Sparse grid

About: Sparse grid is a research topic. Over the lifetime, 1013 publications have been published within this topic receiving 20664 citations.

Regression-Based Stochastic Study of Electromagnetic Fields Due to Lightning Strikes

Abstract: Electromagnetic (EM) fields triggered by lightning strikes are likely to display non-negligible variability in practice, with an apparent effect on various quantities of interest, such as induced voltages on transmission lines. This paper investigates the stochastic properties of lightning-generated fields, when the latter are affected by random ground parameters and/or nondeterministic lightning base current. In essence, the EM components are represented herein by truncated series of orthogonal polynomials, according to the generalized polynomial-chaos theory, and their expansion coefficients are computed via a regression approach. The necessary samplings of the random spaces are constructed with either tensor-based or sparse grids, and their performance is validated and compared. It is shown that reliable calculations of the expectation can be conducted with low-order polynomial approximations, while at least third-order expansions are required for the standard deviation. In addition, we conclude that nontrivial variability is induced in lightning-produced pulses, when variations of the considered stochastic parameters are taken into account.

High Performance Fault-Tolerant Solution of PDEs using the Sparse Grid Combination Technique

Abstract: The data volume of Partial Differential Equation (PDE) based ultra-large-scale scientific simulations is increasing at a higher rate than that of the system’s processing power. To process the increased amount of simulation data within a reasonable amount of time, the evolution of computation is expected to reach the exascale level. One of several key challenges to overcome in these exascale systems is to handle the high rate of component failure arising due to having millions of cores working together with high power consumption and clock frequencies. Studies show that even the highly tuned widely used checkpointing technique is unable to handle the failures efficiently in exascale systems. The Sparse Grid Combination Technique (SGCT) is proved to be a cost-effective method for computing high-dimensional PDE based simulations with only small loss of accuracy, which can be easily modified to provide an Algorithm-Based Fault Tolerance (ABFT) for these applications. Additionally, the recently introduced User Level Failure Mitigation (ULFM) MPI library provides the ability to detect and identify application process failures, and reconstruct the failed processes. However, there is a gap of the research how these could be integrated together to develop fault-tolerant applications, and the range of issues that may arise in the process are yet to be revealed. My thesis is that with suitable infrastructural support an integration of ULFM MPI and a modified form of the SGCT can be used to create high performance robust PDE based applications. The key contributions of my thesis are: (1) An evaluation of the effectiveness of applying the modified version of the SGCT on three existing and complex applications (including a general advection solver) to make them highly fault-tolerant. (2) An evaluation of the capabilities of ULFM MPI to recover from a single or multiple real process/node failures for a range of complex applications computed with the modified form of the SGCT. (3) A detailed experimental evaluation of the faulttolerant work including the time and space requirements, and parallelization on the non-SGCT dimensions. (4) An analysis of the result errors with respect to the number of failures. (5) An analysis of the ABFT and recovery overheads. (6) An in-depth comparison of the fault-tolerant SGCT based ABFT with traditional checkpointing on a non-fault-tolerant SGCT based application. (7) A detailed evaluation of the infrastructural support in terms of load balancing, pureand hybrid-MPI, process layouts, processor affinity, and so on.

ElVibRot-MPI: parallel quantum dynamics with Smolyak algorithm for general molecular simulation.

Abstract: A parallelized quantum dynamics package using the Smolyak algorithm for general molecular simulation is introduced in this work. The program has no limitation of the Hamiltonian form and provides high flexibility on the simulation setup to adapt to different problems. Taking advantage of the Smolyak sparse grids formula, the simulation could be performed with high accuracy, and in the meantime, impressive parallel efficiency. The capability of the simulation could be up to tens of degrees of freedom. The implementation of the algorithm and the package usage are introduced, followed by typical examples and code test results.

A sparse grid approach to balance sheet risk measurement

Abstract: In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distribution. For the pricing and hedging model, we chose a classical Black & Scholes model with a stochastic interest rate following a Hull & White model. The risk management model describing the evolution of the parameters of the pricing and hedging model is a Gaussian model. The new numerical method is compared with the traditional nested simulation approach. We review the convergence of both methods to estimate the risk indicators under consideration. Finally, we provide numerical results showing that the sparse grid approach is extremely competitive for models with moderate dimension.