We analyze a numerical method to solve the time-dependent linear Pauli equation in three space dimensions. The Pauli equation is a semi-relativistic generalization of the Schrödinger equation for 2-spinors which accounts both for magnetic fields and for spin, with the latter missing in preceding numerical work on the linear magnetic Schrödinger equation. We use a four operator splitting in time, prove stability and convergence of the method and derive error estimates as well as meshing strategies for the case of given time-independent electromagnetic potentials, thus providing a generalization of previous results for the magnetic Schrödinger equation.
Pauli-structured preconditioning for quantum linear system solvers
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）
Regularized Iterative Method for Ill-posed Linear Systems Based on Matrix Splitting
本文引入矩阵分裂的概念，通过Tikhonov正则化求解大型稀疏不适定线性系。在正则化过程中，我们将不适定系统转化为适定系统。利用不同类型的矩阵分裂讨论了这样一个适定系统的收敛性。通过操作某些类型的弱分裂，对两个系统进行了比较分析。此外，我们将[Song J and Song Y，Calcolo 48（3），245-260，2011]的双分裂推广到非奇异对称矩阵的II型双弱分裂。此外，利用这类弱双分裂，给出了更多的比较结果。
Arbitrary high order splitting methods for linear Schr{ö}dinger equations with non-trivial compatibility conditions
Nantes Université, CNRS, Laboratoire de Mathématiques Jean Leray, LMJL（南特大学、法国国家科学研究中心、让·勒雷数学实验室）；Université de Genève, Section de mathématiques（日内瓦大学数学系）
Schwarz Modulus Based Matrix Splittings with Minimal Polynomial Extrapolation Acceleration for linear complementarity problems arising from American option pricing
University of Geneva（日内瓦大学）；Lanzhou University（兰州大学）；Lund University（隆德大学）
First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: realizability-preserving splitting scheme and numerical analysis
