Patrick Diehl

Non-intrusive Uncertainty Quantification with Sparse Grids for Multivariate Peridynamic Simulations

Peridynamics is an accepted method in engineering for modeling crack propagation on a macroscopic scale. However, the sensitivity of the method to two important model parameters – elasticity and the particle density – has not yet been studied. Motivated by Silling and Askari (Comput Struct 83(17–18):1526–1535, 2005) and Kidane et al. (J Mech Phys Solids 60(5):983–1001, 2012) we use Peridynamics to simulate a high-speed projectile impacting a plate and study the overall damage on the plate. We have extended the setting by the magnitude of the force of the indenter and selected the parameter range such that a sharp transition in the response function occurs.We describe the simulation setting as an uncertainty quantification problem and use a non-intrusive stochastic collocation method based on spatially adaptive sparse grids to propagate the uncertainty. We show first convincing results of its successful application to Peridynamics and compare to Monte Carlo sampling.If the magnitude of the force is deterministic, a strong sensitivity of the damage in the plate with respect to the elasticity factor can be shown for the 2-dimensional setting. If it is non-deterministic, it dominates the simulation and explains most of the variance of the solution. The error of the expectation value estimation reaches an early saturation point for the studied collocation methods: We found parameter ranges where the quantity of interest oscillates. Moreover, faster convergence and higher robustness than for the Monte Carlo method can be observed.

Closing the Performance Gap with Modern C

On the way to Exascale, programmers face the increasing challenge of having to support multiple hardware architectures from the same code base. At the same time, portability of code and performance are increasingly difficult to achieve as hardware architectures are becoming more and more diverse. Today’s heterogeneous systems often include two or more completely distinct and incompatible hardware execution models, such as GPGPU’s, SIMD vector units, and general purpose cores which conventionally have to be programmed using separate tool chains representing non-overlapping programming models. The recent revival of interest in the industry and the wider community for the C++ language has spurred a remarkable amount of standardization proposals and technical specifications in the arena of concurrency and parallelism. This recently includes an increasing amount of discussion around the need for a uniform, higher-level abstraction and programming model for parallelism in the C++ standard targeting heterogeneous and distributed computing. Such an abstraction should perfectly blend with existing, already standardized language and library features, but should also be generic enough to support future hardware developments. In this paper, we present the results from developing such a higher-level programming abstraction for parallelism in C++ which aims at enabling code and performance portability over a wide range of architectures and for various types of parallelism. We present and compare performance data obtained from running the well-known STREAM benchmark ported to our higher level C++ abstraction with the corresponding results from running it natively. We show that our abstractions enable performance at least as good as the comparable base-line benchmarks while providing a uniform programming API on all compared target architectures.

Simulation of Wave Propagation and Impact Damage in Brittle Materials Using Peridynamics

In this paper we present the results of simulating wave propagation and impact damage in brittle materials, like ceramics, using peridynamics, a non-local generalization of continuum mechanics. Two different bond-based material models, the prototype microelastic material model and its improved version, were used to model aluminum oxynitride (ALON). To validate the simulations, the speed of the wave front is compared with measured data of the edge-on impact (EOI) experiment. The presented simulation results indicate that convergence is attained, however, a modeling error of 10 % remains. Which indicates that simple bond-based peridynamics models may not be sufficient to achieve sufficient accuracy in these applications, but more sophisticated state-based peridynamics models must be employed.

Efficient Neighbor Search for Particle Methods on GPUs

In this paper we present an efficient and general sorting-based approach for the neighbor search on GPUs. Finding neighbors of a particle is a common task in particle methods and has a significant impact on the overall computational effort–especially in dynamics simulations. We extend a space-filling curve algorithm presented in Connor and Kumar (IEEE Trans Vis Comput Graph, 2009) for its usage on GPUs with the parallel computing model Compute Unified Device Architecture (CUDA). To evaluate our implementation, we consider the respective execution time of our GPU search algorithm, for the most common assemblies of particles: a regular grid, uniformly distributed random points and cluster points in 2 and 3 dimensions. The measured computational time is compared with the theoretical time complexity of the extended algorithm and the computational time of its reference single-core implementation. The presented results show a speed up of factor of 4 comparing the GPU and CPU run times.

Extraction of Fragments and Waves After Impact Damage in Particle-Based Simulations

The analysis of simulation results and the verification against experimental data is essential to develop and interpret simulation models for impact damage. We present two visualization techniques to post-process particle-based simulation data, and we highlight new aspects for the quantitative comparison with experimental data. As the underlying simulation model we consider the particle method Peridynamics, a non-local generalization of continuum mechanics. The first analysis technique is an extended component labeling algorithm to extract the fragment size and the corresponding histograms. The distribution of the fragment size can be obtained by real-world experiments as demonstrated in Schram and Meyer (Simulating the formation and evolution of behind armor debris fields. ARL-RP 109, U.S. Army Research Laboratory, 2005), Vogler et al. (Int J Impact Eng 29:735–746, 2003). The second approach focuses on the visualization of the stress after an impact. Here, the particle-based data is re-sampled and rendered with standard volume rendering techniques to address the interference pattern of the stress wave after reflection at the boundary. For the extraction and visual analysis, we used the widely-used Stanford bunny as a complex geometry. For a quantitative study with a simple geometry, the edge-on impact experiment (Schradin, Scripts German Acad Aeronaut Res 40:21–68, 1939; Strassburger, Int J Appl Ceram Technol 1:1:235–242, 2004; Kawai et al., Procedia Eng 103:287–293, 2015) can be applied. With these new visualization approaches, new insights for the quantitative comparison of fragmentation and wave propagation become intuitively accessible.

Visualization of fracture progression in peridynamics

Abstract We present a novel approach for the visualization of fracture processes in peridynamics simulations. In peridynamics simulation, materials are represented by material points linked with bonds, providing complex fracture behavior. Our approach first extracts the cracks from each time step by means of height ridge extraction. To avoid deterioration of the structures, we propose an approach to extract ridges from these data without resampling. The extracted crack geometries are then combined into a spatiotemporal structure, with special focus on temporal coherence and robustness. We then show how this structure can be used for various visualization approaches to reveal fracture dynamics, with a focus on physical mechanisms. We evaluate our approach and demonstrate its utility by means of different data sets.