相关论文: Exponential time integrators for unsteady advectio…

We develop an adaptive method of time layers with a linearly implicit Rosenbrock method as time integrator and symmetric interior penalty Galerkin method for space discretization for the advective Allen-Cahn equation with…

A general high-order fully explicit scheme based on projective integration methods is here presented to solve systems of degenerate parabolic equations in general dimensions. The method is based on a BGK approximation of the…

This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the…

The anisotropic diffusion equation is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and its interplay with the ambient magnetic field. This diffusion term contributes to the highly stiff nature of the…

This paper deals with the application of probabilistic time integration methods to semi-explicit partial differential-algebraic equations of parabolic type and its semi-discrete counterparts, namely semi-explicit differential-algebraic…

Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…

This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…

Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular.…

In this paper, we implement exponential integrators, specifically Integrating Factor (IF) and Exponential Time Differencing (ETD) methods, using pseudo-spectral techniques to solve phase-field equations within a Python framework. These…

Overset meshes are an effective tool for the computational fluid dynamic simulation of problems with complex geometries or multiscale spatio-temporal features. When the maximum allowable timestep on one or more meshes is significantly…

Strongly interacting electrons in solids are generically described by Hubbardtype models, and the impact of solar light can be modeled by an additional time-dependence. This yields a finite dimensional system of ordinary differential…

In this paper, we consider the application of exponential integrators to problems that are advection dominated, either on the entire or on a subset of the domain. In this context, we compare Leja and Krylov based methods to compute the…

This paper presents the first analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains. The analysis is based on non-standard local trace and inverse inequalities…

Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, they suffer performance penalties for certain stiff systems,…

The implementation of the discrete adjoint method for exponential time differencing (ETD) schemes is considered. This is important for parameter estimation problems that are constrained by stiff time-dependent PDEs when the discretized PDE…

Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny time-step across the entire computational domain when using…

Exponential integrators are special time discretization methods where the traditional linear system solves used by implicit schemes are replaced with computing the action of matrix exponential-like functions on a vector. A very general…

In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…

To address the issues of stability and accuracy for reaction-diffusion equations, the development of high order and stable time-stepping methods is necessary. This is particularly true in the context of cardiac electrophysiology, where…

In this paper, we propose a new second-order fast finite difference scheme in time for solving the Tempered Time Fractional Advection-Dispersion Equation. Under the assumption that the solution is nonsmooth at the initial time, we…