相关论文: Streamline integration as a method for structured …
We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points/lines,…
We extend our recent curve-evolution framework based on localized B-spline interpolation to present an adaptive Lagrangian framework for the geometric evolution of point-cloud data representing smooth, codimension-one surfaces in…
Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…
The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines,…
In this paper, we study the mathematical structure and numerical approximation of elliptic problems posed in a (3D) domain $\Omega$ when the right-hand side is a (1D) line source $\Lambda$. The analysis and approximation of such problems is…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…
We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of…
This paper presents a distributed optimization algorithm tailored for solving optimal control problems arising in multi-building coordination. The buildings coordinated by a grid operator, join a demand response program to balance the…
The detection of coherent structures is an important problem in fluid dynamics, particularly in geophysical applications. For instance, knowledge of how regions of fluid are isolated from each other allows prediction of the ultimate fate of…
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity…
Potential flow has many applications, including the modelling of unsteady flows in aerodynamics. For these models to work efficiently, it is best to avoid Biot-Savart interactions. This work presents a grid-based treatment of potential…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
Generating computational anatomical models of cerebrovascular networks is vital for improving clinical practice and understanding brain oxygen transport. This is achieved by extracting graph-based representations based on pre-mapping of…
A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…
Graph-based multi-view spectral clustering methods have achieved notable progress recently, yet they often fall short in either oversimplifying pairwise relationships or struggling with inefficient spectral decompositions in…
Structural balance theory studies stability in networks. Given a $n$-vertex complete graph $G=(V,E)$ whose edges are labeled positive or negative, the graph is considered \emph{balanced} if every triangle either consists of three positive…
The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate…
Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…
This paper presents two kinds of strategies to construct structure-preserving algorithms with homogeneous Neumann boundary conditions for the sine-Gordon equation, while most existing structure-preserving algorithms are only valid for zero…
This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous.…