Author
Xiaonan Wu
Other affiliations: Virginia Tech
Bio: Xiaonan Wu is an academic researcher from Hong Kong Baptist University. The author has contributed to research in topics: Boundary value problem & Mixed boundary condition. The author has an hindex of 18, co-authored 53 publications receiving 1968 citations. Previous affiliations of Xiaonan Wu include Virginia Tech.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, a fully discrete difference scheme is derived for a diffusion-wave system by introducing two new variables to transform the original equation into a low order system of equations. And the solvability, stability and L∞ convergence are proved by the energy method.
949 citations
TL;DR: The convergence and divergence regions for some algorithms are given, and the new algorithms are applied to solve the Stokes equations as well.
Abstract: Several SOR-like methods are proposed for solving augmented systems. These have many different applications in scientific computing, for example, constrained optimization and the finite element method for solving the Stokes equation. The convergence and the choice of optimal parameter for these algorithms are studied. The convergence and divergence regions for some algorithms are given, and the new algorithms are applied to solve the Stokes equations as well.
249 citations
01 Jan 2013
TL;DR: In this paper, when the short-term interest rate is considered as a random variable, there is an unknown function λ(r, t), called the market price of risk, in the governing equation.
Abstract: As pointed out in Sect. 2.3, when the short-term interest rate is considered as a random variable, there is an unknown function λ(r, t), called the market price of risk, in the governing equation.
147 citations
TL;DR: This work has shown how such "covolume" discretizations may be applied to div-curl systems in three dimensions by the Voronoi--Delaunay mesh systems.
Abstract: The Voronoi--Delaunay mesh systems provide a generalization of the classical rectangular staggered meshes to unstructured meshes. In this work, it is shown how such "covolume" discretizations may be applied to div-curl systems in three dimensions. Error estimates are proved and confirmed by a numerical illustration.
86 citations
TL;DR: In this paper, a new mixed finite element method is formulated for the Stokes equations, in which the two components of the velocity and the pressure are defined on different meshes, and first-order error estimates are obtained for both the velocities and pressure.
Abstract: A new mixed finite element method is formulated for the Stokes equations, in which the two components of the velocity and the pressure are defined on different meshes. First-order error estimates are obtained for both the velocity and the pressure. Also, the well-known MAC method is derived from the resulting finite element method.
64 citations
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TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.
Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.
3,015 citations
TL;DR: A large selection of solution methods for linear systems in saddle point form are presented, with an emphasis on iterative methods for large and sparse problems.
Abstract: Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.
2,253 citations
Dissertation•
01 Oct 1948
TL;DR: In this article, it was shown that a metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.
Abstract: IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.
2,042 citations
TL;DR: In this paper, finite element Galerkin schemes for a number of linear model problems in electromagnetism were discussed, and the finite element schemes were introduced as discrete differential forms, matching the coordinate-independent statement of Maxwell's equations in the calculus of differential forms.
Abstract: This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching the coordinate-independent statement of Maxwell's equations in the calculus of differential forms. The asymptotic convergence of discrete solutions is investigated theoretically. As discrete differential forms represent a genuine generalization of conventional Lagrangian finite elements, the analysis is based upon a judicious adaptation of established techniques in the theory of finite elements. Risks and difficulties haunting finite element schemes that do not fit the framework of discrete differential forms are highlighted.
890 citations