Related papers: A sharp-interface mesoscopic model for dendritic g…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
We consider discrete Poisson interface problems resulting from linear unfitted finite elements, also called cut finite elements (CutFEM). Three of these unfitted finite element methods known from the literature are studied. All three…
A deep generative model is developed for representation and analysis of images, based on a hierarchical convolutional dictionary-learning framework. Stochastic {\em unpooling} is employed to link consecutive layers in the model, yielding…
The task of deducing three-dimensional molecular configurations from their two-dimensional graph representations holds paramount importance in the fields of computational chemistry and pharmaceutical development. The rapid advancement of…
We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance is often communication bound. This model correctly describes…
Understanding and predicting interface diffusion phenomena in materials is crucial for various industrial applications, including semiconductor manufacturing, battery technology, and catalysis. In this study, we propose a novel approach…
A method of adapting smoothed particle hydrodynamics (SPH) with periodic boundary conditions for use with the special purpose device GRAPE is presented. GRAPE (GRAvity PipE) solves the Poisson and force equations for an N-body system by…
Insoluble surfactants adsorbed at liquid-liquid or gas-liquid interfaces alter interfacial tension, leading to variations in the normal stress jump and generating tangential Marangoni stresses that can dramatically affect the flow dynamics.…
We develop a sharp-interface model for solid-state dewetting of double-bubble thin films using an energy variational approach based on a newly proposed interfacial energy. This model characterizes the dynamic evolution of interfaces in…
The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
In modern computer vision, images are typically represented as a fixed uniform grid with some stride and processed via a deep convolutional neural network. We argue that deforming the grid to better align with the high-frequency image…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically…
In this paper, we propose a novel meshfree Generalized Finite Difference Method (GFDM) approach to discretize PDEs defined on manifolds. Derivative approximations for the same are done directly on the tangent space, in a manner that mimics…
This study addresses ductile fracture of single grains in metals by modeling of the formation and propagation of transgranular cracks. A proposed model integrates gradient extended hardening, phase-field modeling for fracture, and crystal…
Based on the thermodynamic variation to the free energy functional, we propose a sharp-interface model for simulating solid-state dewetting of thin films on rigid curved substrates in two dimensions. This model describes the interface…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
A novel smooth immersed boundary method (IBM) based on a direct-forcing formulation is proposed to simulate incompressible dense particle-laden flows. This IBM relies on a regularization of the transfer function between the Eulerian grid…
The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires…