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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…
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-…
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…
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…