Lattices of points. More...
Enumerations | |
| enum | type { equispaced = 0, gll = 1, chebyshev = 2, gl = 4, chebyshev_plus_endpoints = 10, gl_plus_endpoints = 11 } |
| enum | simplex_method { none = 0, warp = 1, isaac = 2, centroid = 3 } |
Functions | |
| xt::xtensor< double, 2 > | create (cell::type celltype, int n, lattice::type type, bool exterior, lattice::simplex_method simplex_method=lattice::simplex_method::none) |
Lattices of points.
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strong |
The method used to generate points inside simplices.
lattice::simplex_method::none can be used when no method is needed (eg when making points on a quadrilateral, or when making equispaced points).
lattice::simplex_method::warp will use the warping defined in Hesthaven and Warburton, Nodal Discontinuous Galerkin Methods, 2008, pp 175-180 (https://doi.org/10.1007/978-0-387-72067-8).
lattice::simplex_method::isaac will use the method described in Isaac, Recursive, Parameter-Free, Explicitly Defined Interpolation Nodes for Simplices, 2020 (https://doi.org/10.1137/20M1321802).
lattice::simplex_method::centroid will place points at the centroids of the grid created by putting points on the edges, as described in Blyth and Pozrikidis, A Lobatto interpolation grid over the triangle, 2001 (https://doi.org/10.1093/imamat/hxh077).
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strong |
The type of point spacing to be used in a lattice.
lattice::type::equispaced represents equally spaced points on an interval and a regularly spaced set of points on other shapes.
lattice::type::gll represents the GLL (Gauss-Lobatto-Legendre) points.
lattice::type::chebyshev represents the Chebyshev points.
lattice::type::gl represents the GL (Gauss-Legendre) points.
lattice::type::chebyshev_plus_endpoints represents the Chebyshev points plus the endpoints of the interval. lattice::type::gl_plus_endpoints represents the Chebyshev points plus the endpoints of the interval. These points are only intended for internal use.
| xt::xtensor< double, 2 > basix::lattice::create | ( | cell::type | celltype, |
| int | n, | ||
| lattice::type | type, | ||
| bool | exterior, | ||
| lattice::simplex_method | simplex_method = lattice::simplex_method::none |
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| ) |
Create a lattice of points on a reference cell optionally including the outer surface points
For a given celltype, this creates a set of points on a regular grid which covers the cell, eg for a quadrilateral, with n=2, the points are: [0,0],[0.5,0],[1,0],[0,0.5],[0.5,0.5],[1,0.5],[0,1],[0.5,1],[1,1] If the parameter exterior is set to false, the points lying on the external boundary are omitted, in this case for a quadrilateral with n=2, the points are: [0.5,0.5]. The lattice type can be chosen as "equispaced" or "gll". The "gll" lattice has points spaced along each edge at the Gauss-Lobatto-Legendre quadrature points. These are the same as "equispaced" when n<3.
| celltype | The cell::type |
| n | Size in each direction. There are n+1 points along each edge of the cell. |
| type | A lattice type |
| exterior | If set, includes outer boundaries |
| simplex_method | The method used to generate points on simplices |