Related papers: A diffuse interface approach for vector-valued PDE…
Maps from a source manifold $ {\mathcal M}$ to a target manifold ${\mathcal N}$ appear in liquid crystals, colour image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems…
The goal of this paper is to compare surface-based and volumetric 3D object shape representations, as well as viewer-centered and object-centered reference frames for single-view 3D shape prediction. We propose a new algorithm for…
Most of the existing point-to-mesh distance query solvers, such as Proximity Query Package (PQP), Embree and Fast Closest Point Query (FCPW), are based on bounding volume hierarchy (BVH). The hierarchical organizational structure enables…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
With the aim to characterize the formation and propagation of bulges in cylindrical rubber balloons, we carry out an expansion of the non-linear axisymmetric membrane model assuming slow axial variations. We obtain a diffuse interface model…
We introduce a diffuse interface box method (DIBM) for the numerical approximation on complex geometries of elliptic problems with Dirichlet boundary conditions. We derive a priori $H^1$ and $L^2$ error estimates highlighting the r\^{o}le…
Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the…
High-quality point clouds have practical significance for point-based rendering, semantic understanding, and surface reconstruction. Upsampling sparse, noisy and nonuniform point clouds for a denser and more regular approximation of target…
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with…
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…
This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose…
Vector field design on surfaces was originally motivated by applications in graphics such as texture synthesis and rendering. In this paper, we consider the idea of vector field design with a new motivation from computational topology. We…
We consider an elliptic optimal control problem where the objective functional contains an integral along a surface of codimension 1, also known as a hypersurface. In particular, we use a fidelity term that encourages the state to take…
Parametric finite elements lead to very efficient numerical methods for surface evolution equations. We introduce several computational techniques for curvature driven evolution equations based on a weak formulation for the mean curvature.…
Topological abstractions offer a method to summarize the behavior of vector fields but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach,…
This paper presents an easy-to-control volume peeling method for multi-axis machining based on the computation taken on vector fields. The current scalar field based methods are not flexible and the vector-field based methods do not…
We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…