A new MHD code with adaptive mesh refinement and parallelization for astrophysics

A new code, named MAP, is written in FORTRAN language for magnetohydrodynamics (MHD) simulations with the adaptive mesh refinement (AMR) and Message Passing Interface (MPI) parallelization. There are several optional numerical schemes for computing the MHD part, namely, modified Mac Cormack Scheme (MMC), Lax–Friedrichs scheme (LF), and weighted essentially non-oscillatory (WENO) scheme. All of them are second-order, two-step, component-wise schemes for hyperbolic conservative equations. The total variation diminishing (TVD) limiters and approximate Riemann solvers are also equipped. A high resolution can be achieved by the hierarchical block-structured AMR mesh. We use the extended generalized Lagrange multiplier (EGLM) MHD equations to reduce the non-divergence free error produced by the scheme in the magnetic induction equation. The numerical algorithms for the non-ideal terms, e.g., the resistivity and the thermal conduction, are also equipped in the code. The details of the AMR and MPI algorithms are described in the paper.     

A parallelization of adaptive task partitioning algorithms

An adaptive task partitioning scheme for MIMD architectures is investigated. For many serial adaptive procedures this methodology provides a direct translation into reasonably efficient parallel versions.A proto-type of a two-dimensional integration method has been implemented in this manner. This was facilitated by using a set of high-level macros, layered over the Argonne macro package, which provides the primitives in the adaptive partitioning scheme.Because of the portable nature of the Argonne macro package our code should be readily ported to other MIMD machines with shared memory. A version of the macros for other MIMD architectures is also possible.     

自适应梯度幅值和形态学组合滤波算法

针对传统梯度幅值滤波算法中阈值需人工确定而无法正确判断噪声点和产生新噪声点的问题,提出了一种自适应梯度幅值和多结构元素形态学组合滤波算法。首先使用梯度幅度均值与方差的和作为阈值,以及Otsu算法自适应阈值两种自适应滤波算法对图像进行滤波,以自动确定滤波阈值,最大限度滤除噪声点,保持图像细节;然后使用多结构元素组成串联形态学复合滤波器对自适应梯度幅值滤波后的图像进一步滤波,以解决在自适应滤波过程中产生的新噪声问题。通过实验结果对比与分析,该算法滤波后的图像视觉效果明显好于传统滤波方法,从而验证了该算法既能保持图像细节,又能实现较好的图像滤波效果。     

Parallel adaptive mesh generation

Unstructured meshes have proved to be a powerful tool for adaptive remeshing of finite element idealizations. This paper presents a transputer-based parallel algorithm for two dimensional unstructured mesh generation. A conventional mesh generation algorithm for unstructured meshes is reviewed by the authors, and some program modules of sequential C source code are given. The concept of adaptivity in the finite element method is discussed to establish the connection between unstructured mesh generation and adaptive remeshing.After these primary concepts of unstructured mesh generation and adaptivity have been presented, the scope of the paper is widened to include parallel processing for un-structured mesh generation. The hardware and software used is described and the parallel algorithms are discussed. The Parallel C environment for processor farming is described with reference to the mesh generation problem. The existence of inherent parallelism within the sequential algorithm is identified and a parallel scheme for unstructured mesh generation is formulated. The key parts of the source code for the parallel mesh generation algorithm are given and discussed. Numerical examples giving run times and the consequent “speed-ups” for the parallel code when executed on various numbers of transputers are given. Comparisons between sequential and parallel codes are also given. The “speed-ups” achieved when compared with the sequential code are significant. The “speed-ups” achieved when networking further transputers is not always sustained. It is demonstrated that the consequent “speed-up” depends on parameters relating to the size of the problem.     

Hybrid parallelization of molecular dynamics simulations to reduce load imbalance

The most widely used technique to allow for parallel simulations in molecular dynamics is spatial domain decomposition, where the physical geometry is divided into boxes, one per processor. This technique can inherently produce computational load imbalance when either the spatial distribution of particles or the computational cost per particle is not uniform. This paper shows the benefits of using a hybrid MPI+OpenMP model to deal with this load imbalance. We consider LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator), a prototypical molecular dynamics simulator that provides its own balancing mechanism and an OpenMP implementation for many of its modules, allowing for a hybrid setup. In this work, we extend the current OpenMP implementation of LAMMPS and optimize it and evaluate three different setups: MPI-only, MPI with the LAMMPS balance mechanism, and hybrid setup using our improved OpenMP version. This comparison is made using the five standard benchmarks included in the LAMMPS distribution plus two additional test cases. Results show that the hybrid approach can deal with load balancing problems better and more effectively (50% improvement versus MPI-only for a highly imbalanced test case) than the LAMMPS balance mechanism (only 43% improvement) and improve simulations with issues other than load imbalance.

