We present a kernel-independent, adaptive fast multipole method (FMM) of arbitrary order accuracy for solving elliptic PDEs in three dimensions with radiation and periodic boundary conditions. The algorithm requires only the ability to evaluate the Green's function for the governing equation and a representation of the source distribution (the right-hand side) that can be evaluated at arbitrary points. The performance is accelerated in three ways. First, we construct a piecewise polynomial approximation of the right-hand side and compute far-field expansions in the FMM from the coefficients of this approximation. Second, we precompute tables of quadratures to handle the near-field interactions on adaptive octree data structures, keeping the total storage requirements in check through the exploitation of symmetries. Third, we employ shared-memory parallelization methods and load-balancing techniques to accelerate the major algorithmic loops of the FMM. We present numerical examples for the Laplace, modified Helmholtz and Stokes equations.

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The ever increasing demands placed upon machine performance have resulted in the need for more comprehensive particle accelerator modeling. Computer simulations are key to the success of particle accelerators. Many aspects of particle accelerators rely on computer modeling at some point, sometimes requiring complex simulation tools and massively parallel supercomputing. Examples include the modeling of beams at extreme intensities and densities (toward the quantum degeneracy limit), and with ultra-fine control (down to the level of individual particles). In the future, adaptively tuned models might also be relied upon to provide beam measurements beyond the resolution of existing diagnostics. Much time and effort has been put into creating accelerator software tools, some of which are highly successful. However, there are also shortcomings such as the general inability of existing software to be easily modified to meet changing simulation needs. In this paper possible mitigating strategies are discussed for issues faced by the accelerator community as it endeavors to produce better and more comprehensive modeling tools. This includes lack of coordination between code developers, lack of standards to make codes portable and/or reusable, lack of documentation, among others.

In this paper, we introduce the Theory of Bottleneck Ordering, a mathematical framework that reveals the bottleneck structure of data networks. This theoretical framework provides insights into the inherent topological properties of a network in at least three areas: (1) It identifies the regions of influence of each bottleneck; (2) it reveals the order in which bottlenecks (and flows traversing them) converge to their steady state transmission rates in distributed congestion control algorithms; and (3) it provides key insights into the design of optimized traffic engineering policies. We demonstrate the efficacy of the proposed theory in TCP congestion-controlled networks for two broad classes of algorithms: Congestion-based algorithms (TCP BBR) and loss-based additive-increase/multiplicative-decrease algorithms (TCP Cubic and Reno). Among other results, our network experiments show that: (1) Qualitatively, both classes of congestion control algorithms behave as predicted by the bottleneck structure of the network; (2) flows compete for bandwidth only with other flows operating at the same bottleneck level; (3) BBR flows achieve higher performance and fairness than Cubic and Reno flows due to their ability to operate at the right bottleneck level; (4) the bottleneck structure of a network is continuously changing and its levels can be folded due to variations in the flows' round trip times; and (5) against conventional wisdom, low-hitter flows can have a large impact to the overall performance of a network.

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Existing high-level, source-to-source compilers can accept input programs in a high-level language (e.g., C) and perform complex automatic parallelization and other mappings using various optimizations. These optimizations often require trade-offs and can benefit from the user's involvement in the process. However, because of the inherent complexity, the barrier to entry for new users of these high-level optimizing compilers can often be high. We propose visualization as an effective gateway for non-expert users to gain insight into the effects of parameter choices and so aid them in the selection of levels best suited to their specific optimization goals. A popular optimization paradigm is polyhedral mapping which achieves optimization by loop transformations. We have augmented a commercial polyhedral-model source-to-source compiler (R-Stream) with an interactive visual tool we call the Polyhedral User Mapping and Assistant Visualizer (PUMA-V). PUMA-V is tightly integrated with the R-Stream source-to-source compiler and allows users to explore the effects of difficult mappings and express their goals to optimize trade-offs. It implements advanced multivariate visualization paradigms such as parallel coordinates and correlation graphs and applies them in the novel setting of compiler optimizations. We believe that our tool allows programmers to better understand complex program transformations and deviations of mapping properties on well understood programs. This in turn will achieve experience and performance portability across programs architectures as well as expose new communities in the computational sciences to the rich features of auto-parallelizing high-level source-to-source compilers. 1

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