Related papers: Dimension Splitting and a Long Time-Step Multi-Dim…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…
Sliding meshes are a powerful method to treat deformed domains in computational fluid dynamics, where different parts of the domain are in relative motion. In this paper, we present an efficient implementation of a sliding mesh method into…
This paper presents a characteristic-based flux partitioning for the semi-implicit time integration of atmospheric flows. Nonhydrostatic models require the solution of the compressible Euler equations. The acoustic time-scale is…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
This paper introduces a second-order convex splitting scheme for gradient flows arising in phase-field models, based on the backward differentiation formula (BDF2) for the implicit part and the Adams-Bashforth method for the nonlinear and…
Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time…
We present a machine learning framework that blends image super-resolution technologies with passive, scalar transport in the level-set method. Here, we investigate whether we can compute on-the-fly, data-driven corrections to minimize…
Dynamic discrete choice models are widely employed to answer substantive and policy questions in settings where individuals' current choices have future implications. However, estimation of these models is often computationally intensive…
Developing robust simulation tools for problems involving multiple mathematical scales has been a subject of great interest in computational mathematics and engineering. A desirable feature to have in a numerical formulation for multiscale…
We present a more accurate numerical scheme for the calculation of diffusive shock acceleration of cosmic rays using Stochastic Differential Equations. The accuracy of this scheme is demonstrated using a simple analytical flow profile that…
In this paper, we propose a novel unstructured mesh control volume method to deal with the space fractional derivative on arbitrarily shaped convex domains, which to the best of our knowledge is a new contribution to the literature.…
In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework…
Matrix double splitting iterations are simple in implementation while solving real non-singular (rectangular) linear systems. In this paper, we present two Alternating Double Splitting (ADS) schemes formulated by two double splittings and…
Recently, deep convolutional neural networks have achieved great success for medical image segmentation. However, unlike segmentation of natural images, most medical images such as MRI and CT are volumetric data. In order to make full use…
The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular…
In recent years, mode-division multiplexing (MDM) has been proposed as a promising solution in order to increase the information capacity of optical networks both in free-space and in optical fiber transmission. Here we present the design,…
A new moving mesh scheme based on the Lagrange-Galerkin method for the approximation of the one-dimensional convection-diffusion equation is studied. The mesh movement, which is prescribed by a discretized dynamical system for the nodal…
As a mathematical model of high-speed flow and shock wave propagation in a complex multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes, advection-dominated solutions, and moving shock fronts with sharp…