Sets up a Finite Element basis. It requires a
The basis' functions are globally continuos functions, that are polynomials once restricted to a triangle in the mesh.
The current implementation includes linear finite elements (when
order = 1 in the input
quadratic finite elements (when
order = 2 in the input
FEMbasis object. This contains the
mesh, along with some additional quantities:
orderEither "1" or "2". Order of the Finite Element basis.
nbasisScalar. The number of basis.
transf_coordIt takes value only in the 2D case. It is a list of 4 vectors: diff1x, diff1y, diff2x and diff2y.
Each vector has length #triangles and encodes the information for the tranformation matrix that transforms the
nodes of the reference triangle to the nodes of the i-th triangle.
The tranformation matrix for the i-th triangle has the form [diff1x[i] diff2x[i]; diff1y[i] diff2y[i]].
detJIt takes value only in the 2D case. A vector of length #triangles. The ith element contains
the determinant of the transformation from the reference triangle to the nodes of the i-th triangle.
Its value is also the double of the area of each triangle of the basis.
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## Upload the quasicircle2D data data(quasicircle2D) boundary_nodes = quasicircle2D$boundary_nodes boundary_segments = quasicircle2D$boundary_segments locations = quasicircle2D$locations data = quasicircle2D$data ## Create the 2D mesh mesh = create.mesh.2D(nodes = rbind(boundary_nodes, locations), segments = boundary_segments) ## Plot it plot(mesh) ## Create the basis FEMbasis = create.FEM.basis(mesh) ## Upload the hub2.5D data data(hub2.5D) hub2.5D.nodes = hub2.5D$hub2.5D.nodes hub2.5D.triangles = hub2.5D$hub2.5D.triangles ## Create the 2.5D mesh mesh = create.mesh.2.5D(nodes = hub2.5D.nodes, triangles = hub2.5D.triangles) ## Plot it plot(mesh) ## Create the basis FEMbasis = create.FEM.basis(mesh)
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