62 citations · 143 across the 11 of their papers we have counts for
11 papers
Combinatorial and Hodge Laplacians: Similarity and Difference
Emily Ribando-Gros, Rui Wang, Jiahui Chen +2
As key subjects in spectral geometry and combinatorial graph theory respectively, the (continuous) Hodge Laplacian and the combinatorial Laplacian share similarities in revealing t…
HERMES: Persistent spectral graph software
Rui Wang, Rundong Zhao, Emily Ribando-Gros +3
Persistent homology (PH) is one of the most popular tools in topological data analysis (TDA), while graph theory has had a significant impact on data science. Our earlier work intr…
Evolutionary de Rham-Hodge method
Jiahui Chen, Rundong Zhao, Yiying Tong +1
The de Rham-Hodge theory is a landmark of the 20 Century's mathematics and has had a great impact on mathematics, physics, computer science, and engineering. This work…
The de Rham-Hodge analysis and modeling of biomolecules
Rundong Zhao, Menglun Wang, Yiying Tong +1
Recent years have witnessed a trend that advanced mathematical tools, such as algebraic topology, differential geometry, graph theory, and partial differential equations, have been…
Divide-and-Conquer Strategy for Large-Scale Eulerian Solvent Excluded Surface
Rundong Zhao, Menglun Wang, Yiying Tong +1
Motivation: Surface generation and visualization are some of the most important tasks in biomolecular modeling and computation. Eulerian solvent excluded surface (ESES) software pr…
Parallel Transport Unfolding: A Connection-based Manifold Learning Approach
Max Budninskiy, Glorian Yin, Leman Feng +2
Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a…
Subdivision based Isogeometric Analysis technique for Electric Field Integral Equations for Simply Connected Structures
Jie Li, Daniel Dault, Beibei Liu +2
The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but {\em not} different…
Persistent Homology for The Quantitative Prediction of Fullerene Stability
Kelin Xia, Xin Feng, Yiying Tong +1
Persistent homology is a relatively new tool often used for \emph{qualitative} analysis of intrinsic topological features in images and data originated from scientific and engineer…
Structure-Preserving Discretization of Incompressible Fluids
Dmitry Pavlov, Patrick Mullen, Yiying Tong +3
The geometric nature of Euler fluids has been clearly identified and extensively studied over the years, culminating with Lagrangian and Hamiltonian descriptions of fluid dynamics…
Variational Integrators for Maxwell's Equations with Sources
Ari Stern, Yiying Tong, Mathieu Desbrun +1
In recent years, two important techniques for geometric numerical discretization have been developed. In computational electromagnetics, spatial discretization has been improved by…
Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms
Ari Stern, Yiying Tong, Mathieu Desbrun +1
In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete dif…