Heterogeneous Computing in Resource-Intensive CFD Simulations

A software package implementing a fully heterogeneous mode of computations on CPUs and GPU accelerators for efficient use of hybrid supercomputers has been developed at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences. The package involves a distributed preprocessor ensuring work with fine unstructured meshes. Combined compression of the grid topology is used to reduce the amount of storage required for superlarge grid data. The study involves petascale computational resources.     

A Parallel Algorithm for Computing Minimum Spanning Trees

present a simple and implementable algorithm that computes a minimum spanning tree of an undirected weighted graph G = (V, E) of n = |V| vertices and m = |E| edges on an EREW PRAM in O(log^3/2n) time using n + m processors. This represents a substantial improvement in the running time over the previous results for this problem using at the same time the weakest of the PRAM models. It also implies the existence of algorithms having the same complexity bounds for the EREW PRAM, for connectivity, ear decomposition, biconnectivity, strong orientation, st-numbering and Euler tours problems.     

A New Class of Nonlinear Waves in Parallel Flows

Waves in parallel shear flows are found to have different characteristics depending on whether nonlinear or viscous effects dominate near the critical layer. In this paper a nonlinear theory is developed which gives rise to a class of disturbances not found in the classical viscous theory. It is suggested that the modes found from such an analysis may be of importance in the breakdown of laminar flow due to free stream disturbances.     

Composite Waves for a Cell Population System Modelling Tumor Growth and Invasion

In the recent biomechanical theory of cancer growth, solid tumors are considered as liquid-like materials comprising elastic components. In this fluid mechanical view, the expansion ability of a solid tumor into a host tissue is mainly driven by either the cell diffusion constant or the cell division rate, with the latter depending on the local cell density (contact inhibition) or/and on the mechanical stress in the tumor. For the two by two degenerate parabolic/elliptic reaction-diffusion system that results from this modeling, the authors prove that there are always traveling waves above a minimal speed, and analyse their shapes. They appear to be complex with composite shapes and discontinuities. Several small parameters allow for analytical solutions, and in particular, the incompressible cells limit is very singular and related to the Hele-Shaw equation. These singular traveling waves are recovered numerically.     

Long-Time Dynamics for a Nonlinear Viscoelastic Kirchhoff Plate Equation

This paper is devoted to study the long-time dynamics for a nonlinear viscoelastic Kirchhoff plate equation. Under some growth conditions of g and f, the existence of a global attractor is granted. Furthermore, in the subcritical case, this global attractor has finite Hausdorff and fractal dimensions.     

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The goveming thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.     

蛙交感神经细胞内的孤立脉冲钙波

在一定的胞外环境刺激下,蛙交感神经细胞内存在一类沿着细胞膜径向向内传播的孤立脉冲钙波．该文建立了一个描述蛙交感神经细胞内的钙波动力学模型．在分段线性近似下,模型方程在形式上等同于Sneyd的方程．因此,应用Sneyd的求解方法,我们得到了一维孤立脉冲波速和波形的解析表达式．所求得的孤立钙波的波速为21.5 μm/s,符合实验结果．     

Long-Time Accuracy for Approximate Slow Manifolds in a Finite-Dimensional Model of Balance

We study the slow singular limit for planar anharmonic oscillatory motion of a charged particle under the influence of a perpendicular magnetic field when the mass of the particle goes to zero. This model has been used by the authors as a toy model for exploring variational high-order approximations to the slow dynamics in rotating fluids. In this paper, we address the long time validity of the slow limit equations in the simplest nontrivial case. We show that the first-order reduced model remains O(ε) accurate over a long 1/ε timescale. The proof is elementary, but involves subtle estimates on the nonautonomous linearized dynamics.     

Parallel Strategies Applied to FE Simulations of Multiphasic Problems

While the theoretical background of various porous media models is well understood, it is still a demanding task to deal with these models numerically. In this contribution, a triphasic model is presented, which is capable of describing partially saturated soils. In quasi‐static conditions, this model results in the primary variables solid displacement, pore‐liquid pressure and pore‐gas pressure. For a stable numerical implementation, Taylor‐Hood elements are required, which need quadratic ansatz functions for the displacement and linear ansatz functions for the pressure terms. Looking at numerical simulations in 2‐d, challenging finite element calculations have already been realized in combination with adaptivity in time and space [1]. Nevertheless, new strategies have to be considered for a realization of applications of the model in 3‐d in order to handle the huge amount of unknowns arising from the discretization with Taylor‐Hood elements. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Reflection of Surface Waves by Two Parallel Vertical Barriers

A wave on the free surface of a liquid is incident on two parallelbarriers, each of infinite length and completely submerged tothe same depth. Here we calculate the coefficients of reflectionand transmission for this configuration to the second orderwhen the distance between the plates is large.     

血液动力学中血管流激波与驻波的相互作用

血液动力学问题是生物力学心血管系统中的重要研究课题.血管内斑块处,血管截面和血管壁的材质发生变化,对血液流动产生重要影响.血液流动中基本波及其相互作用对探究血液流动的规律、生理学意义及与疾病的关系有着重要的意义.本文研究血液动力学血液流动简化数学模型的基本波的相互作用.血管流模型是3×3非严格双曲型方程组.构造性地得到了初值为三段常状态时,血管流问题的解,即解决了激波与驻波的相互作用问题.特别地,给出四种后前激波与驻波的相互作用的结果.     

The Evolution in Space and Time of Nonlinear Waves in Parallel Shear Flows

It is shown, using a quite general formulation, that the amplitude evolution equation for slowly varying finite amplitude waves is usually first order in both space and time. One advantage of the present formulation is that it becomes possible to easily identify, from their linear eigensolutions, interesting exceptional cases in which the amplitude evolves according to a partial differential equation that is second order in either space or time. The theory is applied to a number of specific problems, including flows with broken line profiles, and inviscid shear flows having nonlinear critical layers.     

Evaluating Parallel Simulated Evolution Strategies for VLSI Cell Placement

Simulated Evolution (SimE) is an evolutionary metaheuristic that has produced results comparable to well established stochastic heuristics such as SA, TS and GA, with shorter runtimes. However, for optimization problems with a very large set of elements, such as in VLSI cell placement and routing, runtimes can still be very large and parallelization is an attractive option for reducing runtimes. Compared to other metaheuristics, parallelization of SimE has not been extensively explored. This paper presents a comprehensive set of parallelization approaches for SimE when applied to multiobjective VLSI cell placement problem. Each of these approaches are evaluated with respect to SimE characteristics and the constraints imposed by the problem instance. Conclusions drawn can be extended to parallelization of SimE when applied to other optimization problems.      

An Improvement of Multigrid Methods Using Multiple Grids on Each Layer for Parallel Computing

Multigrid methods are widely used and well studied for linear solvers and preconditioners of Krylov subspace methods. The multigrid method is one of the most powerful approaches for solving large scale linear systems;however, it may show low parallel efficiency on coarse grids. There are several kinds of research on this issue. In this paper, we intend to overcome this difficulty by proposing a novel multigrid algorithm that has multiple grids on each layer.Numerical results indicate that the proposed method shows a better convergence rate compared with the existing multigrid method.