Related papers: A diffuse interface approach for vector-valued PDE…
In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…
The dispersion process in particulate porous media at low saturation levels takes place over the surface elements of constituent particles and, as we have found previously by comparison with experiments, can be accurately described by…
Curvature principal directions on geometric surfaces are a ubiquitous concept of Geometry Processing techniques. However they only account for order 2 differential quantities, oblivious of higher order differential behaviors. In this paper,…
In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but…
The aim of this paper is to develop a numerical scheme to approximate evolving interface problems for parabolic equations based on the abstract evolving finite element framework proposed in (C M Elliott, T Ranner, IMA J Num Anal, 41:3,…
We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…
Segmentation of multiple surfaces in medical images is a challenging problem, further complicated by the frequent presence of weak boundary and mutual influence between adjacent objects. The traditional graph-based optimal surface…
This study presents an efficient algebraic scheme known as MULES for sharp interface advection, verified against various schemes including first-order upwind, second-order central, van Leer flux limiter, and Geometric Volume-of-Fluid (VOF).…
We review the construction and analysis of numerical methods for strongly nonlinear PDEs, with an emphasis on convex and nonconvex fully nonlinear equations and the convergence to viscosity solutions. We begin by describing a fundamental…
Surface tension has a strong influence on the shape of fluid interfaces. We propose a method to calculate the corresponding forces efficiently. In contrast to several previous approaches, we discriminate to this end between surface and…
The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color…
We propose to model physical effects at the sharp density interface between atmosphere and ocean with the help of diffuse interface approaches for multiphase flows with variable densities. We use the variable-density model proposed in…
We study the asymptotic limit of diffused surface energy in the van der Waals--Cahn--Hillard theory when an advection term is added and the energy is uniformly bounded. We prove that the limit interface is an integral varifold and the…
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…
Mesh processing pipelines are mature, but adapting them to newer non-mesh surface representations -- which enable fast rendering with compact file size -- requires costly meshing or transmitting bulky meshes, negating their core benefits…
The Gradient Vector Flow (GVF) is a vector diffusion approach based on Partial Differential Equations (PDEs). This method has been applied together with snake models for boundary extraction medical images segmentation. The key idea is to…
Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…
We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and…
The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be…