Xiaohong Chen

Works (4)

Updated: July 5th, 2023 15:36

2018 article

A direct IIM approach for two-phase Stokes equations with discontinuous viscosity on staggered grids

Chen, X., Li, Z., & Álvarez, J. R. (2018, March 10). Computers & Fluids, Vol. 172, pp. 549–563.

By: X. Chen n, Z. Li n  & J. Álvarez*

author keywords: Incompressible Stokes equations; Interface problem; Discontinuous viscosity; Marker and cell scheme; Staggered mesh; Uzawa method; Immersed interface method; Finite difference method
topics (OpenAlex): Lattice Boltzmann Simulation Studies; Advanced Numerical Methods in Computational Mathematics; Computational Fluid Dynamics and Aerodynamics
TL;DR: A direct immersed interface method is proposed to solve two-phase incompressible Stokes equations with an interface and a piecewise constant viscosity on staggered grids that avoids the costs for introducing augmented variables and difficulties in solving them from the corresponding Schur complement system. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: October 19, 2018

2018 article

A direct method for accurate solution and gradient computations for elliptic interface problems

Chen, X., Feng, X., & Li, Z. (2018, March 7). Numerical Algorithms, Vol. 80, pp. 709–740.

By: X. Chen n, X. Feng* & Z. Li n 

author keywords: Elliptic interface problem; Accurate solution and gradient computation; Variable coefficient with discontinuities; Convergence proof; Discrete Green's function; Discrete elliptic maximum principle; Compact finite difference scheme
topics (OpenAlex): Advanced Numerical Methods in Computational Mathematics; Advanced Mathematical Modeling in Engineering; Electromagnetic Simulation and Numerical Methods
TL;DR: A direct method without using the augmented variable is proposed for elliptic interface problems with a variable coefficient that can have a finite jump across an interface. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: April 2, 2019

2018 article

On MultiScale ADI Methods for Parabolic PDEs with a Discontinuous Coefficient

Li, Z., Chen, X., & Zhang, Z. (2018, January 1). Multiscale Modeling and Simulation, Vol. 16, pp. 1623–1647.

By: Z. Li* , X. Chen* & Z. Zhang

author keywords: ADI method; interface problems; discontinuous coefficient; multiscale; jump conditions; augmented variable; stability
topics (OpenAlex): Advanced Numerical Methods in Computational Mathematics; Electromagnetic Simulation and Numerical Methods; Model Reduction and Neural Networks
TL;DR: Alternating direction implicit (ADI) method is one of the most efficient methods in solving parabolic PDEs of initial and boundary value problems and it is challenging to develop efficient ADI methods. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: January 7, 2019

2017 article

Accurate Solution and Gradient Computation for Elliptic Interface Problems with Variable Coefficients

Li, Z., Ji, H., & Chen, X. (2017, January 1). SIAM Journal on Numerical Analysis, Vol. 55, pp. 570–597.

By: Z. Li n , H. Ji & X. Chen n

author keywords: elliptic interface problem; accurate gradient computation; variable coefficient with discontinuity; interface; M-matrix; convergence proof; discrete Green function
topics (OpenAlex): Advanced Numerical Methods in Computational Mathematics; Advanced Mathematical Modeling in Engineering; Numerical methods in engineering
TL;DR: Numerical examples for general elliptic interface problems have confirmed the theoretical analysis and efficiency of the new augmented method and second order convergence for the solution and the gradient from each side of the interface has also been proved. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

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