Applications and accuracy of the parallel diagonal dominant algorithm

The Parallel Diagonal Dominant (PDD) algorithm is a highly efficient, ideally scalable tridiagonal solver. In this paper, a detailed study of the PDD algorithm is given. First the PDD algorithm is introduced. Then the algorithm is extended to solve periodic tridiagonal systems. A variant, the reduced PDD algorithm, is also proposed. Accuracy analysis is provided for a class of tridiagonal systems, the symmetric, and anti-symmetric Toeplitz tridiagonal systems. Implementation results show that the analysis gives a good bound on the relative error, and the algorithm is a good candidate for the emerging massively parallel machines

Hugoniot of shocked liquid deuterium up to 300 GPa: Quantum molecular dynamic simulations

Quantum molecular dynamic (QMD) simulations are introduced to study the thermophysical properties of liquid deuterium under shock compression. The principal Hugoniot is determined from the equation of states, where contributions from molecular dissociation and atomic ionization are also added onto the QMD data. At pressures below 100 GPa, our results show that the local maximum compression ratio of 4.5 can be achieved at 40 GPa, which is in good agreement with magnetically driven flyer and convergent-explosive experiments; At the pressure between 100 and 300 GPa, the compression ratio reaches a maximum of 4.95, which agrees well with recent high power laser-driven experiments. In addition, the nonmetal-metal transition and optical properties are also discussed.Comment: 4.1 pages, 4 figure

A simple parallel prefix algorithm for compact finite-difference schemes

A compact scheme is a discretization scheme that is advantageous in obtaining highly accurate solutions. However, the resulting systems from compact schemes are tridiagonal systems that are difficult to solve efficiently on parallel computers. Considering the almost symmetric Toeplitz structure, a parallel algorithm, simple parallel prefix (SPP), is proposed. The SPP algorithm requires less memory than the conventional LU decomposition and is highly efficient on parallel machines. It consists of a prefix communication pattern and AXPY operations. Both the computation and the communication can be truncated without degrading the accuracy when the system is diagonally dominant. A formal accuracy study was conducted to provide a simple truncation formula. Experimental results were measured on a MasPar MP-1 SIMD machine and on a Cray 2 vector machine. Experimental results show that the simple parallel prefix algorithm is a good algorithm for the compact scheme on high-performance computers

Uncertainty quantification and calibration of physical models

An ecosystem model is a representation of a real complex ecological system, and is usually described by sophisticated mathematical models. Terrestrial Ecosystem Model (TEM) is one of the ecosystem models, that describes the dynamics of car- bon, nitrogen, water and other vegetation related variables. There are uncertainties in the TEM which are attributed to inaccurate input data, insufficient knowledge of the parameters, inherent randomness and simplification of the physical model. Quantification of uncertainty of such an ecosystem model is computationally very heavy. Bayesian calibration method has been used as an efficient way to calibrate and quantify uncertainties of the computer models. In this work, I develop a new approach to emulate the TEM, and to estimate the parameters along with associated uncertainties. TEM has been implemented as a deterministic computer code model. In this computer model, the inputs are envi- ronmental variables and underlying parameters, and the outputs are gross primary production (GPP), net ecosystem production (NEP) and other variables. To make predictions of future outputs from the computer model, I also estimate the under- lying parameters. With an efficient Bayesian approximation, statistical models are developed to obtain inference for the parameters and then make predictions at future time point. Chapter 1 is an introduction to the research problems. In Chapter 2, I discuss the uncertainty arose from temporal scales. In Chapter 3, I discuss the Bayesian uncertainty quantification method and further developed Bayesian calibration of pa- rameters with application to TEM in Chapter 4

Cultural Studies and Heritage Education of Nanyin Performance Art in Quanzhou City, Fujian Province, China

Nanyin, a traditional Chinese music genre originating from Fujian Province, China, encompasses a wide range of singing and instrumental playing techniques. This study aims to analyze the historical development and performance form of Nanyin in Quanzhou, Fujian, China, employing an interdisciplinary approach that incorporates musicology, ethnomusicology, historical musicology, and organology, the study aims to gain a comprehensive understanding of Nanyin and its relevance to cultural studies and heritage education. Key informants, interviews, and observations were utilized as primary research tools, and a systematic data analysis approach was employed. The research results emphasize the enduring popularity and recognition of Nanyin. Nanyin’s development is traced through different periods, highlighting its ancient origins, fusion with diverse musical influences, professionalization, and contemporary revitalization. The performance forms of Nanyin encompass various styles, including duet singing, chorus singing, enchant singing, rotating singing, and group singing, demonstrating the artistic versatility and expressive capabilities of this cultural heritage. The research findings align with theoretical principles in the field of musicology and contribute to a deeper understanding of Nanyin’s cultural significance and its role in preserving China’s traditional culture

Simulation and Control Strategy of a Micro-Turbine Generation System for Grid Connected and Islanding Operations

AbstractThe paper adopts the method of modularized modeling, creating an electro-mechanic simulation model for a Microturbine Generation System (MTGS), including the micro-turbine engine, permanent magnetic synchronous generator, rectifier and inverter. In this paper, control strategy for grid-connected and islanding operations of a micro-turbine generation system is researched, the former adopts output voltage control strategy to maintain the output voltage of the load, and the latter adopts a dual closed-loop control algorithm based on PQ decoupling. A new control strategy to regulate the output power of MTGS based on the combination of decoupled control of output voltage and hysteresis current control is also introduced. Simulations have been done, and result proves the feasibility of the strategy