We present a memory-scalable, parallel, sparse multifrontal solver for solving symmetric postive-definite systems arising in scientific and engineering applications. Factorizing sparse matrices requires memory for both the computed factors and the temporary workspaces for computing each frontal matrix - a data structure commonly used within multifrontal methods. To factorize multiple frontal matrices in parallel, the conventional approach is to allocate a uniform workspace for each hardware thread. In the manycore era, this results in increasing memory usage proportional to the number of hardware threads. We remedy this problem by using dynamic task parallelism with a scalable memory pool. Tasks are spawned while traversing an assembly tree and executed after their dependences are satisfied. We also use an idea to respawn the tasks when certain conditions are not met. Temporary workspace for frontal matrices in each task is allocated from a memory pool designed by us. If the requested memory space is not available in the memory pool, the task is respawned to yield the hardware thread to execute other tasks. The respawned task is executed after high priority tasks are executed. This approach allows to have robust parallel performance within a bounded memory space. Experimental results demonstrate the merits of our implementation on Intel multicore and manycore architectures.
The dragonfly network topology has attracted attention in recent years owing to its high radix and constant diameter. However, the influence of job allocation on communication time in dragonfly networks is not fully understood. Recent studies have shown that random allocation is better at balancing the network traffic, while compact allocation is better at harnessing the locality in dragonfly groups. Based on these observations, this paper introduces a novel allocation policy called Level-Spread for dragonfly networks. This policy spreads jobs within the smallest network level that a given job can fit in at the time of its allocation. In this way, it simultaneously harnesses node adjacency and balances link congestion. To evaluate the performance of Level-Spread, we run packet-level network simulations using a diverse set of application communication patterns, job sizes, and communication intensities. We also explore the impact of network properties such as the number of groups, number of routers per group, machine utilization level, and global link bandwidth. Level-Spread reduces the communication overhead by 16% on average (and up to 71%) compared to the state-of-The-Art allocation policies.
Here, a numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain $\mathcal{C}=\Omega\times[0,\infty)$ following. The resulting degenerate elliptic integer order PDE is then approximated using a hybrid FEM-spectral scheme. Finite elements are used in the direction parallel to the problem domain $\Omega$, and an appropriate spectral method is used in the extruded direction. The spectral part of the scheme requires that we approximate the true eigenvalues of the integer order Laplacian over $\Omega$. We derive an a priori error estimate which takes account of the error arising from using an approximation in place of the true eigenvalues. We further present a strategy for choosing approximations of the eigenvalues based on Weyl's law and finite element discretizations of the eigenvalue problem. The system of linear algebraic equations arising from the hybrid FEM-spectral scheme is decomposed into blocks which can be solved effectively using standard iterative solvers such as multigrid and conjugate gradient. Numerical examples in two and three dimensions suggest that the approach is quasi-optimal in terms of complexity.
Efficiently performing predictive studies of irradiated particle-laden turbulent flows has the potential of providing significant contributions towards better understanding and optimizing, for example, concentrated solar power systems. As there are many uncertainties inherent in such flows, conducting uncertainty quantification analyses is fundamental to improve the predictive capabilities of the numerical simulations. For largescale, multi-physics problems exhibiting high-dimensional uncertainty, characterizing the stochastic solution presents a significant computational challenge as many methods require a large number of high-fidelity, forward model solves. This requirement results in the need for a possibly infeasible number of simulations when a typical converged high-fidelity simulation requires intensive computational resources. To reduce the cost of quantifying high-dimensional uncertainties, we investigate the application of a non-intrusive, bi-fidelity approximation to estimate statistics of quantities of interest associated with an irradiated particle-laden turbulent flow. This method relies on exploiting the low-rank structure of the solution to accelerate the stochastic sampling and approximation processes by means of cheaper-to-run, lower fidelity representations. The application of this bi-fidelity approximation results in accurate estimates of the QoI statistics while requiring a small number of high-fidelity model evaluations. It also enables efficient computation of sensitivity analyses which highlight that epistemic uncertainty plays an important role in the solution of irradiated, particle-laden turbulent flow.
Will quantum computation become an important milestone in human progress? Passionate advocates and equally passionate skeptics abound. IEEE already provides useful, neutral forums for state-of-the-art science and engineering knowledge as well as practical benchmarks for quantum computation evaluation. But could the organization do more.
