arXiv subjects

Tao Tang

Publications and source records attributed to Tao Tang.

124 records · Page 7Linked to original sources

arXiv2018

Tuning Streamed Applications on Intel Xeon Phi: A Machine Learning Based Approach

Many-core accelerators, as represented by the XeonPhi coprocessors and GPGPUs, allow software to exploit spatial and temporal sharing of computing resources to improve the overall system performance. To unlock this performance potential requires software to effectively partition the hardware resource to maximize the overlap between hostdevice communication and accelerator computation, and to match the granularity of task parallelism to the resource partition. However, determining the right resource partition and task parallelism on a per program, per dataset basis is challenging. This is because the number of possible solutions is huge, and the benefit of choosing the right solution may be large, but mistakes can seriously hurt the performance. In this paper, we present an automatic approach to determine the hardware resource partition and the task granularity for any given application, targeting the Intel XeonPhi architecture. Instead of hand-crafting the heuristic for which the process will have to repeat for each hardware generation, we employ machine learning techniques to automatically learn it. We achieve this by first learning a predictive model offline using training programs; we then use the learned model to predict the resource partition and task granularity for any unseen programs at runtime. We apply our approach to 23 representative parallel applications and evaluate it on a CPU-XeonPhi mixed heterogenous many-core platform. Our approach achieves, on average, a 1.6x (upto 5.6x) speedup, which translates to 94.5% of the performance delivered by a theoretically perfect predictor.

cs.PF↗

arXiv2018

Hermite spectral collocation methods for fractional PDEs in unbounded domains

This work is concerned with spectral collocation methods for fractional PDEs in unbounded domains. The method consists of expanding the solution with proper global basis functions and imposing collocation conditions on the Gauss-Hermite points. In this work, two Hermite-type functions are employed to serve as basis functions. Our main task is to find corresponding differentiation matrices which are computed recursively. Two important issues relevant to condition numbers and scaling factors will be discussed. Applications of the spectral collocation methods to multi-term fractional PDEs are also presented. Several numerical examples are carried out to demonstrate the effectiveness of the proposed methods.

math.NA↗

arXiv2016

Energetics of point defects in aluminum via orbital-free density functional theory

The formation and migration energies for various point defects, including vacancies and self-interstitials in aluminum are reinvestigated systematically using the supercell approximation in the framework of orbital-free density functional theory. In particular, the finite-size effects and the accuracy of various kinetic energy density functionals are examined.The calculated results suggest that the errors due to the finite-size effect decrease exponentially upon enlarging the supercell. It is noteworthy that the formation energies of self-interstitials converge much slower than that of vacancy. With carefully chosen kinetic energy density functionals, the calculated results agree quite well with the available experimental data and those obtained by Kohn-Sham density functional theory which has exact kinetic term.

cond-mat.mtrl-sci↗

arXiv2016

Density-functional study of plutonium monoxide monohydride

The structural, electronic, mechanical, optical, thermodynamic properties of plutonium monoxide monohydride (PuOH) are studied by density-functional calculations within the framework of LDA/GGA and LDA/GGA+U.From the total energy calculation, the lowest-energy crystal structure of PuOH is predicted to have space group F-43m (No. 216). Within the LDA+U framework, the calculated lattice parameter of F-43m-PuOH is in good agreement with the experimental value and the corresponding ground state is predicted to be an antiferromagnetic charge-transfer insulator. Furthermore, we investigate the bonding character of PuOH by analyzing the electron structure and find that there are a stronger Pu-O bond and a weaker Pu-H bond.The mechanical properties including the elastic constants, elastic moduli and Debye's temperature, and the optical properties including the reflectivity and absorption coefficient are also calculated. We then compute the phonon spectrum which verified the dynamical stability of F-43m-PuOH. Some thermodynamic quantities such as the specific heat are evaluated. Finally we calculate the formation energy of PuOH, and the reaction energies for the oxidation of PuOH and PuOH-coated Pu, which are in reasonable agreement with the experimental values.

cond-mat.mtrl-sci↗

arXiv2016

Streaming Applications on Heterogeneous Platforms

Using multiple streams can improve the overall system performance by mitigating the data transfer overhead on heterogeneous systems. Currently, very few cases have been streamed to demonstrate the streaming performance impact and a systematic investigation of streaming necessity and how-to over a large number of test cases remains a gap. In this paper, we use a total of 56 benchmarks to build a statistical view of the data transfer overhead, and give an in-depth analysis of the impacting factors. Among the heterogeneous codes, we identify two types of non-streamable codes and three types of streamable codes, for which a streaming approach has been proposed. Our experimental results on the CPU-MIC platform show that, with multiple streams, we can improve the application performance by up 90%. Our work can serve as a generic flow of using multiple streams on heterogeneous platforms.

cs.DC↗

arXiv2016

Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations

Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-order nonlinear dif- fusion, with typical examples like the Cahn-Hilliard equation and the thin film type equation. The up-to-date theoretical explanation of the numerical stability relies on the assumption that the deriva- tive of the nonlinear potential function satisfies a Lipschitz type condition, which in a rigorous sense, implies the boundedness of the numerical solution. In this work we remove the Lipschitz assumption on the nonlinearity and prove unconditional energy stability for the stabilized semi-implicit time-stepping methods. It is shown that the size of stabilization term depends on the initial energy and the perturba- tion parameter but is independent of the time step. The corresponding error analysis is also established under minimal nonlinearity and regularity assumptions.

