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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…
Modern multi-core systems have a large number of design parameters, most of which are discrete-valued, and this number is likely to keep increasing as chip complexity rises. Further, the accurate evaluation of a potential design choice is…
While there have been many developments in computational probes of both strongly-correlated molecular systems and machine-learning accelerated molecular dynamics, there remains a significant gap in capabilities in simulating accurate…
Compared with the remarkable progress made in parallel numerical solvers of partial differential equations,the development of algorithms for generating unstructured triangular/tetrahedral meshes has been relatively sluggish. In this paper,…
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…
Accurate modeling of moving boundaries and interfaces is a difficulty present in many situations of computational mechanics. We use the eXtreme Mesh deformation approach (X-Mesh) to simulate the interaction between two immiscible flows…
The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. This dissertation systematically trailblazes a novel volumetric modeling framework to…
Particle-in-Cell (PIC) simulations are fundamental to plasma physics but often suffer from limited scalability due to particle-grid interaction bottlenecks and particle redistribution costs. Specifically, the particle-grid interaction…
Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural…
In this paper, we introduce Topology Sculptor, Shape Refiner (TSSR), a novel method for generating high-quality, artist-style 3D meshes based on Discrete Diffusion Models (DDMs). Our primary motivation for TSSR is to achieve highly accurate…
Although materials and processes are different from biological cells', brain mimicries led to tremendous achievements in massively parallel information processing via neuromorphic engineering. Inexistent in electronics, we describe how to…
Model biomembrane systems play a crucial role in advancing biomedical research by providing simplified yet effective platforms for exploring complex biological mechanisms. These systems span a wide range of scales, from…
Constructing well-behaved Laplacian and mass matrices is essential for tetrahedral mesh processing. Unfortunately, the \emph{de facto} standard linear finite elements exhibit bias on tetrahedralized regular grids, motivating the development…
We introduce a numerical framework that enables unprecedented direct numerical studies of the electropermeabilization effects of a cell aggregate at the meso-scale. Our simulations qualitatively replicate the shadowing effect observed in…
We present a technique designed for parallelizing large rigid body simulations, capable of exploiting multiple CPU cores within a computer and across a network. Our approach can be applied to simulate both unilateral and bilateral…
We present a framework for characterizing higher-order topological phases directly from the one-particle density matrix, without any reference to an underlying Hamiltonian. Our approach extends the mode-shell correspondence, originally…
This study introduces an open-source computational framework for the generation and permeability evaluation of synthetic porous media. The proposed methodology integrates crystallographic and meshing tools to construct controlled…
Unstructured meshes are characterized by data points irregularly distributed in the Euclidian space. Due to the irregular nature of these data, computing connectivity information between the mesh elements requires much more time and memory…
Meshes are widely used in 3D computer vision and graphics, but their irregular topology poses challenges in applying them to existing neural network architectures. Recent advances in mesh neural networks turn to remeshing and push the…
Metasurfaces, with their superior capability in manipulating the optical wavefront at the subwavelength scale and low manufacturing complexity, have shown great potential for planar photonics and novel optical devices. However, vector field…