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- Weizhang Huang
- SIAM Review
- 1996

In this paper we consider several moving mesh partial diierential equations which are related to the equidistribution principle. Several of these are new, and some correspond to discrete moving mesh equations which have been used by others. An analysis of their stability is done. It is seen that a key term for most of these moving mesh PDEs is a source-like… (More)

- Chris J. Budd, Weizhang Huang, Robert D. Russell
- SIAM J. Scientific Computing
- 1996

In this paper we consider the numerical solution of PDEs with blow-up for which scaling invariance plays a natural role in describing the underlying solution structures. It is a challenging numerical problem to capture the qualitative behaviour in the blow-up region, and the use of nonuniform meshes is essential. We consider moving mesh methods for which… (More)

Moving mesh partial differential equations (MMPDEs) are used in the MMPDE moving mesh method to generate adaptive moving meshes for the numerical solution of time dependent problems. How MMPDEs are formulated and solved is crucial to the efficiency and robustness of the method. In this paper, several practical aspects of formulating and solving MMPDEs are… (More)

- Weizhang Huang, Benedict J. Leimkuhler
- SIAM J. Scientific Computing
- 1997

We discuss the integration of autonomous Hamiltonian systems via dynamical rescaling of the vector field (reparameterization of time). Appropriate rescalings (e.g., based on normalization of the vector field or on minimum particle separation in an N-body problem) do not alter the time-reversal symmetry of the flow, and it is desirable to maintain this… (More)

Several versions of a moving mesh method are developed based on a mesh spatial smoothing technique and on the moving mesh PDEs derived in a previous paper. These versions are quite simple and easy to program. They are applied to three benchmark one-dimensional problems which show diierent solution behaviour. The numerical results clearly demonstrate that… (More)

- Weizhang Huang, Weiwei Sun
- 2003

The key to the success of a variational mesh adaptation method is to define a proper monitor function which controls mesh adaptation. In this paper we study the choice of the monitor function for the variational adaptive mesh method developed in the previous work [J. Comput. Phys. 174 (2001) 924]. Two types of monitor functions, scalar matrix and non-scalar… (More)

- Weizhang Huang
- 2004

It has been amply demonstrated that significant improvements in accuracy and efficiency can be gained when a properly chosen anisotropic mesh is used in the numerical solution for a large class of problems which exhibit anisotropic solution features. In practice, an anisotropic mesh is commonly generated as a quasi-uniform mesh in the metric determined by a… (More)

- Weizhang Huang, Robert D. Russell
- SIAM J. Scientific Computing
- 1998

In this paper we introduce a moving mesh method for solving PDEs in two dimensions. It can be viewed as a higher-dimensional generalization of the moving mesh PDE (MMPDE) strategy developed in our previous work for one-dimensional problems [W. Huang, Y. Ren, and R. D. Russell, SIAM J. Numer. Anal., 31 (1994), pp. 709–730]. The MMPDE is derived from a… (More)

- Weizhang Huang
- 2006

Mesh adaptation is studied from the mesh control point of view. Two principles, equidistribution and alignment, are obtained and found to be necessary and sufficient for a complete control of the size, shape, and orientation of mesh elements. A key component in these principles is the monitor function, a symmetric and positive definite matrix used for… (More)