The detection and correction of silent errors in pipelined Krylov subspace methods [0.03%]
流水线Krylov子空间方法中隐形错误的检测与纠正
Erin Claire Carson,Jakub Hercík
Erin Claire Carson
As computational machines become larger and more complex, the probability of hardware failure rises. "Silent errors", or bit flips, may not be immediately apparent but can cause detrimental effects to algorithm behavior. In this work, we ex...
Optimized Schwarz waveform relaxation methods for wave-heat coupling in one dimensional bounded domains [0.03%]
一维有界域中波-热耦合的优化施瓦兹无源松弛方法
Franz Chouly,Martin J Gander,Véronique Martin
Franz Chouly
We are interested in heterogeneous domain decomposition methods to couple partial differential equations in space-time. The coupling can be used to describe the exchange of heat or forces or both, and has important applications like fluid-s...
Randomized methods for computing joint eigenvalues, with applications to multiparameter eigenvalue problems and root finding [0.03%]
计算联合特征值的随机方法及其在多参数特征值问题和求根中的应用
Haoze He,Daniel Kressner,Bor Plestenjak
Haoze He
It is well known that a family of n × n commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the n joint eigenvalues of the family. In t...
Callum Robert Marples,Philip Michael Williams
Callum Robert Marples
Algorithms for generating uniform random points on a triaxial ellipsoid are non-trivial to verify because of the non-analytical form of the surface area. In this paper, a formula for the surface area of an ellipsoidal patch is derived in th...
VEMcomp: a Virtual Elements MATLAB package for bulk-surface PDEs in 2D and 3D [0.03%]
VEMcomp：一个用于二维和三维主体-表面偏微分方程的虚拟元素MATLAB软件包
Massimo Frittelli,Anotida Madzvamuse,Ivonne Sgura
Massimo Frittelli
We present a Virtual Element MATLAB solver for elliptic and parabolic, linear and semilinear Partial Differential Equations (PDEs) in two and three space dimensions, which is coined VEMcomp. Such PDEs are widely applicable to describing pro...
An efficient numerical method on modified space-time sparse grid for time-fractional diffusion equation with nonsmooth data [0.03%]
修正的时空稀疏网格求解非光滑数据时间分数阶扩散方程的高效数值方法
Bi-Yun Zhu,Ai-Guo Xiao,Xue-Yang Li
Bi-Yun Zhu
In this paper, we focus on developing a high efficient algorithm for solving d-dimension time-fractional diffusion equation (TFDE). For TFDE, the initial function or source term is usually not smooth, which can lead to the low regularity of...
A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting [0.03%]
具有最小提升的复合单调包含的原始对偶分裂算法
Francisco J Aragón-Artacho,Radu I Boţ,David Torregrosa-Belén
Francisco J Aragón-Artacho
In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators. Ou...
Cross-points in the Dirichlet-Neumann method I: well-posedness and convergence issues [0.03%]
Dirichlet-Neumann方法中的交叉点I：适定性与收敛问题
Bastien Chaudet-Dumas,Martin J Gander
Bastien Chaudet-Dumas
Cross-points in domain decomposition, i.e., points where more than two subdomains meet, have received substantial attention over the past years, since domain decomposition methods often need special attention in their definition at cross-po...
Numerical methods for CT reconstruction with unknown geometry parameters [0.03%]
带有未知几何参数的CT图像重建中的数值方法
Chang Meng,James Nagy
Chang Meng
Computed tomography (CT) techniques are well known for their ability to produce high-quality images needed for medical diagnostic purposes. Unfortunately, standard CT machines are extremely large, heavy, require careful and regular calibrat...
Nicola Guglielmi,Ernst Hairer
Nicola Guglielmi
This article considers the numerical treatment of piecewise-smooth dynamical systems. Classical solutions as well as sliding modes up to codimension-2 are treated. An algorithm is presented that, in the case of non-uniqueness, selects a sol...