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     

Importance-driven time-varying data visualization

The ability to identify and present the most essential aspects of time-varying data is critically important in many areas of science and engineering. This paper introduces an importance-driven approach to time-varying volume data visualization for enhancing that ability. By conducting a block-wise analysis of the data in the joint feature-temporal space, we derive an importance curve for each data block based on the formulation of conditional entropy from information theory. Each curve characterizes the local temporal behavior of the respective block, and clustering the importance curves of all the volume blocks effectively classifies the underlying data. Based on different temporal trends exhibited by importance curves and their clustering results, we suggest several interesting and effective visualization techniques to reveal the important aspects of time-varying data.     

Interactive volume rendering of large sparse data sets using adaptive mesh refinement hierarchies

In this paper, we present an algorithm that accelerates 3D texture-based volume rendering of large, sparse data sets, i.e., data sets where only a traction of the voxels contain relevant information. In texture-based approaches, the rendering performance is affected by the fill-rate, the size of texture memory, and the texture I/O bandwidth. For sparse data, these limitations can be circumvented by restricting most of the rendering work to the relevant parts of the volume. In order to efficiently enclose the corresponding regions with axis-aligned boxes, we employ a hierarchical data structure, known as an AMR (adaptive mesh refinement) tree. The hierarchy is generated utilizing a clustering algorithm. A good balance is thereby achieved between the size of the enclosed volume, i.e., the amount to render in graphics hardware and the number of axis-aligned regions, i.e., the number of texture coordinates to compute in software. The waste of texture memory by the power-of-two restriction is minimized by a 3D packing algorithm which arranges texture bricks economically in memory. Compared to an octree approach, the rendering performance is significantly increased and less parameter tuning is necessary.     

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.     

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.     

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     

Multi-scale gas discharge simulations using asynchronous adaptive mesh refinement

The breakdown of a gas gap at high products of pd (pressure × distance) is a multi-scale phenomenon in both time and space. This is especially true when the plasma is interacting with a gas flow, a problem of considerable recent interest in the context of aerodynamic applications of surface discharges. This paper presents a contribution to the numerical modeling of such discharges. We describe here a new approach for adaptive meshing which is suitable for use with the explicit asynchronous integration scheme described in our previous publication. Rather than relying on a family of nested grids as is commonly done, this technique is based on a single unstructured mesh with possible non-conforming cells at the interface between coarse and fine areas. Substantial computational time saving has been achieved for a surface dielectric barrier discharge configuration of the kind proposed as plasma actuators for flow control.     

Development of adaptive mesh refinement scheme for engine spray simulations

Spray modeling is a critical component to engine combustion and emissions simulations. Accurate spray modeling often requires a fine computational mesh for better numerical resolutions. However, computations with a fine mesh will require extensive computer time. This study developed a methodology that uses a locally refined mesh in the spray region. The fine mesh virtually moves with the liquid spray. Such adaptive mesh refinement can enable greater resolution of the liquid-gas interaction while incurring only a small increase in the total number of computational cells. The present study uses an h-refinement adaptive method. A face-based approach is used for the inter-level boundary condition. The prolongation and restriction procedure preserves conservation of properties in performing grid refinement/coarsening. The refinement criterion is based on the total mass of liquid drops and fuel vapor in each cell. The efficiency and accuracy of the present adaptive mesh refinement scheme is described in the paper. Results show that the present scheme can achieve the same level of accuracy in modeling sprays with significantly lower computational cost as compared to a uniformly fine mesh.     

Enabling scalable parallel implementations of structured adaptive mesh refinement applications

Parallel implementations of dynamic structured adaptive mesh refinement (SAMR) methods lead to significant runtime management challenges that can limit their scalability on large systems. This paper presents a runtime engine that addresses the scalability of SAMR applications with localized refinements and high SAMR efficiencies on large numbers of processors (upto 1024 processors). The SAMR runtime engine augments hierarchical partitioning with bin-packing based load-balancing to manage the space-time heterogeneity of the SAMR grid hierarchy, and includes a communication substrate that optimizes the use of MPI non-blocking communication primitives. An experimental evaluation on the IBM SP2 supercomputer using the 3-D Richtmyer-Meshkov compressible turbulence kernel demonstrates the effectiveness of the runtime engine in improving SAMR scalability.

Three-dimensional MHD high-resolution computations with CWENO employing adaptive mesh refinement

Until recently, numerical simulations of discontinuities in highly super-Alfvénic plasmas have been severely limited by comparatively crude resolution and accuracy. Significant progress in the numerical simulation of such plasmas was achieved with the recently implemented Central Weighted Essentially Non-Oscillatory (CWENO) scheme. Combining this technique with that of adaptive mesh refinement (AMR), we have developed a third-order numerical scheme, which is able to efficiently capture strong gradients on spatial scales being small compared to the overall scale of the plasma system considered. Here, we first describe important algorithmic aspects of the scheme as well as the physics included in it. Second, we present the results of various performance tests. And, third, we illustrate its application to ‘real world problems’ using the example of the dynamics of a Sedov-type explosion.     

