高效保结构算法的构造、并行化及其应用

项目名称： 高效保结构算法的构造、并行化及其应用

项目编号： No.11501570

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 钱旭

作者单位： 中国人民解放军国防科技大学

项目金额： 18万元

中文摘要： 本项目研究和发展非线性偏微分方程的高效保结构算法的基本理论和构造方法，并以此为基础，建立基于MPI＋CUDA的异构并行保结构算法，最后将其应用于旋量玻色—爱因斯坦凝聚的数值模拟。研究内容包含三个部分：1、研究发展保结构算法的基本理论，包括显式或半显式格式的构造、快速的高阶时间离散算法、分裂步算法、基于非结构网格的实现、以及建立保结构算法构造的一般框架。2、研究保结构算法并行化的技术，特别是利用MPI+CUDA平台对算法进行并行加速改进。3、基于高维耦合Gross-Pitaevskii方程组，研究保结构算法在旋量玻色—爱因斯坦凝聚中的应用。本项目的研究将进一步充实和完善保结构算法的理论基础和数值计算，也将为凝聚态物理的研究提供更高效、更可靠、更精确的数值计算方法。

中文关键词： 非线性偏微分方程；保结构算法；异构并行；旋量玻色—爱因斯坦凝聚；Gross-Pitaevskii方程

英文摘要： In this project, we investigate and develop the basic theory and techniques of efficient structure-preserving algorithms for the nonlinear partial differential equations. Meanwhile, we construct some parallel structure-preserving algorithms, which are based on MPI+CUDA heterogeneous system. Furthermore, the proposed structure-preserving algorithms will be applied to numerical simulation of spinor Bose-Einstein condensation. The main content of this project includes the following three aspects: In first part, we develop the basic theory of structure-preserving algorithm, including the constructions of explicit or semi-explicit schemes, fast high-order algorithms for temporal discretization, split-step algorithms, the combination of structure-preserving algorithms with unstructured meshes, the establishment of general framework for the construction of structure-preserving algorithms. In the second part, we study the parallel structure-preserving algorithms, especially, implement the MPI+CUDA heterogeneous platform and effectively improve the efficiency of the original algorithm. In the third part, we study the application of structure-preserving algorithms in the numerical simulation of spinor Bose-Einstein condensation, which is based on the high-dimensional coupled Gross-Pitaevskii equations. This project will not only further enrich and optimize the basic theory and numerical calculation of the structure-preserving algorithms, but provide efficient, reliable and accurate numerical algorithms for the condensed matter physics.

英文关键词： Nonlinear partial differential equation;Structure-preserving algorithms;Heterogeneous parallel;Spinor Bose-Einstein condensation;Gross-Pitaevskii equation