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Register a new userFlexible and scalable particle-in-cell methods for massively parallel computations
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Particle-in-cell methods couple mesh-based methods for the solution of continuum mechanics problems, with the ability to advect and evolve particles. They have a long history and many applications in scientific computing. However, they have most often only been implemented for either sequential codes, or parallel codes with static meshes that are statically partitioned. In contrast, many mesh-based codes today use adaptively changing, dynamically partitioned meshes, and can scale to thousands or tens of thousands of processors. Consequently, there is a need to revisit the data structures and algorithms necessary to use particle methods with modern, mesh-based methods. Here we review commonly encountered requirements of particle-in-cell methods, and describe efficient ways to implement them in the context of large-scale parallel finite-element codes that use dynamically changing meshes. We also provide practical experience for how to address bottlenecks that impede the efficient implementation of these algorithms and demonstrate with numerical tests both that our algorithms can be implemented with optimal complexity and that they are suitable for very large-scale, practical applications. We provide a reference implementation in ASPECT, an open source code for geodynamic mantle-convection simulations built on the deal.II library.
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We present a highly scalable Monte Carlo (MC) three-dimensional photon transport simulation platform designed for heterogeneous computing systems. Through the development of a massively parallel MC algorithm using the Open Computing Language (OpenCL) framework, this research extends our existing graphics processing unit (GPU)-accelerated MC technique to a highly scalable vendor-independent heterogeneous computing environment, achieving significantly improved performance and software portability. A number of parallel computing techniques are investigated to achieve portable performance over a wide range of computing hardware. Furthermore, multiple thread-level and device-level load-balancing strat- egies are developed to obtain efficient simulations using multiple central processing units (CPUs) and GPUs.
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of classical graph problems. So far, the only way to argue lower bounds for this model is to condition on conjectures about the hardness of some specific problems, such as graph connectivity on promise graphs that are either one cycle or two cycles, usually called the one cycle vs. two cycles problem. This is unlike the traditional arguments based on conjectures about complexity classes (e.g., $textsf{P} eq textsf{NP}$), which are often more robust in the sense that refuting them would lead to groundbreaking algorithms for a whole bunch of problems. In this paper we present connections between problems and classes of problems that allow the latter type of arguments. These connections concern the class of problems solvable in a sublogarithmic amount of rounds in the MPC model, denoted by $textsf{MPC}(o(log N))$, and some standard classes concerning space complexity, namely $textsf{L}$ and $textsf{NL}$, and suggest conjectures that are robust in the sense that refuting them would lead to many surprisingly fast new algorithms in the MPC model. We also obtain new conditional lower bounds, and prove new reductions and equivalences between problems in the MPC model.
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively parallel computations in commutative algebra and algebraic geometry. In this note, we give an overview on the current capabilities of this framework by looking into three sample applications: determining smoothness of algebraic varieties, computing GIT-fans in geometric invariant theory, and determining tropicalizations. These applications employ algorithmic methods originating from commutative algebra, sheaf structures on manifolds, local geometry, convex geometry, group theory, and combinatorics, illustrating the potential of the framework in further problems in computer algebra.
A revised version of the massively parallel simulator of a universal quantum computer, described in this journal eleven years ago, is used to benchmark various gate-based quantum algorithms on some of the most powerful supercomputers that exist today. Adaptive encoding of the wave function reduces the memory requirement by a factor of eight, making it possible to simulate universal quantum computers with up to 48 qubits on the Sunway TaihuLight and on the K computer. The simulator exhibits close-to-ideal weak-scaling behavior on the Sunway TaihuLight,on the K computer, on an IBM Blue Gene/Q, and on Intel Xeon based clusters, implying that the combination of parallelization and hardware can track the exponential scaling due to the increasing number of qubits. Results of executing simple quantum circuits and Shors factorization algorithm on quantum computers containing up to 48 qubits are presented.
A massively parallel simulation code, called textit{dHybrid}, has been developed to perform global scale studies of space plasma interactions. This code is based on an explicit hybrid model; the numerical stability and parallel scalability of the code are studied. A stabilization method for the explicit algorithm, for regions of near zero density, is proposed. Three-dimensional hybrid simulations of the interaction of the solar wind with unmagnetized artificial objects are presented, with a focus on the expansion of a plasma cloud into the solar wind, which creates a diamagnetic cavity and drives the Interplanetary Magnetic Field out of the expansion region. The dynamics of this system can provide insights into other similar scenarios, such as the interaction of the solar wind with unmagnetized planets.
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