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d2LTManifold Class Reference

This class represents an initial attracting 2-dimensional manifold, over which nearby manifolds will be graphed. More...

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Detailed Description

This class represents an initial attracting 2-dimensional manifold, over which nearby manifolds will be graphed.

A d2LTManifold object gives a discrete approximation to a 2-dimensional manifold, together with its tangent bundle and normal bundle. This class approximates a manifold by a simplicial complex and provides adaptive non-uniform refinement of the simplices (so the mesh may be finer where the manifold has greater curvature, and coarse where the manifold is nearly flat). It also keeps track of the nodes in each simplex which correspond to the principal lattice of order p, where p = 1, 2, or 3, for use in conjunction with the "d2graphMan" class. These nodes are used to obtain an approximation of order greater than 1. Continuity is maintained during non-uniform refinement by using the technique of interface constraints.

Examples:
d2StableODE.C and d2StableTruncMap.C.

Member Function Documentation

d2LTManifold::d2LTManifold(int ambDim,int numCoarseElts,int numElts,int numTDs,int k,int numNodes,int numVNodes,int irrGrid,int wAElts)

The semi-explicit constructor for the class d2LTManifold.

Typically, this constructor is invoked just prior to reading in data for the d2LTManifold from a file using the member function readFromFile(char []).

Parameters:
ambDim - a positive integer specifying the ambient dimension.
numCoarseElts - a positive integer specifying the number of 2-simplices in the coarsest uniform mesh of the simplicial complex.
numElts - a positive integer, greater than or equal to numCoarseElts, specifying the total number of 2-simplices in the simplicial complex.
numTDs - a positive integer specifying the number of truncated dimensions.
k - a positive integer, either 1, 2, or 3, specifying the desired order of approximation for manifolds near the initial manifold represented by this d2LTManifold.
numNodes - a positive integer specifying the total number of grid points. This is the number of distinct points in the set: (points corresponding to the principal lattice of order k of a 2-simplex), summed over all the 2-simplices in the simplicial complex.
numVNodes - a positive integer specifying the total number of grid points that are vertices of a 2-simplex. This is the number of distinct points in the set: (points corresponding to the vertices of a simplex), summed over all the 2-simplices in the simplicial complex.
irrGrid - an integer, either 0 or 1, which specifies whether to use non-uniform refinement.
wAElts - an integer, either 0 or 1, which specifies whether to allocate space for and use a polynomial locally approximating the initial manifold for each element.
Returns:
a d2LTManifold object.

d2LTManifold::d2LTManifold(int ambDim,int numCoarseElts,int numTDs,int k,int numNodes,int numVNodes,baseVector<d2GridPt *> &nodeList,Matrix<int> &fitData,int irrGrid,int wAElts)

The explicit constructor for the class d2LTManifold.

Parameters:
ambDim - a positive integer specifying the ambient dimension.
numCoarseElts - a positive integer specifying the number of 2-simplices in the coarsest uniform mesh of the simplicial complex. The d2LTManifold returned from this constructor has a uniform mesh, so this is also the number of 2-simplices in the starting simplicial complex for this d2LTManifold.
numTDs - a positive integer specifying the number of truncated dimensions.
k - a positive integer, either 1, 2, or 3, specifying the desired order of approximation for manifolds near the initial manifold represented by this d2LTManifold.
numNodes - a positive integer specifying the total number of grid points. This is the number of distinct points in the set: (points corresponding to the principal lattice of order k of a 2-simplex), summed over all the 2-simplices in the simplicial complex.
numVNodes - a positive integer specifying the total number of grid points that are vertices of a 2-simplex. This is the number of distinct points in the set: (points corresponding to the vertices of a simplex), summed over all the 2-simplices in the simplicial complex.
nodeList - a reference to a "baseVector" of pointers to "d2GridPt"s. The "baseVector" should have size numNodes, and the "d2GridPt"s should have tangent data and normal data. The base points of the "d2GridPt"s must all lie on the polyhedron determined by the underlying simplicial complex, and must correspond to the principal lattice of order k for some 2-simplex.
fitData - a reference to a "Matrix" of ints. The "Matrix" should have size (numCoarseElts x 5 + (k + 1)*(k + 2)/2), (however, it may change size later). This matrix of integers specifies how all the simplices (and their corresponding elements) and all the grid points fit together. This data allows for an approximation by a simplicial complex of 2-simplices with non-uniform mesh.
irrGrid - an integer, either 0 or 1, which specifies whether to use non-uniform refinement.
wAElts - an integer, either 0 or 1, which specifies whether to allocate space for and use a polynomial locally approximating the initial manifold for each element.
Returns:
a d2LTManifold object.

The documentation for this class was generated from the following files:
Generated at Sat Oct 16 03:55:28 1999 for Computing Invariant Manifolds Library by doxygen  written by Dimitri van Heesch, © 1997-1998