Related papers: Domain decomposition and locality optimization for…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
A novel Lattice Boltzmann Method applicable to compressible fluid flows is developed. This method is based on replacing the governing equations by a relaxation system and the interpretation of the diagonal form of the relaxation system as a…
We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formulate a non-iterative domain decomposition approach. Such…
Many numerical studies of blood flow impose a rigid wall assumption due to the simplicity of its implementation compared to a full coupling to a solid mechanics model. In this paper, we present a localised method for incorporating the…
Polymer dynamics in a turbulent flow is a problem spanning several orders of magnitude of length and time scales. A microscopic simulation covering all those scales from the polymer segment to the inertial scale of turbulence seems…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
A simple and efficient one-dimensional discrete Boltzmann method is developed for compressible flows with tunable specific heat ratios by incorporating extra degrees of freedom. To guarantee Galilean invariance in numerical simulations, a…
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…
This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
A modified lattice Boltzmann model with a stochastic relaxation mechanism mimicking "virtual'' collisions between free-streaming particles and solid walls is introduced. This modified scheme permits to compute plane channel flows in…
We implement and analyse a sparse / indirect-addressing data structure for the Lattice Boltzmann Method to support efficient compute kernels for fluid dynamics problems with a high number of non-fluid nodes in the domain, such as in porous…
Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…
Domain decomposition has been shown to be a computationally efficient distributed method for solving large scale entropic optimal transport problems. However, a naive implementation of the algorithm can freeze in the limit of very fine…
Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…
Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the…
We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…
A high-performance gas kinetic solver using multi-level parallelization is developed to enable pore-scale simulations of rarefied flows in porous media. The Boltzmann model equation is solved by the discrete velocity method with an…
In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the $d$-dimensional advection-diffusion equation, our proposal is a two-level algorithm…
The modified Born series (MBS) is a fast and accurate method for simulating wave propagation in complex structures. In the current implementation of the MBS, the simulation size is limited by the working memory of a single computer or…