Related papers: A surface moving mesh method based on equidistribu…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…
This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry,…
We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference schemes are nonlinearly unstable. We build convergent finite…
Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
We examine the use of domain decomposition for potentially more efficient mean curvature flow of surface meshes, whose faces are arbitrary simple polygons. We first test traditional domain decomposition methods with and without overlap of…
This paper surveys recent numerical advances in the phase field method for geometric surface evolution and related geometric nonlinear partial differential equations (PDEs). Instead of describing technical details of various numerical…
Surface growth, by association or dissociation of material on the boundaries of a body, is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a…
We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is…
Many adaptive mesh methods explicitly or implicitly use equidistribution and alignment. These principles can be considered central to mesh adaption. A Metric Tensor is the tool by which one describes the desired level of mesh anisotropy. In…
The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…
In moving mesh methods, the underlying mesh is dynamically adapted without changing the connectivity of the mesh. We specifically consider the generation of meshes which are adapted to a scalar monitor function through equidistribution.…
Bone surface mapping technique is proposed on the bases of two kinds of uniqueness of bone in vivo, (i) magnitude of the principal moments of inertia, (ii) the direction cosines of principal axes of inertia relative to inertia reference…
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…
Fundamental biological and biomimetic processes, from tissue morphogenesis to soft robotics, rely on the propagation of chemical and mechanical surface waves to signal and coordinate active force generation. The complex interplay between…
An elastic surface model is investigated by using the canonical Monte Carlo simulation technique on triangulated spherical meshes. The model undergoes a first-order collapsing transition and a continuous surface fluctuation transition. The…
In this paper we present approaches that address two issues that can occur when the level-set method is used to simulate two-fluid flows in engineering practice. The first issue concerns regularizing the Heaviside function on arbitrary…
In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a…
Currently, the area of geometric modeling and the construction of 3D models based on point clouds from laser sensors is actively developing. One of the basic tasks of geometric modeling is the reconstruction of a surface from a cloud of…