Related papers: Multigrid waveform relaxation for the time-fractio…
We present a waveform relaxation version of the Dirichlet-Neumann method for parabolic problem. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain decomposition, and the iteration…
We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…
We propose a new computational framework that combines the recently developed time-parallel (TP) and the compound wavelet matrix (CWM) methods. The framework, termed tpCWM, offers significant computational acceleration by making…
This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…
We present a new computation method for simulating reflection high-energy electron diffraction and the total-reflection high-energy positron diffraction experiments. The two experiments are used commonly for the structural analysis of…
Exceptionally elegant formulae exist for the fractional Laplacian operator applied to weighted classical orthogonal polynomials. We utilize these results to construct a solver, based on frame properties, for equations involving the…
Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve…
Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that…
In this paper, three efficient ensemble algorithms are proposed for fast-solving the random fluid-fluid interaction model. Such a model can be simplified as coupling two heat equations with random diffusion coefficients and a friction…
In this paper, a multiscale approach with partially explicit time discretization is proposed. The idea is to use a partially explicit time scheme, considering a filtration problem in a fractured medium, where the implicit scheme is used for…
In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system…
In this paper we apply the boundary elements method (BEM) and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of two-dimensional time-fractional partial differential equations (TFPDEs). The fractional…
The prosperous development of both hardware and algorithms for quantum computing (QC) potentially prompts a paradigm shift in scientific computing in various fields. As an increasingly active topic in QC, the variational quantum algorithm…
We introduce an efficient and accurate staggered-grid finite-difference (SGFD) method to solve the two-dimensional elastic wave equation. We use a coupled first-order stress-velocity formulation. In the standard implementation of SGFD…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
The dispersive character of the Hall-MHD solutions, in particular the whistler waves, is a strong restriction to numerical treatments of this system. Numerical stability demands a time step dependence of the form $\Delta t\propto (\Delta…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
A new iterative method for non-LTE multilevel polarized radiative transfer in hydrogen lines is presented. Iterative methods (such as the Jacobi method) tend to damp out high-frequency components of the error fast, but converges poorly due…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
We propose a controllability method for the numerical solution of time-harmonic Maxwell's equations in their first-order formulation. By minimizing a quadratic cost functional, which measures the deviation from periodicity, the…