**Scalable Eigensolver for Quantum Many-body Problems**

Prof. Chao Yang

Lawrence Berkeley National Laboratory

CYang@lbl.gov

**Abstract. **Solving a quantum many-body problem efficiently and accurately is one of the biggest challenges in computational physics and chemistry. There are broadly two approaches to seeking an approximate solution to this high-dimensional eigenvalue problem. One relies on projecting the many-body Hamiltonian onto a carefully chosen subspace of many-body basis functions. The other relies on constructing an effective mean-field model to capture the essential many-body physics that governs the interaction among different particles. These approaches yield algebraic eigenvalue problems that have different characteristics. Developing efficient computational schemes to tackle these problems on massively parallel computers requires choosing appropriate data structures to represent both the discretized Hamiltonian and the eigenvector to be computed, mapping such data structures onto a distribute memory multi-core processor grid, exploiting multiple threads within a computational node and improving the scalability of the computation by generating multiple levels of concurrency and reducing communication overhead. In this talk, I will give an overview on recent progress in these areas and point out the remaining challenges.

**Parallel Orbital Updating Approach for Electronic Structure Calculations**

Prof. Xiaoying Dai

The Academy of Mathematics and Systems Science, the Chinese Academy of Sciences

daixy@lsec.cc.ac.cn

**Abstract. **In this talk, I will introduce our parallel orbital updating approach for electronic structure calculations. By our parallel orbital updating approach, the solution of the nonlinear eigenvalue problem is reduced to some solutions of independent linear boundary value problems and a small scale algebraic eigenvalue problem. We also apply this approach/idea to the associated minimization problem and design a parallel orbital-updating based optimization algorithm. Our parallel orbital updating approach is valid for any finite dimensional discretization, including both real space discretization and the plane wave discretization. Our numerical experiments show that our the parallel orbital updating approaches are quite efficient. In particular, the feature of two level parallel parllelization for our approaches makes it have the potential for Exascale computing.

**Mathematical Problems of Natural Gas Hydrate Depressurization in Non-conventional Oil and Gas Exploration**

Prof. Yanfei Wang

Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics,

Chinese Academy of Sciences

yfwang@mail.iggcas.ac.cn

**Abstract.** Natural gas hydrates (NGH), as a concentrated form of natural gas storage, become an active research area in the oil and gas industry nowadays. Key parameters of NGH are water depths (pressure), geothermal gradients, gas composition, pore water salinity, total organic content of sediments, and faults and fractures. There are many unsolved issues, e.g., lack of high-resolution geophysical (e.g., seismic) imaging methods for identifying NGH; lack of accurate quantitative model of thermodynamics to describe the stable existence range of NGH formation and decomposition; insufficient study of control theory and methods of solid-liquid-gas three phases/four phases conversion for natural gas hydrate in complex physical field (stress and temperature); ill-conditioning system and noise propagation problems during simulation, and high performance computing issues for big data problems of NGH. In this talk, I will discuss about these issues and possible solution methods.

**Decoupling Techniques for Coupled Models in Multi-Physics Supercomputing**

Prof. Mo Mu

Department of Mathematics, Hong Kong University of Science and Technology

mamu@ust.hk

**Abstract.** We discuss decoupling issues for numerical computation with coupled PDE models in large scale simulation of multi-physics systems. An abstract mathematical framework is presented for devising effective and efficient decoupled numerical methods. Applications in mixed fluid-porous media flows and fluid-structure interactions (FSI) will be examined. Approximation and stability issues will be addressed, with special attention to the added-mass effect in decoupling FSI computation.

**Scalable Localized Exponential Time Differencing Methods**

Prof. Lili Ju

Department of Mathematics, University of South Carolina

ju@math.sc.edu

**Abstract. **The localized exponential time differencing (ETD) method was first developed in 2016 for extreme-scale phase field simulations of 3D coarsening dynamics, which displayed excellent parallel scalability on the Sunway TaihuLight supercomputer. ETD methods have been proven to very effective for solving stiff problems in the past decades, and their costs are obviously dominated by calculations of matrix exponentials and their products with vectors. Localized ETD methods use domain decomposition techniques to reduce the size of the problem by solving instead a sequence of smaller-sized subdomain problems using locally computed matrix exponentials, thus are much less expensive and more scalable. In this talk we will present some recent advances in algorithms, analysis and applications of localized ETD methods.

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**A C++ infrastructure library with adaptive mesh refinement and parallel computing for fourth- and higher-order simulations of free-surface flows.**

Prof. Qinghai Zhang

School of Mathematical Sciences, Zhejiang University

0015089@zju.edu.cn

**Abstract. **This talks consists of several parts, all of which converges to the theme in the title. First, I will present a finite-volume method for simulating single-phase incompressible flows. In addition to its fourth-order accuracy both in time and in space, this method is of optimal complexity: the CPU time of advancing the solution within each time step is linearly proportional to the number of control volumes. With the support of parallel computing and adaptive mesh refinement, users of this solver have the flexibility to further augment the computational resource and/or to spend the computational resource wisely. Second, I will discuss our strategy of minimizing the communication cost in the parallel computing context on how to handle irregular and moving boundaries. The focus will be on hyperbolic problems through the recently developed theory on donating regions. Third, I will briefly mention some of our design choices from the viewpoint of software engineering. For example, the space of use cases can be regarded as a linear space, of which a proper choice of orthogonal input parameters servers as a basis and contributes to user-friendliness of the library. Template-based meta-programming has proven to be a useful technique.

**模拟天文****N****体问题的数值方法**

王武 研究员

中国科学院超级计算中心

模拟天文N体问题有助于研究行星系统、恒星聚集、银河系演化、暗物质晕等天文现象。从早期的树算法（Tree）、快速多极子方法（FMM）、粒子网格方法（PM）、多重网格方法（MG）、自适应网格加密（AMR），到快速高效的混合算法，如Tree-PM，模拟N体问题的快速数值方法得到很大的发展。随着高性能计算技术的发展，迫切需要研究上述算法相应的并行算法和性能优化实现技术，从而在最先进的高性能计算平台上模拟超大规模的复杂天文N体问题。报告将介绍N体问题模拟的数值方法、发展现状和相关的高性能技术。