A novel class of high-order uniformly accurate exponential integrators with local linear extension for the charged-particle dynamics under strong magnetic field
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；University of Science and Technology Beijing（北京科技大学）
In this paper, we develop a novel class of high-order uniformly accurate exponential integrators for charged-particle dynamics under strong magnetic field. The small parameter $0<\varepsilon\ll 1$ induces rapid temporal oscillations, rendering traditional numerical methods prohibitively expensive due to severe step-size restrictions. To address this issue, a linearization technology that introduces auxiliary polynomial variables is employed to recast the original charged-particle dynamics as a higher-dimensional system. Classical exponential integrators are subsequently applied to this augmented formulation, which inherently carries richer structural information, thereby yielding a family of uniformly accurate exponential integrators that can reach arbitrarily high order without requiring any order conditions. For strong magnetic fields under the maximal-ordering scaling, we rigorously establish through algebraic techniques that the schemes with auxiliary polynomial variables of degree $k\geq2$ achieve an improved position error bound of $\mathcal{O}(\min\{\varepsilon^{k+1}h,\varepsilon h^{k+1}\})$ and a uniform velocity error bound of $\mathcal{O}(\min\{\varepsilon^{k}h,h^{k+1}\})$, where $h$ denotes the time-step size. Under the additional condition that the magnetic field gradient vanishes at the origin, these bounds sharpen to $\mathcal{O}(\min\{\varepsilon^{k+2},\varepsilon h^{k+1}\})$ and $\mathcal{O}(\min\{\varepsilon^{k+1},h^{k+1}\})$ for the position and velocity, respectively, for $k\geq1$. The same sharper bounds hold for constant strong magnetic fields. Numerical experiments confirm the advantages of the proposed methods.
Uniformly accurate exponential-type integrators for klein-gordon equations with asymptotic convergence to classical splitting schemes in the nonlinear schroedinger limit
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；INRIA & ENS Rennes（法国国家信息与自动化研究所与雷恩高等师范学院）
A multi-physics structure-preserving integrator with uniform error bounds for relativistic charged-particle dynamics under strong magnetic fields
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学科学重点实验室）
A Uniformly Accurate Multiscale Time Integrator for the Klein-Gordon-Schrödinger Equations in the Nonrelativistic Regime via Simplified Transmission Conditions
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；Department of Mathematics, National University of Singapore（新加坡国立大学数学系）
A uniformly accurate (UA) multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime
National University of Singapore（新加坡国立大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Purdue University（普渡大学）；Université de Lorraine（洛林大学）；Inria Nancy-Grand Est（南锡大东部国家研究学院）
A uniformly accurate multiscale time integrator for the nonlinear Klein-Gordon equation in the nonrelativistic regime via simplified transmission conditions
A uniformly accurate (UA) multiscale time integrator Fourier pseoduspectral method for the Klein-Gordon-Schrodinger equations in the nonrelativistic limit regime
An exponential integrator for a highly oscillatory Vlasov equation
Université Européenne de Bretagne, LMBA (UMR CNRS 6205), Université de Bretagne-Sud（欧洲布列塔尼大学，LMBA（CNRS联合研究单位6205），南布列塔尼大学）；Inria Nancy-Grand Est, CALVI Project & IRMA (UMR CNRS 7501), Université de Strasbourg（法国国家信息与自动化研究所南斯特拉斯堡分部，CALVI项目，IRMA（CNRS联合研究单位7501），斯特拉斯堡大学）；Max Planck Institute for Plasma Physics, EURATOM Association（马克斯·普朗克等离子体物理研究所，EURATOM协会）
Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrodinger equation with wave operator
National University of Singapore（新加坡国立大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；University of Maryland（马里兰大学）
From efficient symplectic exponentiation of matrices to symplectic integration of high-dimensional Hamiltonian systems with slowly varying quadratic stiff potentials
