We shall first analyze the influence of the numerical integrations over the interface on the (non-conforming) approximate solution. Then we will propose a simple approach to construct multiplier spaces, one of which can be simply spanned by some smooth basis functions with local compact supports, and thus makes the numerical integrations on the interface rather simple and inexpensive. Also it is shown this multiplier space can generate an optimal approximate solution. Numerical results are presented to compare the new method with the point to point method widely used in engineering.