Weizhang Huang

Learn More
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)
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)
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)
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)
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)
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)