     

基于自适应网格的快速步进法

针对形状重建及Eikonal方程求解问题,提出了一种根据曲面曲率动态地对网格进行细化的快速步进法,证明了该方法在一阶差分情形下符合因果律,在实现中利用哈希表对邻接点进行快速定位。实验结果表明,该方法较已有方法计算误差小,对噪声适应力较强,可有效处理从明暗恢复形状问题。     

二维自适应前沿推进网格生成

针对二维平面问题,通过曲率计算和基于中轴理论的邻近特征计算控制区域边界曲线的离散;修改经典的前沿推进算法,利用边界驱动的单元尺寸控制方式在区域内部布置疏密过渡合理的三角网格;结合几何和拓扑策略提升网格质量。实验表明,上述算法可生成单元质量高、尺寸过渡合理的计算网格。     

高精度自适应的四边形网格重建

提出了海量数据点集的四边形网格重建算法。首先根据精度要求简化数据 点,按一定规则连接相邻的简化数据点生成多边形网格,对网格中高斯曲率较大的顶点进行 局部细分提高其精度,然后对多边形网格进行整体细分使其全部转化为四边形网格,最后分 裂度较大的顶点对其进行优化。实验结果表明,算法对拓扑结构较为复杂的海量数据点集的 四边形网格重建是行之有效的。     

Parallel adaptive mesh generation and decomposition

An important class of methodologies for the parallel processing of computational models defined on some discrete geometric data structures (i.e. meshes, grids) is the so calledgeometry decomposition or splitting approach. Compared to the sequential processing of such models, the geometry splitting parallel methodology requires an additional computational phase. It consists of the decomposition of the associated geometric data structure into a number of balancedsubdomains that satisfy a number of conditions that ensure the load balancing and minimum communication requirement of the underlying computations on a parallel hardware platform. It is well known that the implementation of the mesh decomposition phase requires the solution of a computationally intensive problem. For this reason several fast heuristics have been proposed. In this paper we explore a decomposition approach which is part of a parallel adaptive finite element mesh procedure. The proposed integrated approach consists of five steps. It starts with a coarse background mesh that isoptimally decomposed by applying well known heuristics. Then, the initial mesh is refined in each subdomain after linking the new boundaries introduced by its decomposition. Finally, the decomposition of the new refined mesh is improved so that it satisfies the objectives and conditions of the mesh decomposition problem. Extensive experimentation indicates the effectiveness and efficiency of the proposed parallel mesh and decomposition approach.     

Boolean operations on multi-region solids for mesh generation

An algorithm for Boolean operations on non-manifold models is proposed to allow the treatment of solids with multiple regions (internal interfaces) and degenerate portions (shells and wires), in the context of mesh generation. In a solid modeler, one of the most powerful tools to create three-dimensional objects with any level of geometric complexity is the Boolean set operators. They are intuitive and popular ways to combine solids, based on the operations applied to point sets. To assure that the resulting objects have the same dimension as the original objects, without loose or dangling parts, a regularization process is usually applied after a Boolean operation. In practice, the regularization is performed classifying the topological elements and removing internal or lower-dimensional structures. However, in many engineering applications, the adopted geometric model may contain idealized internal parts, as in the case of multi-region models, or lower-dimensional parts, as in the case of solids that contain dangling slabs that are represented as zero-thickness surfaces or wireframes in the model. Therefore, the aim of this work is the development of a generic algorithm that allows the application of the Boolean set operations in a geometric modeling environment applied to finite and boundary element mesh generation. This environment adopts a non-manifold boundary representation that considers an undefined number of topological entities (group concept), and works with objects of different dimensions and with objects not necessarily plane or polyhedral (parametric curved surfaces). Numerical examples are presented to illustrate the proposed methodology.     

Texture-based volume rendering of adaptive mesh refinement data

Many phenomena in nature and engineering happen simultaneously on rather diverse spatial and temporal scales. In other words, they exhibit a multi-scale character. A special numerical multilevel technique associated with a particular hierarchical data structure is adaptive mesh refinement (AMR). This scheme achieves locally very high spatial and temporal resolutions. Due to its popularity, many scientists are in need of interactive visualization tools for AMR data. In this article, we present a 3D texture-based volume-rendering algorithm for AMR data that directly utilizes the hierarchical structure. Thereby fast rendering performance is achieved even for high-resolution data sets. To avoid multiple rendering of regions that are covered by grids of different levels of resolution, we propose a space partitioning scheme to decompose the volume into axis-aligned regions of equal-sized cells. Furthermore the problems of interpolation artifacts, opacity corrections, and texture memory limitations are addressed. Published online: November 6, 2002 Correspondence to: R. K?hler     

