Elements

set_nodal_interpolation!(surface_function::SurfaceFunction)

Sets the interpolation nodes surface_function to be the nodal positions.

copy_interpolation_nodes!(physics_function::SurfaceFunction,surfaceFunction::Triangular)

Sets interpolating nodes of physics_function to be the same as the surfaceFunction.

Defines a Triangle with node placements

                                      3     

                                      1 2

and basis functions defined as

\[\mathbf{N}(u,v) = \begin{bmatrix} 1 - u - v \newline u \newline v \end{bmatrix},\quad u \in [0,1], v\in [0,1-u].\]

Defines a Triangle with node placements

                                      3         

                                      6  5      

                                      1  4  2

and basis functions defined as

\[\mathbf{N}(u,v) = \begin{bmatrix} (1 - v - u)(1 - 2v - 2u) \newline u(2u - 1) \newline v(2v - 1) \newline 4u(1 - v - u) \newline 4uv \newline 4v(1 - v - u) \end{bmatrix},\quad u \in [0,1], v\in [0,1-u].\]

Defines a Triangle with node placement on the middle of the triangle.

\[\mathbf{N}(u,v) = [1]\]

Defines a Quadrilateral with node placements

                                        3 -- 4   

                                        |    |   

                                        1 -- 2

and basis functions defined as

\[\mathbf{N}(u,v) = \begin{bmatrix} (1 - u)(1 - v)/4 \newline (1 + u)(1 - v)/4 \newline (1 - u)(1 + v)/4 \newline (1 + u)(1 + v)/4 \newline \end{bmatrix}, \quad u, v \in [-1, 1].\]

Defines a Quadrilateral with node placements

                                        3  9  4  

                                        6  7  8  

                                        1  5  2

and basis functions defined as

\[\mathbf{N}(u,v) = \begin{bmatrix} u(1 - u)v(1 - v)/4 \newline -u(1 + u)v(1 - v)/4 \newline -u(1 - u)v(1 + v)/4 \newline u(1 + u)v(1 + v)/4 \newline -(1 + u)(1 - u)v(1 - v)/2 \newline -u(1 - u)(1 + v)(1 - v)/2 \newline (1 - u^2)(1 - v^2) \newline u(1 + u)(1 + v)(1 - v)/2 \newline (1 + u)(1 - u)(1 + v)v/2 \end{bmatrix}, \quad u, v \in [-1, 1]\]

Defines a Quadrilateral with node placements

                                        4  7  3 

                                        8     6 

                                        1  5  2

and basis functions defined as

\[\mathbf{N}(u,v) = \begin{bmatrix} [(1 - u)(v - 1)(u + v + 1)/4 \newline (1 + u)(v - 1)(v - u + 1)/4 \newline (1 + u)(v + 1)(u + v - 1)/4 \newline (u - 1)(v + 1)(u - v + 1)/4 \newline (1 - v)(1 - u^2)/2 \newline (1 + u)(1 - v^2)/2 \newline (1 + v)(1 - u^2)/2 \newline (1 - u)(1 - v^2)/2 \end{bmatrix}, \quad u, v \in [-1, 1].\]

Defines a Quadrilateral with node placements

                                          ---    

                                        |  1  |  

                                          ---

and basis functions defined as

\[\mathbf{N}(u,v) = [1], \quad u,v \in [-1,1 ]\]

Defines a Quadrilateral with node placements

                                          ---    

                                        | 3 4 |  

                                        | 1 2 |  

                                          ---

and basis functions defined as

\[\mathbf{N}(u,v) = \text{quadrilateralLinear4}(u/(1-\beta),v/(1-\beta)), \quad u,v \in [-1,1 ]\]

Defines a Quadrilateral with node placements

                                          -------   

                                        | 3  9  4 | 

                                        | 6  7  8 | 

                                        | 1  5  2 | 

                                          -------

and basis functions defined as

\[\mathbf{N}(u,v) = \text{quadrilateralQuadraticLagrange}(u/(1-\beta),v/(1-\beta)), \quad u,v \in [-1,1 ]\]