math.NA↗

arXiv2016

Gradient bounds for a thin film epitaxy equation

We consider a gradient flow modeling the epitaxial growth of thin films with slope selection. The surface height profile satisfies a nonlinear diffusion equation with biharmonic dissipation. We establish optimal local and global wellposedness for initial data with critical regularity. To understand the mechanism of slope selection and the dependence on the dissipation coefficient, we exhibit several lower and upper bounds for the gradient of the solution in physical dimensions $d\le 3$.

math.AP↗

arXiv2016

Evaluating the Performance Impact of Multiple Streams on the MIC-based Heterogeneous Platform

Using \textit{multiple streams} can improve the overall system performance by mitigating the data transfer overhead on heterogeneous systems. Prior work focuses a lot on GPUs but little is known about the performance impact on (Intel Xeon) Phi. In this work, we apply multiple streams into six real-world applications on Phi. We then systematically evaluate the performance benefits of using multiple streams. The evaluation work is performed at two levels: the microbenchmarking level and the real-world application level. Our experimental results at the microbenchmark level show that data transfers and kernel execution can be overlapped on Phi, while data transfers in both directions are performed in a serial manner. At the real-world application level, we show that both overlappable and non-overlappable applications can benefit from using multiple streams (with an performance improvement of up to 24\%). We also quantify how task granularity and resource granularity impact the overall performance. Finally, we present a set of heuristics to reduce the search space when determining a proper task granularity and resource granularity. To conclude, our evaluation work provides lots of insights for runtime and architecture designers when using multiple streams on Phi.

cs.DC↗

arXiv2015

Spline Galerkin methods for the Sherman-Lauricella equation on contours with corners

Spline Galerkin approximation methods for the Sherman-Lauricella integral equation on simple closed piecewise smooth contours are studied, and necessary and sufficient conditions for their stability are obtained. It is shown that the method under consideration is stable if and only if certain operators associated with the corner points of the contour are invertible. Numerical experiments demonstrate a good convergence of the spline Galerkin methods and validate theoretical results. Moreover, it is shown that if all corners of the contour have opening angles located in interval $(0.1π, 1.9π)$, then the corresponding Galerkin method based on splines of order $0$, $1$ and $2$ is always stable. These results are in strong contrast with the behaviour of the Nyström method, which has a number of instability angles in the interval mentioned.

math.NA↗

arXiv2014

On discrete least square projection in unbounded domain with random evaluations and its application to parametric uncertainty quantification

This work is concerned with approximating multivariate functions in unbounded domain by using discrete least-squares projection with random points evaluations. Particular attention are given to functions with random Gaussian or Gamma parameters. We first demonstrate that the traditional Hermite (Laguerre) polynomials chaos expansion suffers from the \textit{instability} in the sense that an \textit{unfeasible} number of points, which is relevant to the dimension of the approximation space, is needed to guarantee the stability in the least square framework. We then propose to use the Hermite/Laguerre {\em functions} (rather than polynomials) as bases in the expansion. The corresponding design points are obtained by mapping the uniformly distributed random points in bounded intervals to the unbounded domain, which involved a mapping parameter $L$. By using the Hermite/Laguerre {\em functions} and a proper mapping parameter, the stability can be significantly improved even if the number of design points scales \textit{linearly} (up to a logarithmic factor) with the dimension of the approximation space. Apart from the stability, another important issue is the rate of convergence. To speed up the convergence, an effective scaling factor is introduced, and a principle for choosing quasi-optimal scaling factor is discussed. Applications to parametric uncertainty quantification are illustrated by considering a random ODE model together with an elliptic problem with lognormal random input.

math.NA↗

arXiv2013

Finite-State Markov Modeling of Tunnel Channels in Communication-based Train Control (CBTC) Systems

Communication-based train control (CBTC) is gradually adopted in urban rail transit systems, as it can significantly enhance railway network efficiency, safety and capacity. Since CBTC systems are mostly deployed in underground tunnels and trains move in high speed, building a train-ground wireless communication system for CBTC is a challenging task. Modeling the tunnel channels is very important to design and evaluate the performance of CBTC systems. Most of existing works on channel modeling do not consider the unique characteristics in CBTC systems, such as high mobility speed, deterministic moving direction, and accurate train location information. In this paper, we develop a finite state Markov channel (FSMC) model for tunnel channels in CBTC systems. The proposed FSMC model is based on real field CBTC channel measurements obtained from a business operating subway line. Unlike most existing channel models, which are not related to specific locations, the proposed FSMC channel model takes train locations into account to have a more accurate channel model. The distance between the transmitter and the receiver is divided into intervals, and an FSMC model is applied in each interval. The accuracy of the proposed FSMC model is illustrated by the simulation results generated from the model and the real field measurement results.

