Abstracts
Abstracts
Title: From Basic FEM to Polytopal Mixed FEM in Voronoi-polytopal Mesh
Abstract
The Finite Element Method (FEM) is a numerical method used for solving differential equations. FEM breaks down a whole system into smaller, simpler elements, such as intervals in 1D and triangles or quadrilaterals in 2D. FEM is computationally efficient, in that one can compute one local matrix of one element and reuse it for other elements. FEM is memory-efficient, in that basis functions have small supports, so the global matrix is sparse. In contrast to standard FEM, mixed FEM introduces additional variables. For instance, in fluid dynamics, mixed FEM proves effective for simultaneously computing pressure and (Darcy) velocity fields.
The polytopal FEM has many applications in engineering, such as material science. For example, polygonal elements were shown to be better than triangular and quadrilateral elements under bending and shear loadings (Talischi et al., 2010). A lowest order H(div) conforming elements on polytopal mesh was introduced where rational functions and convex polygons are required (Chen and Wang, 2017).
A new stable mixed finite element on a polytopal mesh was introduced. It (i) does not require the polygon to be convex; (ii) is a high order method with any degree of polynomial k; (iii) can be exactly integrated. The idea is to construct a piecewise polynomial on a polygon so that its divergence is a one-piece polynomial on the whole polygon (Lin et al., 2021).
Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology (Voronoi diagram - Wikipedia). For example, the Voronoi cell finite element method (VCFEM) has been developed for mechanical modeling of non-uniform materials (Ghosh, 2011). The presentation will cover a review of FEM in 1D, FEM in 2D, mixed FEM in 2D, and an in-depth study of this new polytopal mixed FEM.
Title: Advancing TLM Analysis : a Focus on Improving Linear Current Equations with Variables Parameters
Abstract
For a TLM (Transfer Length Method) analysis, we often aim to extract important parameters like Diffusion current, Linear current, and Saturation current. In this presentation, we highlight a new method to evaluate the Linear current equations while considering the variables .
One common challenge in TLM analysis is figuring out the (threshold voltage). Unfortunately, there isn’t a universally accepted method for accurately determining it. To tackle this issue, we propose a simple approach where we treat as a constant value and use it in our new method to calculate (contact resistance) and (mobility).
By examining the results obtained through various Iterative method, we aim to show how this approach can enhance the accuracy of Linear current calculations in TLM analysis.
Title: Numerical Analysis of 3D Isotropic Turbulence with Pseudo-Spectral Method.
Abstract
Understanding and predicting turbulence is a fundamental challenge across various fields. Turbulence occurs in most engineering applications, but it is a complex phenomenon because it is governed by the Navier-Stokes equation. In turbulence analysis, there are two approaches: turbulence model and Direct Numerical Simulation (DNS). While DNS comes with some limitations, it provides significantly enhanced accuracy compared to turbulence models. This presentation will introduce the process of analyzing turbulence using DNS, with a specific example of 3D isotropic turbulence using the Pseudo-Spectral method. The pseudo-Spectral method is one of the DNS methods, which is based on the Fourier Transformto and has more precise accuracy than conventional DNS methods.
Title: Weyl actions on Picard group of Rational surfaces
Abstract
In this talk, we discuss the Picard group of del Pezzo surfaces from the view of Root lattices and Dual lattices along the Weyl groups. We consider the special divisor classes of Picard group which are lattices points called lines, ruling and exceptional systems. Based on the correspondence with Weyl actions between these special divisor classes of del Pezzo surfaces and the geometry of Gosset polytopes of type (r - 4)_21, we study certain Er-type root lattices embedded within the standard Lorentzian lattice Zr+1 (3 ≤ r ≤ 8). We explain the hierarchy of periodicity of affine lattice planes as the roots lattices and their duals. This is a joint work with Jae-hyouk Lee.
송윤영
Title: Improvement of Butterfly Subdivision Scheme using Radial Basis Function
Abstract
Butterfly subdivision scheme is an interpolatory subdivision scheme for 3D surface generation, which gives accuracy of order 4 for smooth, C^4 curves. However, at non-smooth, non- differentiable points on the surface, we cannot avoid inaccuracy, oscillation and decrement of the order. Hence, our goal in this research is to avoid inaccurate surface generation using radial basis function kernels.
신지연
Title: Introduction to NeRF (Neural Radiance Fields)
Abstract
NeRF has generated attention for its breakthrough in 3D scene representation and novel view
synthesis using deep learning. This technology reconstructs detailed 3D scenes from 2D images,
allowing for realistic image synthesis from unobserved viewpoints. NeRF's capability to generate
immersive and natural images from novel perspectives presents innovative possibilities for
visualization and simulation in virtual or real-world environments.
Title: Efficient Scalar Mutilplications over Twisted Edwards Curves of Isogeny-based PQC
Abstract
In the context of PQC, a research result has been published stating that SIDH based on isogeny is vulnerable to polynomial-time attacks. Currently, various research methods are being published to address this vulnerability. All of these protocols used in these diverse research methods always involve scalar multiplication operations. To maximize efficiency in all isogeny-based cryptographic systems, improving isogeny computations or enhancing scalar multiplication calculations used within the cryptographic system are the most common approaches. We implemented scalar multiplication in Isogeny-based cryptographic systems using both Montgomery curves and twisted Edwards curves. In particular, we utilized the GLV method on twisted Edwards curves to increase the efficiency of scalar multiplication. This resulted in an improvement of approximately 45% to 58% in efficiency at each bit.
Title: Critical thresholds in plasma ion dynamics
Abstract
We investigate the critical thresholds phenomena for Euler-Poisson (EP) system with the Boltzmann relation in one dimension, which describes the dynamics of ions in a electrostatic plasma. We propose a new method based on Lyapunov functions to construct the supercritical region with finite-time breakdown and the subcritical region with global-in-time regularity of $C^1$ solutions for the pressureless damped EP system with Boltzmann relation.