Adaptive triangular mesh generation
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Erlebacher, Gordon↗
Engineering topics
Eiseman, Peter R.
Publications and source records attributed to Eiseman, Peter R..
Adaptive grid generation
The fundamental principles of adaptive grid generation for the numerical analysis of physical phenomena described by systems of partial differential equations are examined in an analytical review. Topics addressed include weight functions, equidistribution in one dimension, the specification of coefficients in the linear weight, the attraction to a given grid on a curve, evolutionary forces, and metric notation. Consideration is given to curve-by-curve methods, finite-volume methods, variational methods, and temporal aspects.
Eiseman, Peter R.↗
Grid generation for the solution of partial differential equations
A general survey of grid generators 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 meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured 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 parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the 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 generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.
Eiseman, Peter R.↗
Grid generation on surfaces in 3 dimensions
The development of a surface grid generation algorithm was initiated. The basic adaptive movement technique of mean-value-relaxation was extended from the viewpoint of a single coordinate grid over a surface described by a single scalar function to that of a surface more generally defined by vector functions and covered by a collection of smoothly connected grids. Within the multiconnected assemblage, the application of control was examined in several instances.
Eiseman, Peter R.↗
The creation of local clusters in arbitrarily given grids
A method is presented to smoothly insert pointwise clusters into any given grid regardless of its origin, its topology, or its dimensionality. The process amounts to a local movement of the given coordinate curves or surfaces to more highly resolve an object. The object about which clustering is created can be a point, a curve, a surface, or segments of a curve or surface. The basic clustering capability is established by forming a grid operator for a single cluster. With a view toward multiple clusters being created about various objects, the basic operator is seen as an elementary operator. An algorithm is presented to execute the general elementary operation in three dimensions. In FORTRAN, this assumes the form of a subroutine which is fully operational and is presented to serve as a basic model for any such elementary clustering operation.
Eiseman, Peter R.↗
Solution adaptive grid generation
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Eiseman, Peter R.↗