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Related papers: Multicontinuum splitting schemes for multiscale wa…

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In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…

Numerical Analysis · Mathematics 2021-06-02 Yalchin Efendiev , Sai-Mang Pun , Petr N. Vabishchevich

We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…

Numerical Analysis · Mathematics 2016-02-11 Simone Cacace , Maurizio Falcone

In this paper, we investigate the use of a mass lumped fully explicit time stepping scheme for the discretisation of the wave equation with underlying material parameters that vary at arbitrarily fine scales. We combine the leapfrog scheme…

Numerical Analysis · Mathematics 2021-09-08 Sjoerd Geevers , Roland Maier

We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is…

Numerical Analysis · Mathematics 2023-12-01 Andrea Bressan , Annalisa Buffa , Alen Kushova , Rafael Vázquez

Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such…

Numerical Analysis · Mathematics 2025-06-27 Wei Xie , Viet Ha Hoang , Yin Yang , Yunqing Huang

In this paper, we discuss a general framework for multicontinuum homogenization. Multicontinuum models are widely used in many applications and some derivations for these models are established. In these models, several macroscopic…

Numerical Analysis · Mathematics 2023-09-18 E. Chung , Y. Efendiev , J. Galvis , W. T. Leung

We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…

Numerical Analysis · Mathematics 2022-10-26 Siyang Wang , Gunilla Kreiss

This study addresses the challenge of simulating realistic particle systems by proposing a novel particle decomposition scheme that improves the parallel performance of surface resolved particle simulations. Realistic particle systems often…

Fluid Dynamics · Physics 2024-03-21 J. E. Marquardt , N. Hafen , M. J. Krause

Mortar methods are widely used techniques for discretizations of partial differential equations and preconditioners for the algebraic systems resulting from the discretizations. For problems with high contrast and multiple scales, the…

Numerical Analysis · Mathematics 2016-09-12 Eric T. Chung , Shubin Fu , Yanfang Yang

A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…

Optimization and Control · Mathematics 2009-02-26 H. Attouch , L. M. Briceno-Arias , P. L. Combettes

Numerical simulation of flow problems and wave propagation in heterogeneous media has important applications in many engineering areas. However, numerical solutions on the fine grid are often prohibitively expensive, and multiscale model…

Numerical Analysis · Mathematics 2019-09-30 Siu Wun Cheung , Eric T. Chung , Wing Tat Leung

In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…

Astrophysics · Physics 2009-11-07 A. Brandenburg , W. Dobler

Recent developments in decomposition methods for multi-stage stochastic programming with block separable recourse enable the solution to large-scale stochastic programs with multi-timescale uncertainty. Multi-timescale uncertainty is…

Optimization and Control · Mathematics 2024-09-04 Hongyu Zhang , Erlend Heir , Asbjørn Nisi , Asgeir Tomasgard

We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…

Numerical Analysis · Mathematics 2024-04-29 Alexandre L. Madureira , Marcus Sarkis

We propose a primal-dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling…

Numerical Analysis · Mathematics 2014-10-17 Hédy Attouch , Luis M. Briceño-Arias , Patrick L. Combettes

The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…

Analysis of PDEs · Mathematics 2016-04-26 Stig Larsson , Takayasu Matsuo , Klas Modin , Matteo Molteni

In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…

Numerical Analysis · Mathematics 2022-02-01 Xiaorong Wang , Xiaodi Zhang

Invariant discretization schemes are derived for the one- and two-dimensional shallow-water equations with periodic boundary conditions. While originally designed for constructing invariant finite difference schemes, we extend the usage of…

Mathematical Physics · Physics 2013-01-04 Alexander Bihlo , Roman O. Popovych

This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…

Numerical Analysis · Mathematics 2015-07-31 Weizhang Huang

In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region…

Analysis of PDEs · Mathematics 2021-04-09 Mohammad Akil , Ali Wehbe