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An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics
  • P. Lin, Chun Liu, Hui Zhang
  • Mathematics, Computer Science
  • J. Comput. Phys.
  • 1 December 2007
Finite element methods are used to simulate the hydrodynamical systems governing the motions of nematic liquid crystals in a bounded domain and a discrete energy law is derived for a modified midpoint time discretization scheme. Expand
Image Segmentation Using Some Piecewise Constant Level Set Methods with MBO Type of Projection
Some algorithms are obtained which are essentially applying the MBO scheme for the authors' segmentation models by using the AOS and MOS schemes to solve the Euler-Lagrange equations for the minimization problems. Expand
Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method
The improved numerical algorithm based on the front tracking method, originally proposed by Tryggvason and his co-workers, is extended to simulate 3D bubbles rising in viscous liquids with high Reynolds and Bond numbers and with large density and viscosity ratios representative of the common air-water two-phase flow system. Expand
A Sequential Regularization Method for Time-Dependent Incompressible Navier--Stokes Equations
The objective of the paper is to present a method, called the sequential regularization method (SRM), for the nonstationary incompressible Navier--Stokes equations from the viewpoint ofExpand
Sequential Regularization Methods for Higher Index DAEs with Constraint Singularities: The Linear Index-2 Case
Standard stabilization techniques for higher index differential-algebraic equations (DAEs) often involve elimination of the algebraic solution components. This may not work well if there areExpand
A Primal-Dual Active-Set Method for Non-Negativity Constrained Total Variation Deblurring Problems
The contribution of this work is a fast and robust numerical algorithm to solve the non-negatively constrained image deblurring problem as a primal-dual program which is a variant of the formulation proposed by Chan, Golub, and Mulet for unconstrained problems. Expand
Simulations of singularity dynamics in liquid crystal flows: A C0 finite element approach
  • P. Lin, Chun Liu
  • Mathematics, Computer Science
  • J. Comput. Phys.
  • 1 June 2006
This paper presents a C^0 finite element method for a 2D hydrodynamic liquid crystal model which is simpler than existing C^1 element methods and mixed element formulation and recommends a fast and reliable algorithm for this model. Expand
An operator-splitting method for a liquid crystal model
Abstract In this paper an operator-splitting method is applied to find the micro-structure of a liquid crystal model with a simplified Oseen–Frank energy functional. Both projection and penaltyExpand
Moisture Transport and Diffusive Instability During Bread Baking
This paper studies multiphase models for simultaneous heat and mass transfer processes during bread baking to provide an explanation and a remedy to the observed erroneous results. Expand
Numerical analysis of Biot's consolidation process by radial point interpolation method
An algorithm is proposed to solve Biot's consolidation problem using meshless method called a radial point interpolation method (radial PIM). The radial PIM is advantageous over the meshless methodsExpand