Related papers: A mesh-constrained discrete point method for incom…
We design a monotone meshfree finite difference method for linear elliptic equations in the non-divergence form on point clouds via a nonlocal relaxation method. The key idea is a novel combination of a nonlocal integral relaxation of the…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatially varying computational node regularity. Rather than covering the entire domain with…
A systematic study is carried out on a fully resolved fluid-particle model which couples the Lattice Boltzmann Method (LBM) and the Discrete Element Method (DEM) using an immersed moving boundary technique. Similar algorithms have been…
This paper makes the first attempt to apply newly developed upwind GFDM for the meshless solution of two-phase porous flow equations. In the presented method, node cloud is used to flexibly discretize the computational domain, instead of…
We consider the problem of solving partial differential equations (PDEs) in domains with complex microparticle geometry that is impractical, or intractable, to model explicitly. Drawing inspiration from volume rendering, we propose tackling…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
This study proposes an algorithm for modeling compressible flows in spherical shells in nearly incompressible and weakly compressible regimes based on an implicit direction splitting approach. The method retains theoretically expected…
This paper considers the problems of unconstrained minimization of large scale smooth convex functions having block-coordinate-wise Lipschitz continuous gradients. The block coordinate descent (BCD) method are among the first optimization…
When objects are forced to flow through constrictions their transport can be frustrated temporarily or permanently due to the formation of arches in the region of the bottleneck. While such systems have been intensively studied in the case…
An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…
In this paper we present a numerical approach to solve the Navier-Stokes equations on moving domains with second-order accuracy. The space discretization is based on the ghost-point method, which falls under the category of unfitted…
The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by…
In this paper we present a novel approach for the prescription of high order boundary conditions when approximating the solution of the Euler equations for compressible gas dynamics on curved moving domains. When dealing with curved…
A new formulation of the immersed boundary method, which facilitates accurate simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for accurate linear stability analysis of the…
We present a framework for solving partial different equations on evolving surfaces. Based on the grid-based particle method (GBPM) [18], the method can naturally resample the surface even under large deformation from the motion law. We…
The particles on demand (PonD) method is a new kinetic theory model that allows for simulation of high speed compressible flows. While standard Lattice-Boltzmann is limited by a fixed reference frame, significantly reducing the range of…
Continuum dislocation dynamics (CDD) represents the evolution of systems of curved and connected dislocation lines in terms of density-like field variables which include the volume density of loops (or 'curvature density') as an additional…
Many real-world problems are categorized as large-scale problems, and metaheuristic algorithms as an alternative method to solve large-scale problem; they need the evaluation of many candidate solutions to tackle them prior to their…
Momentum Stochastic Gradient Descent (MSGD) algorithm has been widely applied to many nonconvex optimization problems in machine learning, e.g., training deep neural networks, variational Bayesian inference, and etc. Despite its empirical…