Related papers: Multicontinuum splitting schemes for multiscale wa…
We present a numerical method which is able to approximate traveling waves (e.g. viscous profiles) in systems with hyperbolic and parabolic parts by a direct long-time forward simulation. A difficulty with long-time simulations of traveling…
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
In this paper, we present splitting algorithms to solve multicomponent transport models with Maxwell-Stefan-diffusion approaches. The multicomponent models are related to transport problems, while we consider plasma processes, in which the…
We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy…
We study the numerical anisotropy existent in compact difference schemes as applied to hyperbolic partial differential equations, and propose an approach to reduce this error and to improve the stability restrictions based on a previous…
A discretization scheme for variable coefficient Helmholtz problems on two-dimensional domains is presented. The scheme is based on high-order spectral approximations and is designed for problems with smooth solutions. The resulting system…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…
Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome…
We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…
In this paper, we develop a class of robust numerical methods for solving dynamical systems with multiple time scales. We first represent the solution of a multiscale dynamical system as a transformation of a slowly varying solution. Then,…
In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. Based on the framework of strong…
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…
In this paper, we present the derivation of a multicontinuum model for the coupled flow and transport equations by applying multicontinuum homogenization. We perform the multicontinuum expansion for both flow and transport solutions and…
In this paper, we propose a multirate iterative scheme with multiphysics finite element method for a fluid-saturated poroelasticity model. Firstly, we reformulate the original model into a fluid coupled problem to apply the multiphysics…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The…
This paper applies topology optimisation to the design of structures with periodic microstructural details without length scale separation, i.e. considering the complete macroscopic structure and its response, while resolving all…
We present a matrix-free parallel scalable multilevel deflation preconditioned method for heterogeneous time-harmonic wave problems. Building on the higher-order deflation preconditioning proposed by Dwarka and Vuik (SIAM J. Sci. Comput.…
Asymptotic homogenisation is considered for problems with integral constraints imposed on a slowly-varying microstructure; an insulator with an array of perfectly dielectric inclusions of slowly varying size serves as a paradigm. Although…