Related papers: Efficient Mesh Optimization Using the Gradient Flo…
The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient…
Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. Most common is to use linear…
This paper describes a method for fast simplification of surface meshes. Whereas past methods focus on visual appearance, our goal is to solve equations on the surface. Hence, rather than approximate the extrinsic geometry, we construct a…
Gradient reconstruction is a key process for the spatial accuracy and robustness of finite volume method, especially in industrial aerodynamic applications in which grid quality affects reconstruction methods significantly. A novel gradient…
Recently, machine learning has been used to substitute parts of conventional computational fluid dynamics, e.g. the cell-face reconstruction in finite-volume solvers or the curvature computation in the Volume-of-Fluid (VOF) method. The…
The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…
We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed…
The present paper considers volume formulae, as well as trigonometric identities, that hold for a tetrahedron in 3-dimensional spherical space of constant sectional curvature +1. The tetrahedron possesses a certain symmetry: namely rotation…
Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live…
We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface…
Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…
Global optimization techniques are increasingly preferred over human-driven methods in the design of electromagnetic structures such as metasurfaces, and careful construction and parameterization of the physical structure is critical in…
We test a new "hybrid" scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to…
In this paper, the compact gas-kinetic scheme for compressible flow is extended to hybrid unstructured mesh. Based on both cell-averaged flow variables and their gradients updated from time accurate gas evolution model at cell interfaces, a…
Neural volume rendering became increasingly popular recently due to its success in synthesizing novel views of a scene from a sparse set of input images. So far, the geometry learned by neural volume rendering techniques was modeled using a…
We systematically validate the static local mesh refinement capabilities of a recently proposed IMEX-DG scheme implemented in the framework of the deal.II library. Non-conforming meshes are employed in atmospheric flow simulations to…
In a recent publication we established an analogy between the free energy of a hard sphere system and the energy of an elastic network [1]. This result enables one to study the free energy landscape of hard spheres, in particular to define…
We develop a stabilized cut finite element method for the stationary convection diffusion problem on a surface embedded in ${\mathbb{R}}^d$. The cut finite element method is based on using an embedding of the surface into a three…
Recent developments for mathematical modeling and numerical simulation of biomolecular systems raise new demands for qualified, stable, and efficient surface meshing, especially in implicit-solvent modeling. In our former work, we have…
A comprehensive scheme for the spatial discretisation of continuity equation, momentum advection and normal and shear stresses at the fluid interfaces is presented for numerically simulating the incompressible two phase flows based on the…