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Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations
Dynamical low-rank integrators for matrix differential equations recently attracted a lot of attention and have proven to be very efficient in...
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A new class of structure-preserving stochastic exponential Runge-Kutta integrators for stochastic differential equations
In this article, a new class of stochastic exponential Runge-Kutta (SERK) methods is developed for solving stochastic differential equations. The...
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A robust second-order low-rank BUG integrator based on the midpoint rule
Dynamical low-rank approximation has become a valuable tool to perform an on-the-fly model order reduction for prohibitively large matrix...
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High Order Structure-Preserving Finite Difference WENO Schemes for MHD Equations with Gravitation in all Sonic Mach Numbers
In this paper, we develop a high-order semi-implicit (SI) structure-preserving finite difference weighted essentially nonoscillatory (WENO) scheme...
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Structure-Preserving Recurrent Neural Networks for a Class of Birkhoffian Systems
In this paper, the authors propose a neural network architecture designed specifically for a class of Birkhoffian systems — The Newtonian system. The...
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Arbitrary high-order structure-preserving methods for the quantum Zakharov system
In this paper, we present a new methodology to develop arbitrary high-order structure-preserving methods for solving the quantum Zakharov system. The...
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Numerical Methods for Stochastic Differential Equations
This chapter is devoted to providing a bridge from the numerical discretization of deterministic differential equations to the case of stochastic...
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Variational Framework for Structure-Preserving Electromagnetic Particle-in-Cell Methods
In this article we apply a discrete action principle for the Vlasov–Maxwell equations in a structure-preserving particle-field discretization...
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A new framework for polynomial approximation to differential equations
In this paper, we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The...
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A Fictitious Time Lie-Group Integrator for the Brinkman–Forchheimer Momentum Equation Modeling Flow of Fully Developed Forced Convection
AbstractA numerical scheme for the Brinkman–Forchheimer momentum equation modeling flow in a saturated porous duct is considered. There is no natural...
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Dictionary-based online-adaptive structure-preserving model order reduction for parametric Hamiltonian systems
Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection...
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Structure-Preserving Algorithms with Uniform Error Bound and Long-time Energy Conservation for Highly Oscillatory Hamiltonian Systems
Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper,...
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Dynamic symmetry breaking and structure-preserving analysis on the longitudinal wave in an elastic rod with a variable cross-section
The longitudinal wave propagating in an elastic rod with a variable cross-section owns wide engineering background, in which the longitudinal wave...
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High-Order Linearly Implicit Structure-Preserving Exponential Integrators for the Nonlinear Schrödinger Equation
A novel class of high-order linearly implicit energy-preserving integrating factor Runge–Kutta methods are proposed for the nonlinear Schrödinger...
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Casimir preserving stochastic Lie–Poisson integrators
Casimir preserving integrators for stochastic Lie–Poisson equations with Stratonovich noise are developed, extending Runge–Kutta Munthe-Kaas methods....
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Geometric Methods for Adjoint Systems
Adjoint systems are widely used to inform control, optimization, and design in systems described by ordinary differential equations or...
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Second-Order Accurate Structure-Preserving Scheme for Solute Transport on Polygonal Meshes
We analyze mimetic properties of a conservative finite-volume (FV) scheme on polygonal meshes used for modeling solute transport on a surface with...
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Structure-Preserving Reduced- Order Modeling of Non-Traditional Shallow Water Equation
An energy- preserving reduced -order model (ROM) is developed for the non-traditional shallow water equation (NTSWE) with full Coriolis force. The...
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Structure-preserving stochastic conformal exponential integrator for linearly damped stochastic differential equations
In this paper, we study the linearly damped stochastic differential equations, which have the invariants satisfying a linear differential equation...
