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09/08/2023
Riemannian Langevin Monte Carlo schemes for sampling PSD matrices with fixed rank
This paper introduces two explicit schemes to sample matrices from Gibbs...
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07/19/2023
A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system
For time-dependent PDEs, the numerical schemes can be rendered bound-pre...
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05/09/2023
A positivity-preserving implicit-explicit scheme with high order polynomial basis for compressible Navier-Stokes equations
In this paper, we are interested in constructing a scheme solving compre...
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02/09/2023
On the convergence of orthogonalization-free conjugate gradient method for extreme eigenvalues of Hermitian matrices: a Riemannian optimization interpretation
In many applications, it is desired to obtain extreme eigenvalues and ei...
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01/24/2023
On the convergence of Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem
We study the convergences of three projected Sobolev gradient flows to t...
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10/29/2022
Structure preserving schemes for Fokker-Planck equations of irreversible processes
In this paper, we introduce second order and fourth order space discreti...
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04/16/2022
Riemannian optimization using three different metrics for Hermitian PSD fixed-rank constraints: an extended version
We consider smooth optimization problems with a Hermitian positive semi-...
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04/23/2021
Discrete Maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation
We consider solving a generalized Allen-Cahn equation coupled with a pas...
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03/31/2021
Positivity-preserving and energy-dissipative finite difference schemes for the Fokker-Planck and Keller-Segel equations
In this work, we introduce semi-implicit or implicit finite difference s...
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02/28/2021
Accuracy of spectral element method for wave, parabolic and Schrödinger equations
The spectral element method constructed by the Q^k (k≥ 2) continuous fin...
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10/14/2020