Related papers: Patch dynamics with buffers for homogenization pro…

We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The…

We present a "multipatch" infrastructure for numerical simulation of fluid problems in which sub-regions require different gridscales, different grid geometries, different physical equations, or different reference frames. Its key element…

We develop a multiscale patch scheme for studying the system level characteristics of heterogeneous functional graded beams. The algorithm computes the detailed beam dynamics on the microscale, but only in small patches of the beam domain,…

Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…

We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…

The Gaussian phase-space representation can be used to implement quantum dynamics for fermionic particles numerically. To improve numerical results, we explore the use of dynamical diffusion gauges in such implementations. This is achieved…

Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…

Transport across heterogeneous, patchy environments is a ubiquitous phenomenon spanning fields of study including ecological movement, intracellular transport and regions of specialised function in a cell. These regions or patches may be…

For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…

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…

Parallel multiphysics simulations often suffer from load imbalances originating from the applied coupling of algorithms with spatially and temporally varying workloads. It is thus desirable to minimize these imbalances to reduce the time to…

In homogenization theory, mathematical models at the macro level are constructed based on the solution of auxiliary cell problems at the micro level within a single periodicity cell. These problems are formulated using asymptotic expansions…

The simulation of three dimensional magnetostatic problems plays an important role, for example when simulating synchronous electric machines. Building on prior work that developed a domain decomposition algorithm using isogeometric…

The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…

The solution of partial differential equations (PDEs) on complex domains often presents a significant computational challenge by requiring the generation of fitted meshes. The Diffuse Domain Method (DDM) is an alternative which reformulates…

Diffusion models are powerful, but they require a lot of time and data to train. We propose Patch Diffusion, a generic patch-wise training framework, to significantly reduce the training time costs while improving data efficiency, which…

We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…

The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…

We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…