Addressing spatiotemporal and computational heterogeneity in structured adaptive mesh refinement

Structured adaptive mesh refinement (SAMR) techniques can provide accurate and cost- effective solutions to realistic scientific and engineering simulations modeling complex physical phenomena. However, the adaptive nature and inherent space–time heterogeneity of SAMR applications result in significant runtime management challenges. Moreover, certain SAMR applications involving reactive flows exhibit pointwise varying workloads and cannot be addressed by traditional parallelization approaches, which assume homogeneous loads. This paper presents hierarchical partitioning, bin-packing based load balancing, and Dispatch structured partitioning strategies to manage the spatiotemporal and computational heterogeneity in SAMR applications. Experimental evaluation of these schemes using 3-D Richtmyer–Meshkov compressible turbulence and 2-D reactive-diffusion kernels demonstrates the improvement in overall performance.     

Electromagnetic particle-in-cell simulations on magnetic reconnection with adaptive mesh refinement

The electromagnetic particle-in-cell (EM-PIC) model using the adaptive mesh refinement (AMR) is reconsidered so that it is properly and efficiently applied to the current sheet evolution associated with magnetic reconnection. It is very important to adequately select the refinement criteria for cell splitting. It is demonstrated that fine cells have to be distributed not only in the region where the electron Debye length is small, but also in the region where the electron-scale structure is expected to be significant. While the AMR reduces the number of cells drastically, the total simulation cost is also controlled by the number of particles. In order to reduce the total number of particles in the entire system, the present code controls the local number of particles per cell by splitting or coalescing particles. It is shown that the particle splitting and coalescence are quite effective as well as the AMR to enhance the efficiency of the EM-PIC simulations. A new 3D code extended from the 2D code is also introduced. The code is checked against the tearing instability and the lower hybrid drift instability, and it is confirmed that the code has been successfully developed. It is also found that the 3D simulations can gain more efficiency by using the AMR than the 2D simulations.     

面向时变体数据的特征可视化方法

目的 自然界中的大部分现象本质上都是在空间上随时间的流逝不断发展变化的物理或化学过程,可以表述为含有时间变量的数据场,这些数据场称为时变体数据。随着科学计算技术、计算机仿真技术以及现代观测技术的发展,能够以前所未有的精度对自然现象进行仿真或者观测,但同时也面临时变体数据体积大、时间长以及变量数目多的难题。为了更有效地显示时变体数据并挖掘数据中的关键信息,针对时变体数据的可视化,本文提出一种基于数据特征的方法,用于探索时变体数据中感兴趣区域(即特征)的特点与变化。方法 通过将特征提取、特征跟踪、运动检测和提出的3种特征可视化方法(数据帧特征可视化、单个运动过程特征可视化和空间多运动过程特征可视化)置于同一个框架之中,提供一种从时间域和空间域探索多变量时变体数据的一站式解决方案,并突出时变体数据的动力学特性。结果 本文方法在4组不同的时变体数据上应用,对数据中特征各变量的变化以及感兴趣的运动进行了特征可视化。结论 实验结果显示本文方法能以较小的时间成本有效显示数据中的特征以及用户定义的运动,方法的有效性与实用性得到了验证。     

Texture-based feature tracking for effective time-varying data visualization

Analyzing, visualizing, and illustrating changes within time-varying volumetric data is challenging due to the dynamic changes occurring between timesteps. The changes and variations in computational fluid dynamic volumes and atmospheric 3D datasets do not follow any particular transformation. Features within the data move at different speeds and directions making the tracking and visualization of these features a difficult task. We introduce a texture-based feature tracking technique to overcome some of the current limitations found in the illustration and visualization of dynamic changes within time-varying volumetric data. Our texture-based technique tracks various features individually and then uses the tracked objects to better visualize structural changes. We show the effectiveness of our texture-based tracking technique with both synthetic and real world time-varying data. Furthermore, we highlight the specific visualization, annotation, registration, and feature isolation benefits of our technique. For instance, we show how our texture-based tracking can lead to insightful visualizations of time-varying data. Such visualizations, more than traditional visualization techniques, can assist domain scientists to explore and understand dynamic changes.     

A methodology for adaptive mesh refinement in optimum shape design problems

This work presents a methodology based on the use of adaptive mesh refinement (AMR) techniques in the context of shape optimization problems analyzed by the Finite Element Method (FEM). A suitable and very general technique for the parametrization of the optimization problem using B-splines to define the boundary is first presented. Then, mesh generation using the advancing front method, the error estimation and the mesh refinement criteria are dealt with in the context of a shape optimization problems. In particular, the sensitivities of the different ingredients ruling the problem (B-splines, finite element mesh, design behaviour, and error estimator) are studied in detail. The sensitivities of the finite element mesh coordinates and the error estimator allow their projection from one design to the next, giving an “a priori knowledge” of the error distribution on the new design. This allows to build up a finite element mesh for the new design with a specified and controlled level of error. The robustness and reliability of the proposed methodology is checked out with some 2D examples.     

The NIRVANA code: Parallel computational MHD with adaptive mesh refinement

I report on a new version of the magnetohydrodynamics code NIRVANA¹ which is targeted at the study of astrophysical problems. The new version allows for distributed-memory simulations supporting adaptive mesh refinement. Numerical algorithms include dissipative terms (viscosity, Ohmic diffusion, thermal heat conduction) in a conservative form. Domain decomposition is preferably block-wise in case of unigrid applications but adopts space-filling curve techniques for adaptive mesh applications with a hierarchical block-structured mesh. The code architecture facilitates workload balancing among processors for arbitrary mesh refinement depths maintaining intra-level data locality via space-filling curve mappings and, at the same time, ensuring inter-level data locality by applying a novel technique called block sharing. This way, it is demonstrated that comparable performance can be achieved for problems with locally highly refined grid. The data transfer between processors extensively utilizes the coarse-granularity concept of parallel computing and makes use of the MPI library. Conservation properties of the numerical method carry over to the parallel framework. In particular, the solenoidality condition for the magnetic field is preserved to roundoff precision applying the constrained transport machinery. This paper has its focus of discussion on implementation details related to the parallelization and on a code performance analysis.     

Massively parallel adaptive mesh refinement and coarsening for dynamic fracture simulations

We use the graphical processing unit (GPU) to perform dynamic fracture simulation using adaptively refined and coarsened finite elements and the inter-element cohesive zone model. Due to the limited memory available on the GPU, we created a specialized data structure for efficient representation of the evolving mesh given. To achieve maximum efficiency, we perform finite element calculation on a nodal basis (i.e., by launching one thread per node and collecting contributions from neighboring elements) rather than by launching threads per element, which requires expensive graph coloring schemes to avoid concurrency issues. These developments made possible the parallel adaptive mesh refinement and coarsening schemes to systematically change the topology of the mesh. We investigate aspects of the parallel implementation through microbranching examples, which has been explored experimentally and numerically in the literature. First, we use a reduced-scale version of the experimental specimen to demonstrate the impact of variation in floating point operations on the final fracture pattern. Interestingly, the parallel approach adds some randomness into the finite element simulation on the structured mesh in a similar way as would be expected from a random mesh. Next, we take advantage of the speedup of the implementation over a similar serial implementation to simulate a specimen whose size matches that of the actual experiment. At this scale, we are able to make more direct comparisons to the original experiment and find excellent agreement with those results.     

A survey of high level frameworks in block-structured adaptive mesh refinement packages

Over the last decade block-structured adaptive mesh refinement (SAMR) has found increasing use in large, publicly available codes and frameworks. SAMR frameworks have evolved along different paths. Some have stayed focused on specific domain areas, others have pursued a more general functionality, providing the building blocks for a larger variety of applications. In this survey paper we examine a representative set of SAMR packages and SAMR-based codes that have been in existence for half a decade or more, have a reasonably sized and active user base outside of their home institutions, and are publicly available. The set consists of a mix of SAMR packages and application codes that cover a broad range of scientific domains. We look at their high-level frameworks, their design trade-offs and their approach to dealing with the advent of radical changes in hardware architecture. The codes included in this survey are BoxLib, Cactus, Chombo, Enzo, FLASH, and Uintah.     

Radiative cooling in numerical astrophysics: The need for adaptive mesh refinement

Energy loss through optically thin radiative cooling plays an important part in the evolution of astrophysical gas dynamics and should therefore be considered a necessary element in any numerical simulation. Although the addition of this physical process to the equations of hydrodynamics is straightforward, it does create numerical challenges that have to be overcome in order to ensure the physical correctness of the simulation. First, the cooling has to be treated (semi-)implicitly, owing to the discrepancies between the cooling timescale and the typical timesteps of the simulation. Secondly, because of its dependence on a tabulated cooling curve, the introduction of radiative cooling creates the necessity for an interpolation scheme. In particular, we will argue that the addition of radiative cooling to a numerical simulation creates the need for extremely high resolution, which can only be fully met through the use of adaptive mesh refinement.