Related papers: A Fully Lagrangian Meshfree Framework for PDEs on …
In this paper, a moving mesh discontinuous Galerkin (dG) method is developed for nonlinear partial differential equations (PDEs) with traveling wave solutions. The moving mesh strategy for one dimensional PDEs is based on the rezoning…
Experimental and field investigations for solution mining processes have improved intensely in recent years. Due to today's computing capacities, three-dimensional simulations of potential salt solution caverns can further enhance the…
We present a meshfree collocation scheme to discretize intrinsic surface differential operators over scalar fields on smooth curved surfaces with given normal vectors and a non-intersecting tubular neighborhood. The method is based on…
Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which…
We develop and analyze a B-spline based arbitrary Lagrangian-Eulerian method of fundamental solutions (ALE-MFS) for curvature-driven motion of two-dimensional evolving domains. Boundary points move with the material to track the geometric…
Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
In most classical approaches of computational geophysics for seismic wave propagation problems, complex surface topography is either accounted for by boundary-fitted unstructured meshes, or, where possible, by mapping the complex…
ESFEM is a method introduced in order to solve a linear advection-diffusion equation on an evolving two-dimensional surface with finite elements by using a moving grid with nodes sitting on and evolving with the surface. The evolution of…
Solutions of partial differential equations (PDEs) on manifolds have provided important applications in different fields in science and engineering. Existing methods are majorly based on discretization of manifolds as implicit functions,…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
A so-called grid-overlay finite difference method (GoFD) was proposed recently for the numerical solution of homogeneous Dirichlet boundary value problems of the fractional Laplacian on arbitrary bounded domains. It was shown to have…
Solving partial differential equations (PDEs) on manifolds defined by randomly sampled point clouds is a challenging problem in scientific computing and has broad applications in various fields. In this paper, we develop a two-step…
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…
This paper explores an efficient Lagrangian approach for evolving point cloud data on smooth manifolds. In this preliminary study, we focus on analyzing plane curves, and our ultimate goal is to provide an alternative to the conventional…
A new arbitrary Lagrangian-Eulerian (ALE) formulation for Navier-Stokes flow on self-evolving surfaces is presented. It is based on a general curvilinear surface parameterization that describes the motion of the ALE frame. Its in-plane part…
We propose a level-set-based semi-Lagrangian method on graded adaptive Cartesian grids to address the problem of surface reconstruction from point clouds. The goal is to obtain an implicit, high-quality representation of real shapes that…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
This research explored a novel explicit total Lagrangian Fragile Points Method (FPM) for finite deformation of hyperelastic materials. In contrast to mesh-based methods, where mesh distortion may pose numerical challenges, meshless methods…
This paper develops and evaluates a novel 3D fully-Lagrangian (particle-based) numerical model, based on the hybrid discrete element method (DEM) and moving particle semi-implicit (MPS) mesh-free techniques, for modeling the highly-dynamic…