50 citations · 211 across the 33 of their papers we have counts for
35 papers
Generalised Soft Finite Element Method for Elliptic Eigenvalue Problems
Jipei Chen, Victor M. Calo, Quanling Deng
The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtract…
Exploring the cloud of feature interaction scores in a Rashomon set
Sichao Li, Rong Wang, Quanling Deng +1
Interactions among features are central to understanding the behavior of machine learning models. Recent research has made significant strides in detecting and quantifying feature…
Physics-Informed Neural Networks for Discovering Localised Eigenstates in Disordered Media
Liam Harcombe, Quanling Deng
The Schrödinger equation with random potentials is a fundamental model for understanding the behaviour of particles in disordered systems. Disordered media are characterised by com…
Particle-Continuum Multiscale Modeling of Sea Ice Floes
Quanling Deng, Samuel N. Stechmann, Nan Chen
Sea ice profoundly influences the polar environment and the global climate. Traditionally, Sea ice has been modeled as a continuum under Eulerian coordinates to describe its large-…
Spectral analysis of a family of nonsymmetric fractional elliptic operators
Quanling Deng, Yulong Li
In this work, we investigate the spectral problem where is a fractional elliptic operator involving left- and right-sided Riemann-Liouville derivatives. These operato…
Soft isogeometric analysis of the Bound States of a Quantum Three-Body Problem in 1D
Danyang Li, Quanling Deng
The study of quantum three-body problems has been centered on low-energy states that rely on accurate numerical approximation. Recently, isogeometric analysis (IGA) has been adopte…
SoftIGA: soft isogeometric analysis
Quanling Deng, Pouria Behnoudfar, Victor M. Calo
We extend the softFEM idea to isogeometric analysis (IGA) to reduce the stiffness (consequently, the condition numbers) of the IGA discretized problem. We refer to the resulting ap…
High-Order Enriched Finite Element Methods for Elliptic Interface Problems with Discontinuous Solutions
Champike Attanayake, So-Hsiang Chou, Quanling Deng
Elliptic interface problems whose solutions are continuous have been well studied over the past two decades. The well-known numerical methods include the strongly stable gene…
Isogeometric Analysis of Bound States of a Quantum Three-Body Problem in 1D
Quanling Deng
In this paper, we initiate the study of isogeometric analysis (IGA) of a quantum three-body problem that has been well-known to be difficult to solve. In the IGA setting, we repres…
A boundary-penalized isogeometric analysis for second-order hyperbolic equations
Quanling Deng, Pouria Behnoudfar, Victor Calo
Explicit time-marching schemes are popular for solving time-dependent partial differential equations; one of the biggest challenges these methods suffer is increasing the critical…
Superfloe Parameterization with Physics Constraints for Uncertainty Quantification of Sea Ice Floes
Nan Chen, Quanling Deng, Samuel N. Stechmann
The discrete element method (DEM) is providing a new modeling approach for describing sea ice dynamics. It exploits particle-based methods to characterize the physical quantities o…
Higher-order generalized- methods for parabolic problems
Pouria Behnoudfar, Quanling Deng, Victor M. Calo
We propose a new class of high-order time-marching schemes with dissipation user-control and unconditional stability for parabolic equations. High-order time integrators can delive…
Outlier removal for isogeometric spectral approximation with the optimally-blended quadratures
Quanling Deng, Victor Calo
It is well-known that outliers appear in the high-frequency region in the approximate spectrum of isogeometric analysis of the second-order elliptic operator. Recently, the outlier…
SoftFEM: revisiting the spectral finite element approximation of second-order elliptic operators
Quanling Deng, Alexandre Ern
We propose, analyze mathematically, and study numerically a novel approach for the finite element approximation of the spectrum of second-order elliptic operators. The main idea is…
A boundary penalization technique to remove outliers from isogeometric analysis on tensor-product meshes
Quanling Deng, Victor Calo
We introduce a boundary penalization technique to improve the spectral approximation of isogeometric analysis (IGA). The technique removes the outliers appearing in the high-freque…
Analytical solutions to some generalized and polynomial eigenvalue problems
Quanling Deng
It is well-known that the finite difference discretization of the Laplacian eigenvalue problem leads to a matrix eigenvalue problem (EVP) where the matrix …
Split generalized- method: A linear-cost solver for a modified generalized-method for multi-dimensional second-order hyperbolic systems
Pouria Behnoudfar, Quanling Deng, Victor M. Calo
We propose a variational splitting technique for the generalized- method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splittin…
Higher-order generalized- methods for hyperbolic problems
Pouria Behnoudfar, Quanling Deng, Victor M. Calo
The generalized- time-marching method provides second-order accuracy in time and controls the numerical dissipation in the high-frequency region of the discrete spectrum. This m…
Isogeometric Residual Minimization Method (iGRM) with Direction Splitting Preconditoner for Stationary Advection-Diffusion Problems
Victor M Calo, Marcin Łoś, Quanling Deng +2
In this paper, we introduce the isoGeometric Residual Minimization (iGRM) method. The method solves stationary advection-dominated diffusion problems. We stabilize the method via r…
High-order generalized- methods
Quanling Deng, Pouria Behnoudfar, Victor M. Calo
The generalized- method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation and the…
Residual minimization for isogeometric analysis in reduced and mixed forms
Victor M. Calo, Quanling Deng, Sergio Rojas +1
Most variational forms of isogeometric analysis use highly-continuous basis functions for both trial and test spaces. For a partial differential equation with a smooth solution, is…
A variationally separable splitting for the generalized- method for parabolic equations
Pouria Behnoudfar, Victor M. Calo, Quanling Deng +1
We present a variationally separable splitting technique for the generalized- method for solving parabolic partial differential equations. We develop a technique for a tensor-pr…
Higher order stable generalized finite element method for the elliptic eigenvalue problem with an interface in 1D
Quanling Deng, Victor Calo
We study the generalized finite element methods (GFEMs) for the second-order elliptic eigenvalue problem with an interface in 1D. The linear stable generalized finite element metho…
Optimal spectral approximation of -order differential operators by mixed isogeometric analysis
Quanling Deng, Vladimir Puzyrev, Victor Calo
We approximate the spectra of a class of -order differential operators using isogeometric analysis in mixed formulations. This class includes a wide range of differential opera…