Book ChapterDOI
Applications of operator splitting methods to the numerical solution of nonlinear problems in continuum mechanics and physics
Edward J. Dean,C.H. Li,Roland Glowinski,Roland Glowinski +3 more
- pp 13-64
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TLDR
In this article, the main goal is to describe operator splitting methods for the solution of time dependent differential equations, and to discuss their application to the numerical solution of nonlinear problems such as the Navier-Stokes equations for incompressible viscous fluids, the linear eigenvalue problem, the Hartree equation for the Helium atom, and finally to the non-convex problem from the calculus of variations associated to the physics of liquid crystals.Abstract:
The main goal of this paper is to describe operator splitting methods for the solution of time dependent differential equations, andto discuss their application to the numerical solution of nonlinear problems such as the Navier-Stokes equations for incompressible viscous fluids, the linear eigenvalue problem, the Hartree equation for the Helium atom, and finally to the solution of a non convex problemfrom the calculus of variations associated to the physics of liquid crystals. Numerical results will be presented showing the potential of such methods.read more
Citations
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Journal ArticleDOI
Recent Developments in the Modeling, Analysis, and Numerics of Ferromagnetism
Martin Kruzík,Andreas Prohl +1 more
TL;DR: Micromagnetics is a continuum variational theory describing magnetization patterns in ferromagnetic media that leads to rich behavior and pattern formation and is also the reason for severe problems in analysis, model validation, reductions, and numerics.
Journal ArticleDOI
A New Algorithm For Computing Liquid Crystal Stable Configurations: The Harmonic Mapping Case
TL;DR: A new algorithm for minimizing the energy of a nematic liquid crystal based on the equal elastic constants Oseen--Frank model is proposed and the convergence of this algorithm is proved in a continuous setting.
Journal ArticleDOI
An optimum spacing problem for three chips mounted on a vertical substrate in an enclosure
Yang Liu,Nhan Phan-Thien +1 more
TL;DR: In this paper, the optimum spacing problem for three heated chips mounted on a conductive substrate in a two-dimensional enclosure filled with air is solved by an operator-splitting pseudo-timestepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux.
Journal ArticleDOI
Modelling and numerical simulation of low-mach-number compressible flows
Chin-Hsien Li,Roland Glowinski +1 more
TL;DR: In this paper, a segregated time-marching solution scheme is proposed for solving the low-Mach-number flow model with the acoustic waves being filtered out, which does not rely on the correction for global mass conservation to maintain solution accuracy.
Journal ArticleDOI
A complete conjugate conduction convection and radiation problem for a heated block in a vertical differentially heated square enclosure
Yang Liu,Nhan Phan-Thien +1 more
TL;DR: In this paper, the complete conjugate heat conduction, convection and radiation problem for a heated block in a differentially heated square enclosure is solved by an operator-splitting pseudo-time-stepping finite element method.
References
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Book
The physics of liquid crystals
P. G. de Gennes,Richard Alben +1 more
TL;DR: In this paper, the authors define an order parameter statistical theories of the nematic order phenomonological description of the nematic-isotopic mixtures and describe the properties of these mixtures.
Journal ArticleDOI
The Numerical Solution of Parabolic and Elliptic Differential Equations
D. W. Peaceman,H. H. Rachford +1 more
Journal ArticleDOI
Splitting Algorithms for the Sum of Two Nonlinear Operators
P. L. Lions,B. Mercier +1 more
TL;DR: This work studies two splitting algorithms for (stationary and evolution) problems involving the sum of two monotone operators with real-time requirements.