Publications of Erlebacher, Gordon

• Grid Generation for the Solution of Partial Differential Equations

  Eiseman P.R., Erlebacher G.

  Published in 1989

  A general survey of grid generation is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for such meshed, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstrutured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic part, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes.

  The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generations and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.

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• Adaptive Triangular Mesh Generation

  Erlebacher G., Eiseman P.R.

  Published in 1987

  A general adaptive algorithm is developed on triangular meshes. The adaptivity is provided by a combination of node addition, dynamic node connectivity and a simple node movement strategy. While the local restructuring process and the node addition mechanism take place in the physical plane, the nodes are displaced on a monitor surface, constructed from the salient features of the physical problem. An approximation to mean curvature detects changes in the direction of the monitor surface, and provides the pulling force on the nodes. Solutions to the axisymmetric Grand-Shafranov equation demonstrate the capturing, by triangles, of the plasma-vacuum interface in a free boundary equilibrium configuration.

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