research
∙
05/17/2023
Exploring the cloud of feature interaction scores in a Rashomon set
Interactions among features are central to understanding the behavior of...
share
research
∙
05/11/2023
Physics-Informed Neural Networks for Discovering Localised Eigenstates in Disordered Media
The Schrödinger equation with random potentials is a fundamental model f...
research
∙
03/14/2023
Particle-Continuum Multiscale Modeling of Sea Ice Floes
Sea ice profoundly influences the polar environment and the global clima...
research
∙
12/22/2022
Spectral analysis of a family of nonsymmetric fractional elliptic operators
In this work, we investigate the spectral problem Au = λu where A is a f...
research
∙
10/13/2022
Soft isogeometric analysis of the Bound States of a Quantum Three-Body Problem in 1D
The study of quantum three-body problems has been centered on low-energy...
research
∙
08/04/2022
SoftIGA: soft isogeometric analysis
We extend the softFEM idea to isogeometric analysis (IGA) to reduce the ...
research
∙
04/15/2022
Higher-Order SGFEM for One-Dimensional Interface Elliptic Problems with Discontinuous Solutions
We study a class of enriched unfitted finite element or generalized fini...
research
∙
03/23/2022
A boundary-penalized isogeometric analysis for second-order hyperbolic equations
Explicit time-marching schemes are popular for solving time-dependent pa...
research
∙
02/21/2022
Isogeometric Analysis of Bound States of a Quantum Three-Body Problem in 1D
In this paper, we initiate the study of isogeometric analysis (IGA) of a...
research
∙
05/28/2021
Lagrangian Data Assimilation and Uncertainty Quantification for Sea Ice Floes with an Efficient Physics-Constrained Superfloe Parameterization
The discrete element method (DEM) is providing a new modeling approach f...
research
∙
02/15/2021
Outlier removal for isogeometric spectral approximation with the optimally-blended quadratures
It is well-known that outliers appear in the high-frequency region in th...
research
∙
02/11/2021
Higher-order generalized-α methods for parabolic problems
We propose a new class of high-order time-marching schemes with dissipat...
research
∙
02/01/2021
On the Application of Stable Generalized Finite Element Method for Quasilinear Elliptic Two-Point BVP
In this paper, we discuss the application of the Generalized Finite Elem...
research
∙
11/13/2020
SoftFEM: revisiting the spectral finite element approximation of elliptic operators
We propose, analyze mathematically, and study numerically a novel approa...
research
∙
10/16/2020
A boundary penalization technique to remove outliers from isogeometric analysis on tensor-product meshes
We introduce a boundary penalization technique to improve the spectral a...
research
∙
07/16/2020
Analytical solutions to some generalized matrix eigenvalue problems
We present analytical solutions to two classes of generalized matrix eig...
research
∙
11/11/2019
Split generalized-α method: A linear-cost solver for a modified generalized-method for multi-dimensional second-order hyperbolic systems
We propose a variational splitting technique for the generalized-α metho...
research
∙
06/16/2019
Isogeometric Residual Minimization Method (iGRM) with Direction Splitting Preconditoner for Stationary Advection-Diffusion Problems
In this paper, we propose the Isogeometric Residual Minimization (iGRM) ...
research
∙
06/14/2019