A Split-Form, Stable CG/DG-SEM for Wave Propagation Modeled by Linear Hyperbolic Systems

Domain decomposition and partitioning methods for mixed finite element discretizations of the Biot system of poroelasticity

We develop non-overlapping domain decomposition methods for the Biot system of poroelasticity in a mixed form. The solid deformation is modeled with a mixed three-field formulation with weak stress symmetry. The fluid flow is modeled with a mixed Darcy formulation. We introduce displacement and pressure Lagrange multipliers on the subdomain interfaces to impose weakly continuity of normal stress and normal velocity, respectively. The global problem is reduced to an interface problem for the Lagrange multipliers, which is solved by a Krylov space iterative method. We study both monolithic and s…

具有动态边界条件的半线性波方程的分裂格式

Splitting schemes for the semi-linear wave equation with dynamic boundary conditions

本文为具有半线性动力学和声学边界条件的波方程提出了一阶和二阶体-面分裂格式，通过将系统重新解释为耦合系统或利用自然分离特性，在数值实验中实现了相应的收敛性。

Modified Strang splitting for semilinear parabolic problems

We consider applying the Strang splitting to semilinear parabolic problems. The key ingredients of the Strang splitting are the decomposition of the equation into several parts and the computation of approximate solutions by combining the time evolution of each split equation. However, when the Dirichlet boundary condition is imposed, order reduction could occur due to the incompatibility of the split equations with the boundary condition. In this paper, to overcome the order reduction, a modified Strang splitting procedure is presented for the one-dimensional semilinear parabolic equation wit…

非交换算子半线性问题的分裂指数积分器分析

Analysis of split exponential integrators for semilinear problems with noncommuting operators

本文分析非交换算子半线性问题的分裂指数积分器，推导新误差表示并证明分裂指数欧拉与二阶指数龙格-库塔方法的收敛性，数值实验验证其稳定性与效率。

基于谱元离散的壁面建模大涡模拟

Wall-modeled large-eddy simulation based on spectral-element discretization

本文在Nek5000中结合代数壁面模型与显式SGS建模，验证SEM可实现高精度、大规模并行的高阶壁面建模大涡模拟。

关于随机人口过程耦合方法的渐近关系

An asymptotic relationship between coupling methods for stochastically modeled population processes

本文研究了两种常见耦合方法在连续时间马尔可夫链模型中的渐近关系，揭示了它们与局部CRP耦合方法的联系，解释了Split耦合方法为何具有更低的方差。