Fast animation of lightning using an adaptive mesh

We present a fast method for simulating, animating, and rendering lightning using adaptive grids. The "dielectric breakdown model" is an elegant algorithm for electrical pattern formation that we extend to enable animation of lightning. The simulation can be slow, particularly in 3D, because it involves solving a large Poisson problem. Losasso et al. recently proposed an octree data structure for simulating water and smoke, and we show that this discretization can be applied to the problem of lightning simulation as well. However, implementing the incomplete Cholesky conjugate gradient (ICCG) solver for this problem can be daunting, so we provide an extensive discussion of implementation issues. ICCG solvers can usually be accelerated using "Eisenstat's trick," but the trick cannot be directly applied to the adaptive case. Fortunately, we show that an "almost incomplete Cholesky" factorization can be computed so that Eisenstat's trick can still be used. We then present a fast rendering method based on convolution that is competitive with Monte Carlo ray tracing but orders of magnitude faster, and we also show how to further improve the visual results using jittering     

Query-driven visualization of time-varying adaptive mesh refinement data

The visualization and analysis of AMR-based simulations is integral to the process of obtaining new insight in scientific research. We present a new method for performing query-driven visualization and analysis on AMR data, with specific emphasis on time-varying AMR data. Our work introduces a new method that directly addresses the dynamic spatial and temporal properties of AMR grids that challenge many existing visualization techniques. Further, we present the first implementation of query-driven visualization on the GPU that uses a GPU-based indexing structure to both answer queries and efficiently utilize GPU memory. We apply our method to two different science domains to demonstrate its broad applicability.     

An algorithm for adaptive mesh refinement inn dimensions

The author describes a fast algorithm for local adaptive mesh refinement inn dimensions based on simplex bisection. A ready-to-use implementation of the algorithm in C++ pseudocode is given. It is proven that the scheme satisfies all conditions one usually places on grid refinement in the context of finite-element calculations. Bisection refinement also offers an interesting additional feature over the usual, regular, refinement scheme: all linear finite-element basis functions of one generation are of disjoint support. In the way the scheme is presented here, all generated simplex meshes satisfy a ‘structural condition’ which is exploited to simplify bookkeeping of the neighbour graph. However, bisection refinement places certain restrictions on the initial, coarsest grid. For a simply connected domain, a precise and useful criterion for the applicability of the described refinement scheme is formulated and proven.     

可拓自适应混杂控制

针对自适应控制只能处理渐变问题和量变问题的局限性,探讨运用可拓控制对自适应控制进行补充的问题,建立一种新型的控制方法———可拓自适应混杂控制方法.该控制方法的体系结构由自适应控制器和可拓控制器两个部分组成,中间通过基于可拓集合的智能开关来转换连接.自适应控制器的输出计算是基于可拓集合的测度模式的,它只依赖于控制特征量的先验经典域和节域,无需预先提供数学模型或控制结构信息.可拓控制器由可拓模型、关联度计算、可拓分析、可拓变换和优度评价5个模块组成,它善于处理非渐变和质变的控制问题.     

Parallelization of structured,hierarchical adaptive mesh refinement algorithms

We describe an approach to parallelization of structured adaptive mesh refinement algorithms. This type of adaptive methodology is based on the use of local grids superimposed on a coarse grid to achieve sufficient resolution in the solution. The key elements of the approach to parallelization are a dynamic load-balancing technique to distribute work to processors and a software methodology for managing data distribution and communications. The methodology is based on a message-passing model that exploits the coarse-grained parallelism inherent in the algorithms. The approach is illustrated for an adaptive algorithm for hyperbolic systems of conservation laws in three space dimensions. A numerical example computing the interaction of a shock with a helium bubble is presented. We give timings to illustrate the performance of the method. Received: 28 April 1999 / Accepted: 25 November 1999     

Practical applications of adaptive mesh refinement (Rezoning)

A collection of finite element problems that have been examined with a posteriori convergence measures is presented. Results show these local convergence measures can be used to indicate the quality of a finite element solution and to suggest boundaries for mesh rezones.     

Topological operations for editing the singularity on a hex mesh

This paper introduces topological operations for editing the singularity on a hex mesh while maintaining the connectivity of hexahedral mesh. The operations include (1) an enhanced column collapse operation that can avoid generating the poor-quality elements; (2) a column insertion operation that is the opposite operation of column collapse; (3) four semantic operations for achieving the movement of different types of singularity pairs based on column operations. To demonstrate their effectiveness, two related applications are provided. One is moving face-based hex mesh editing, in which the interface between the original mesh and the new region mesh is made structured using the semantic operations. The other is hex mesh structure simplification based on the topological operations.