Two moving mesh partial differential equations (MMPDEs) with spatial smoothing are derived based upon the equidistribution principle. This smoothing technique is motivated by the robust moving mesh method of Dorfi and Drury [J. Comput. Phys., 69 (1987), pp. 175–195]. It is shown that under weak conditions the basic property of no node-crossing is preserved by the spatial smoothing, and a local ...

We propose algorithms to modify a mesh of a PSLG through out the interactive addition/deletion of elements to/from the PSLG, keeping the quality of the mesh all along the process. Our algorithms achieve quality by deleting, moving or inserting Steiner points.

We present a novel approach to parallel computing, where (virtual) PRAM processors are represented as lightweight threads, and each physical processor is capable of managing several threads. Instead of moving read and write requests, and replies between processor&memory pairs (and caches), we move the lightweight threads. Consequently , the processor load balancing problem reduces to the proble...

We describe a new method for surface reconstruction based on unorganized point clouds without normals. We also present a new algorithm for refining the inital triangulation. The output of the method is a refined triangular mesh with points on the moving least squares surface of the original point cloud.

We introduce a novel method for the generation of fully adaptive streak surfaces in time-varying flow fields based on particle advection and adaptive mesh refinement. Moving least squares approximation plays an important role in multiple stages of the proposed algorithm, which adaptively refines the surface based on curvature approximation and circumradius properties of the underlying Delaunay ...

A new adaptive local mesh refinement method is presented for thin film flow problems containing moving contact lines. Based on adaptation on an optimal interpolation error estimate in the L norm (1 < p 61) [L. Chen, P. Sun, J. Xu, Multilevel homotopic adaptive finite element methods for convection dominated problems, in: Domain Decomposition Methods in Science and Engineering, Lecture Notes in ...

The typical elements in a numerical simulation of fluid flow using moving meshes are a time integration scheme, a rezone method in which a new mesh is defined, and a remapping (conservative interpolation) in which a solution is transferred to the new mesh. The objective of the rezone method is to move the computational mesh to improve the robustness, accuracy and eventually efficiency of the si...

This paper presents a variety of novel uses of space-filling curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes – both structured and unstructured. We demonstrate the use of single O ( N log N ) SFC-based reordering to produce single-pass ( O ( N )) algorithms for ...

In this paper we describe a one-dimensional adaptive moving mesh method and its application to hyperbolic conservation laws from magnetohydrodynamics (MHD). The method is robust, because it employs automatic control of mesh adaptation when a new model is considered, without manually-set parameters. Adaptive meshes are a common tool for increasing the accuracy and reducing computational costs wh...

In this paper we introduce a novel self-organizing method of moving surface reconstruction from the data obtained from measuring real-world objects. The core of the approach is using Kohonen’s Self Organizing Maps model. As that model is not traditionally applied to mesh deformation or surface reconstruction, in the paper we propose its modification enforcing input data approximation and time-s...