Related papers: Gaussian Integral Method for Void Fraction
The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…
In the context of simulating precision laser interferometers, we compare via several examples two wavefront decomposition methods: the Mode Expansion Method (MEM) and the Gaussian beam decomposition (GBD) for their precision and…
The immersed interface method (IIM) for models of fluid flow and fluid-structure interaction imposes jump conditions that capture stress discontinuities generated by forces that are concentrated along immersed boundaries. Most prior work…
Computational fluid dynamics (CFD) studies have been increasingly used for blood flow simulations in intracranial aneurysms (ICAs). However, despite the continuous progress of body-fitted CFD solvers, generating a high quality mesh is still…
Advances in deep learning have enabled physics-informed neural networks to solve partial differential equations. Numerical differentiation using the finite-difference (FD) method is efficient in physics-constrained designs, even in…
In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…
The authors propose a new modeling approach based on the impedance field method (IFM) to analyze the general geometric variations in device simulations. Compared with the direct modeling of multiple variational devices, the proposed…
We present a direct Poisson solver for massively parallel simulations on three-dimensional Cartesian grids with non-uniform spacing. The method uses a tensor-based formulation in which the operator is diagonalized numerically along two…
This paper studies the problem of estimating physical properties (system identification) through visual observations. To facilitate geometry-aware guidance in physical property estimation, we introduce a novel hybrid framework that…
Cartesian-grid methods in combination with immersed-body and volume-of-fluid methods are ideally suited for simulating breaking waves around ships. A surface panelization of the ship hull is used as input to impose body-boundary conditions…
The Method of Invariant Grid (MIG) is an iterative procedure for model reduction in chemical kinetics which is based on the notion of Slow Invariant Manifold (SIM) [1-4]. Important role, in that method, is played by the initial grid which,…
In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on Generalized Multiscale Finite Element Method (GMsFEM), where we represent the fracture effects on a coarse grid via…
The Method of Invariant Grid (MIG) is a model reduction technique based on the concept of slow invariant manifold (SIM), which approximates the SIM by a set of nodes in the concentration space (invariant grid). In the present work, the MIG…
In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…
We introduce a new Eulerian simulation framework for liquid animation that leverages both finite element and finite volume methods. In contrast to previous methods where the whole simulation domain is discretized either using the finite…
Cartesian-grid methods in combination with immersed-body and volume-of-fluid methods are ideally suited for simulating breaking waves around ships. A surface panelization of the ship hull is used as input to impose body-boundary conditions…
Development of algorithms and growth of computational resources in the past decades have enabled simulations of sediment transport processes with unprecedented fidelities. The Computational Fluid Dynamics--Discrete Element Method (CFD--DEM)…
We perform numerical analysis of a nonlinear gradient flow, which can be regarded as a parabolic minimal surface problem or a regularised total variation flow, using the gradient discretisation method (GDM). GDM is a unified convergence…
3D Gaussian Splatting (3DGS) has recently emerged as a powerful representation of geometry and appearance for dense Simultaneous Localization and Mapping (SLAM). Through rapid, differentiable rasterization of 3D Gaussians, many 3DGS SLAM…
The gas-kinetic scheme(GKS) is a promising computational fluid dynamics (CFD) method for solving the Navier-Stokes equations. It is based on the analytical solution of the BGK equation, which enables accurate and robust simulations. While…