Clemens-August Thole

Multigrid methods on parallel computers—a survey of recent developments

Abstract Multigrid methods have been established as being among the most efficient techniques for solving complex elliptic equations. We sketch the multigrid idea, emphasizing that a multigrid solution is generally obtainable in a time directly proportional to the number of unknown variables on serial computers. Despite this, even the most powerful serial computers are not adequate for solving the very large systems generated, for instance, by discretization of fluid flow in three dimensions. A breakthrough can be achieved here only by highly parallel supercomputers. On the other hand, parallel computers are having a profound impact on computational science. Recently, highly parallel machines have taken the lead as the fastest supercomputers, a trend that is likely to accelerate in the future. We describe some of these new computers, and issues involved in using them. We describe standard parallel multigrid algorithms and discuss the question of how to implement them efficiently on parallel machines. The natural approach is to use grid partitioning. One intrinsic feature of a parallel machine is the need to perform interprocessor communication. It is important to ensure that time spent on such communication is maintained at a small fraction of computation time. We analyze standard parallel multigrid algorithms in two and three dimensions from this point of view, indicating that high performance efficiencies are attainable under suitable conditions on moderately parallel machines. We also demonstrate that such performance is not attainable for multigrid on massively parallel computers, as indicated by an example of poor efficiency on 65,536 processors. The fundamental difficulty is the inability to keep 65,536 processors busy when operating on very coarse grids. This example indicates that the straightforward parallelization of multigrid (and other) algorithms may not always be optimal. However, parallel machines open the possibility of finding really new approaches to solving standard problems. In particular, we present an intrinsically parallel variant of standard multigrid. This “PSMG” (parallel superconvergent multigrid) method allows all processors to be used at all times. even when processing on the coarsest grid levels. The sequential version of this method is not a sensible algorithm

Europort-1: Porting industrial codes to parallel architectures

Europort is a European initiative (within the ESPRIT III programme) the goal of which is to demonstrate the benefit of parallel computer technology for industry by porting a vast range of real industrial applications to parallel platforms. This porting action will serve as an exemplar for industry to increase the awareness of parallel high performance computing (HPC) within industry at large and demonstrate the cost-effectiveness of parallel systems. Europort as a whole is subdivided into two projects, Europort-1 and Europort-2. This paper gives an overview of the Europort-1 project, namely, those activities dealing with fluid dynamics and structural mechanics. Europort-1 is partially funded by the European Commission under contract EP 8421.

A short note on standard parallel multigrid algorithms for 3D problems

We present some results concerning parallel multigrid (MG) algorithms for 3D problems. For certain-practically important-anisotropic cases, plane relaxation is needed for smoothing if standard MG (coarsening etc.) is used. Parallel versions of these sophisticated MG algorithms are described, and their time complexity and multiprocessor efficiency is studied.

Parallel multigrid methods: implementation on SUPRENUM-like architectures and applications

Multigrid (MG) methods for partial differential equations (and for other important mathematical models in scientific computing) have turned out to be optimal on sequential computers. Clearly, one wants to apply them also on vector and parallel computers in order to exploit both, the high MG-efficiency (compared to classical methods) and the full computational power of modern supercomputers. For this purpose, parallel MG methods are needed. It turns out that certain well-known standard MG methods (with RB and zebra-type relaxation, as described in [25]) already contain a sufficiently high degree of parallelism.

Towards interactive simulation in automotive design

One of the important tasks in Mechanical Engineering is to increase the safety of the vehicle and decrease its production costs. This task is typically solved by means of Multiobjective Optimization, which formulates the problem as a mapping from the space of design variables to the space of target criteria and tries to find an optimal region in these multidimensional spaces. Due to high computational costs of numerical simulations, the sampling of this mapping is usually very sparse and scattered. Combining design of experiments methods, metamodeling, new interpolation schemes and innovative graphics methods, we enable the user to interact with simulation parameters, optimization criteria, and come to a new interpolated crash result within seconds. We denote this approach as Simulated Reality, a new concept for the interplay between simulation, optimization and interactive visualization. In this paper we show the application of Simulated Reality for solution of real life car design optimization problems.

Collaborative Visualization of Tang Chang'an over the Internet

In this paper we introduce Simulated Reality (SR) as a new concept for the interplay between simulation, optimization and interactive visualization. We see SR as a new metaphor for the interactive visual exploration of simulation and optimization results. The vision of Simulated Reality implies interactive behavior of simulations. Fact is today that simulations might still need hours of computation time, especially in crash worthiness. This paper shows approaches to come closer to the vision of SR. Combining design of experiments methods, metamodeling, new interpolation schemes and innovative graphics methods, we enable to user to interact with simulation parameters, optimization criteria and come to a new interpolated crash result within seconds. The approaches have been successfully applied for solution of real life car design optimization problems.

Analysis of Bulky Crash Simulation Results: Deterministic and Stochastic Aspects

Crash simulation results show both deterministic and stochastic behavior. For optimization in automotive design it is very important to distinguish between effects caused by variation of simulation parameters and effects triggered, for example, by buckling phenomena. We propose novel methods for the exploration of a simulation database featuring non-linear multidimensional interpolation, tolerance prediction, sensitivity analysis, robust multiobjective optimization as well as reliability and causal analysis. The methods are highly optimized for handling bulky data produced by modern crash simulators. The efficiency of these methods is demonstrated for industrially relevant benchmark cases.

Data mining on crash simulation data

The work presented in this paper is part of the cooperative research project AUTO–OPT carried out by twelve partners from the automotive industries. One major work package concerns the application of data mining methods in the area of automotive design. Suitable methods for data preparation and data analysis are developed. The objective of the work is the re–use of data stored in the crash–simulation department at BMW in order to gain deeper insight into the interrelations between the geometric variations of the car during its design and its performance in crash testing. In this paper a method for data analysis of finite element models and results from crash simulation is proposed and application to recent data from the industrial partner BMW is demonstrated. All necessary steps from data pre–processing to re–integration into the working environment of the engineer are covered.

AUTOBENCH/AUTO-OPT: Towards an Integrated Construction Environment for Virtual Prototyping in the Automotive Industry

The present paper describes two cooperative projects (AUTOBENCH and AUTO-OPT) carried out with partners in the automotive industries (AUDI, BMW, DaimlerChrysler, Karmann and Porsche), software vendors of simulation software (ESI, INTES, INPRO, SFE) and technology providers (Uni Stuttgart, FhG- SCAI and DLR-SISTEC). Both projects aim at the development of integrated working environments for virtual automotive prototypes. Special focus is on simulation of functional behaviour of the car body, production of its parts and their improvement. New technologies have been developed for the handling of numerical grids, integration of CAE tools, numerical algorithms and visualisation. Parallel computing is supported throughout the projects on a simulation level as well as for optimisation purposes. Ongoing work concentrates on the interactive simulation and optimisation as well as the reuse of the vast amount of resulting data.

High Scalability of Parallel PAM-CRASH with a New Contact Search Algorithm

The numerical simulation of crashworthiness plays an important role in the vehicle design-cycle. PAM-CRASH, from ESI, has been successfully exploited for industrial simulation on massively parallel systems. The most time critical part of the parallel simulation is the contact handling. ESI and GMD have developed a new contact search algorithm (CSA) [1]. The implementation of this algorithm into PAM-CRASH leads to a better scalability. Results of measurements on a 128-processor SGI machine demonstrate the good performance of PAM-CRASH with CSA.