cs.DM↗

arXiv2013

Finite-State Markov Modeling of Leaky Waveguide Channels in Communication-based Train Control (CBTC) Systems

Leaky waveguide has been adopted in communication based train control (CBTC) systems, as it can significantly enhance railway network efficiency, safety and capacity. Since CBTC systems have high requirements for the train ground communications, modeling the leaky waveguide channels is very important to design the wireless networks and evaluate the performance of CBTC systems. In the letter, we develop a finite-state Markov channel (FSMC) model for leaky waveguide channels in CBTC systems based on real field channel measurements obtained from a business operating subway line. The proposed FSMC channel model takes train locations into account to have a more accurate channel model. The overall leaky waveguide is divided into intervals, and an FSMC model is applied in each interval. The accuracy of the proposed FSMC model is illustrated by the simulation results generated from the model and the real field measurement results.

cs.DM↗

arXiv2013

Parallel in time algorithm with spectral-subdomain enhancement for Volterra integral equations

This paper proposes a parallel in time (called also time parareal) method to solve Volterra integral equations of the second kind. The parallel in time approach follows the same spirit as the domain decomposition that consists of breaking the domain of computation into subdomains and solving iteratively the sub-problems in a parallel way. To obtain high order of accuracy, a spectral collocation accuracy enhancement in subdomains will be employed. Our main contributions in this work are two folds: (i) a time parareal method is designed for the integral equations, which to our knowledge is the first of its kind. The new method is an iterative process combining a coarse prediction in the whole domain with fine corrections in subdomains by using spectral approximation, leading to an algorithm of very high accuracy; (ii) a rigorous convergence analysis of the overall method is provided. The numerical experiment confirms that the overall computational cost is considerably reduced while the desired spectral rate of convergence can be obtained.

math.NA↗

arXiv2006

Numerical investigations on the finite time singularity in two-dimensional Boussinesq equations

To investigate the finite time singularity in three-dimensional (3D) Euler flows, the simplified model of 3D axisymmetric incompressible fluids (i.e., two-dimensional Boussinesq approximation equations) is studied numerically. The system describes a cap-like hot zone of fluid rising from the bottom, while the edges of the cap lag behind, forming eye-like vortices. The hot liquid is driven by the buoyancy and meanwhile attracted by the vortices, which leads to the singularity-forming mechanism in our simulation. In the previous 2D Boussinesq simulations, the symmetricial initial data is used. However, it is observed that the adoption of symmetry leads to coordinate singularity. Moreover, as demonstrated in this work that the locations of peak values for the vorticity and the temperature gradient becomes far apart as $t$ approaches the predicted blow-up time. This suggests that the symmetry assumption may be unreasonable for searching solution blow-ups. One of the main contributions of this work is to propose an appropriate asymmetric initial condition, which avoids coordinate singularity and also makes the blow-up to occur much earlier than that given by the previously simulations. The shorter simulation time suppresses the development of the round-off error. On the numerical side, the pseudo-spectral method with filtering technique is adopted. The resolutions adopted in this study vary from $1024^2$, $2048^2$, $4096^2$ to $6144^2$. With our proposed asymmetric initial condition, it is shown that the $4096^2$ and $6144^2$ runs yield convergent results when $t$ is fairly close to the predicted blow-up time. Moreover, as expected the locations of peak values for the vorticity and the temperature gradient are very close to each other as $t$ approaches the predicted blow-up time.

physics.flu-dyn↗

arXiv2005

Resolving Small-scale Structures in Two-dimensional Boussinesq Convection by Spectral Methods with High Resolutions

Two-dimensional Boussinesq convection is studied numerically with very fine spatial resolutions up to 4096^2. Our numerical study starts with a smooth asymmetric initial condition, which is chosen to make the flow field well confined in the computational domain until the blow-up time (T_c). Our study shows that the vorticity will blow up at a finite time with |ω|_{max} \~{(T_c-t)}^{-1.61} and |\nabla θ|_{max} ~ {(T_c - t)}^{-3.58}.

physics.flu-dyn↗

arXiv2004

A new parallel strategy for two-dimensional incompressible flow simulations using pseudo-spectral methods

A novel parallel technique for Fourier-Galerkin pseudo-spectral methods with applications to two-dimensional Navier-Stokes equations and inviscid Boussinesq approximation equations is presented. It takes the advantage of the programming structure of the phase-shift de-aliased scheme for pseudo-spectral codes, and combines the task-distribution strategy [Yin, Clercx and Montgomery, Comput. Fluids, 33, 509 (2004)] and parallelized Fast Fourier Transform scheme. The performances of the resulting MPI Fortran90 codes with the new procedure on SGI 3800 are reported. For fixed resolution of the same problem, the peak speed of the new scheme can be twice as fast as the old parallel methods. The parallelized codes are used to solve some challenging numerical problems governed by the Navier-Stokes equations and the Boussinesq equations. Two interesting physical problems, namely, the double-valued $ω$-$ψ$ structure in two-dimensional decaying turbulence and the collapse of the bubble cap in the Boussinesq simulation, are solved by using the proposed parallel algorithms.

physics.comp-ph↗