The Strong Scaling Advantage of FPGAs in HPC for N-body Simulations

N-body methods are one of the essential algorithmic building blocks of high-performance and parallel computing. Previous research has shown promising performance for implementing n-body simulations with pairwise force calculations on FPGAs. However, to avoid challenges with accumulation and memory access patterns, the presented designs calculate each pair of forces twice, along with both force sums of the involved particles. Also, they require large problem instances with hundreds of thousands of particles to reach their respective peak performance, limiting the applicability for strong scaling scenarios. This work addresses both issues by presenting a novel FPGA design that uses each calculated force twice and overlaps data transfers and computations in a way that allows to reach peak performance even for small problem instances, outperforming previous single precision results even in double precision, and scaling linearly over multiple interconnected FPGAs. For a comparison across architectures, we provide an equally optimized CPU reference, which for large problems actually achieves higher peak performance per device, however, given the strong scaling advantages of the FPGA design, in parallel setups with few thousand particles per device, the FPGA platform achieves highest performance and power efficiency.

The Fracture Behavior of 316L Stainless Steel with Defects Fabricated by SLM Additive Manufacturing

In this paper, the fracture behaviors of 316L stainless steel with defects fabricated by the Selective Laser Melting (SLM) additive manufacturing are studied by a peridynamic method. Firstly, the incremental formulations in the peridynamic framework are presented for the elastic-plastic problems. Then, the pairwise force of a bond for orthotropic material model is proposed according to both the local and the global coordinate systems. A simple three-step approach is developed to describe the void defects that generated in the processing of the SLM additive manufacturing in the numerical model. Next, some representative numerical examples are carried out, whose results explain the validation and accuracy of the present method, and demonstrate that the orthotropic features, micro-cracks and voids of the materials have a significant influence on the ultimate bearing capacity, crack propagation and branching of the corresponding structures. It is also revealed that the crack initiations are induced actively by the defects and the crack branching is contributed to the complex multiple-crack propagation. Finally, the achievements of this paper lay a foundation for the engineering applications of the SLM additive manufacturing materials.

An Implicit Coupling Finite Element and Peridynamic Method for Dynamic Problems of Solid Mechanics with Crack Propagation

An implicit coupling finite element and peridynamic (PD) method is developed in this paper for the dynamic problems of solid mechanics with crack propagation. In this method, an implicit PD formulation is derived from the bond-based pairwise force that is described as a linear function of the displacements by using the first-order Taylor’s expansion technique. The equivalent incremental equations of the PD method and the finite element method are obtained on the basis of the Newmark and the Newton–Raphson schemes. To combine these two methods, the system is partitioned into two subregions and a convenient and efficient coupling strategy is proposed to form the coupling equivalent equation. The coupling domain is achieved by considering that the nodes and material points share the common information. Furthermore, displacement and load control-based incremental-iterative methods are adopted to solve the nonlinear equations. Several representative numerical examples are carried out and the results demonstrate the effectiveness and accuracy of the proposed coupling method.

Peridynamic Simulation of Fatigue Crack Growth Behaviour with the Effect of Microstructure

The purpose of this paper is to explore the influences of microstructures on crack growth behaviour in 2324-T39 aluminum alloy based on peridynamic(PD) theory. The microelastic bond-based peridynamic constitutive is modified as microplastic to describe the plasticity of aluminum alloys. A new method to establish polycrystalline models based on metallographs is adopted, and grains are reflected in simulations by setting transgranular and intergranular pairwise force in the corresponding bonds. Two kinds of microstructures are modeled according to metallographs, and a special kind of crack branch resulted from the link-up of the secondary crack with the main crack and the growth of the branched crack is successfully captured. The PD simulations reveal that microstructure orientation characteristics have an impact on crack propagation paths and crack growth modes, and it is easier for the secondary-crack resulted macroscopic crack branching to appear if grain boundaries locate not too close to the leading crack tip but within the crack tip plastic zone. The numerical results are verified by experiments and fractographic analysis.

A Recursive Body-Body Formulation for Reducing the Computational Cost of Pairwise Coulomb Force Computation for Modeling and Simulation of Biopolymers, Using a Multibody Approach to Model Reduction

This work presents a method for recursively assembling tensor-like quantities that parameterize the charge distribution of rigid bodies, which result from model reduction of biopolymeric systems using an articulated multibody approach. This is done with the goal of reducing the computational cost associated with the pairwise force determination encountered in molecular dynamics simulations. To achieve a linear computational cost complexity of the force determination, with respect to the number of bodies in the system (N), a recursive assembly and disassembly (evaluation) sweep is proposed. This work proposes assembling these tensor quantities (pseudo-inertia tensors), which are associated with the body’s charge distribution, with a method that uses the standard parallel axis theorem to shift these tensors to a common point so they may be summed. This work presents a preliminary numerical example that examines the accuracy of the force and moment computation using a pseudo-inertia tensor resulting after one level of recursive assembly. The Coulomb force and associated moment on a target body due to the assembled body is computed. The test problem approximates a system that is highly negatively or positively charged. The orientation of the bodies that are assembled is varied, along with the distance between the assembly and the target body. The preliminary results presented herein suggest that this is a viable method of efficiently representing the charge distribution of an assembly. The numerical example presented determines the Coulomb force and the associated moment, as a function of distance and the pseudo-inertia tensor. However, the approximation can be used for any force that is of the form 1/rs, where s is any power.