Distributed and Adaptive Fast Multipole Method In Three Dimensions

一般区域中泊松方程的 p-自适应树码解法

A $p$-adaptive treecode solution of the Poisson equation in the general domain

本文提出一种 p-自适应树码算法，通过系统误差分析、非均匀多极展开阶数分配策略和层次几何树结构，在保证精度的同时显著降低一般区域泊松方程求解的计算复杂度。

一种基于强递归骨架化的简化快速多极子方法

A Simplified Fast Multipole Method Based on Strong Recursive Skeletonization

本文提出一种基于强递归骨架化的简化快速多极子方法，通过仅用近邻列表和新型平移算子简化实现，支持并行与GPU加速，适用于拉普拉斯和低频亥姆霍兹核。

Periodic Fast Multipole Method

A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmholtz, Stokes and modified Stokes equations. The approach extends to the oscillatory equations of mathematical physics, including the Helmholtz and Maxwell equations, but we will address these in a companion paper, since the nature of the problem is somewhat different and includes the consideration of quasiperiodic boundary conditions and resonances. Unlike lattice sum-based methods, the scheme is insensitive to the u…

自适应有限元方法在扩散系统分布式流体重构中的收敛性

Convergence of an Adaptive Finite Element Method for Distributed Flux Reconstruction

本文研究了自适应有限元方法在扩散系统中重构分布式流体的收敛性，基于后验误差估计器证明了离散解序列在能量范数下收敛于满足最优条件的真三元组，误差估计器渐进行收敛于零。

Kernel Aggregated Fast Multipole Method: Efficient summation of Laplace and Stokes kernel functions

Many different simulation methods for Stokes flow problems involve a common computationally intense task -- the summation of a kernel function over $O(N^2)$ pairs of points. One popular technique is the Kernel Independent Fast Multipole Method (KIFMM), which constructs a spatial adaptive octree for all points and places a small number of equivalent multipole and local equivalent points around each octree box, and completes the kernel sum with $O(N)$ cost, using these equivalent points. Simpler kernels can be used between these equivalent points to improve the efficiency of KIFMM. Here we prese…

快速多极方法的数据驱动执行

Data-Driven Execution of Fast Multipole Methods

针对快速多极方法在非规则粒子分布下的负载均衡难题，提出将最耗时阶段分解为任务，利用QUARK运行时环境异步调度任务，实现数据驱动的无序执行，在四路四核Intel Xeon系统上获得线性加速。

Adaptive Uncertainty-Weighted ADMM for Distributed Optimization

We present AUQ-ADMM, an adaptive uncertainty-weighted consensus ADMM method for solving large-scale convex optimization problems in a distributed manner. Our key contribution is a novel adaptive weighting scheme that empirically increases the progress made by consensus ADMM scheme and is attractive when using a large number of subproblems. The weights are related to the uncertainty associated with the solutions of each subproblem, and are efficiently computed using low-rank approximations. We show AUQ-ADMM provably converges and demonstrate its effectiveness on a series of machine learning app…

调和电荷分布确定的不同方法：高维最小二乘逼近的概率方法

Reconciling alternate methods for the determination of charge distributions: A probabilistic approach to high-dimensional least-squares approximations

本文提出并改进了SADM算法，通过蒙特卡洛方法近似求解高维或病态的最小二乘问题，用于从量子力学静电势推导分布式原子多极矩。

自适应共识ADMM用于分布式优化

Adaptive Consensus ADMM for Distributed Optimization

本文提出自适应共识ADMM方法，通过为每个节点定制参数提升分布式优化性能，并证明其O(1/k)收敛速率。

分布式内存并行自适应张量列交叉逼近

Distributed memory parallel adaptive tensor-train cross approximation

针对高维张量逼近问题，提出基于分布式内存多维进程网格的子张量并行自适应TT交叉方法，推导迭代公式并验证其高精度、低存储及优良的可扩展性。

Fast multipole methods for evaluation of layer potentials with locally-corrected quadratures

While fast multipole methods (FMMs) are in widespread use for the rapid evaluation of potential fields governed by the Laplace, Helmholtz, Maxwell or Stokes equations, their coupling to high-order quadratures for evaluating layer potentials is still an area of active research. In three dimensions, a number of issues need to be addressed, including the specification of the surface as the union of high-order patches, the incorporation of accurate quadrature rules for integrating singular or weakly singular Green's functions on such patches, and their coupling to the oct-tree data structures on w…