1. Geometry

1.1. Points

1.1.1. Current Point:

Feel++ Keyword

Math Object

Description

Dimension

P()

\(\overrightarrow{P}\)

\((P_x, P_y, P_z)^T\)

\(d \times 1\)

Px()

\(P_x\)

\(x\) coordinate of \(\overrightarrow{P}\)

\(1 \times 1\)

Py()

\(P_y\)

\(y\) coordinate of \(\overrightarrow{P}\) (value is 0 in 1D)

\(1 \times 1\)

Pz()

\(P_z\)

\(z\) coordinate of \(\overrightarrow{P}\) (value is 0 in 1D and 2D)

\(1 \times 1\)

1.1.2. Element Barycenter Point:

Feel++ Keyword Math Object Description Dimension

C()

\(\overrightarrow{C}\)

\((C_x, C_y, C_z)^T\)

\(d \times 1\)

Cx()

\(C_x\)

\(x\) coordinate of \(\overrightarrow{C}\)

\(1 \times 1\)

Cy()

\(C_y\)

\(y\) coordinate of \(\overrightarrow{C}\) (value is 0 in 1D)

\(1 \times 1\)

Cz()

\(C_z\)

\(z\) coordinate of \(\overrightarrow{C}\) (value is 0 in 1D and 2D)

\(1 \times 1\)

1.1.3. Normal at Current Point:

Feel++ Keyword

Math Object

Description

Dimension

N()

\(\overrightarrow{N}\)

\((N_x, N_y, N_z)^T\)

\(d \times 1\)

Nx()

\(N_x\)

\(x\) coordinate of \(\overrightarrow{N}\)

\(1 \times 1\)

Ny()

\(N_y\)

\(y\) coordinate of \(\overrightarrow{N}\) (value is 0 in 1D)

\(1 \times 1\)

Nz()

\(N_z\)

\(z\) coordinate of \(\overrightarrow{N}\) (value is 0 in 1D and 2D)

\(1 \times 1\)

1.1.4. Extra informations on elements and face of element:

Feel++ Keyword Math Object Description Dimension

h()

\(h\)

maximum edge size in element

1

hMin()

\(h_{\mathrm{min}}\)

minimum edge size in element

1

hFace()

\(h_{\mathrm{f}}\)

maximum edge size of current face

1

meas()

stem:[

\cdot

]

measure of the current element

1

measFace()

stem:[

\cdot

]

measure of the current face

1

eid()

id of the current element

1

emarker()

marker of the current element

1

emarker2()

marker2 of the current element

1

fmarker()

marker of the face in the current element when iterating over faces

1

epid()

pid of the current element

1

1.2. Geometric Transformations

1.2.1. Jacobian Matrix

You can access to the jacobian matrix, \(J\), of the geometric transformation, using the keyword: J() There are some tools to manipulate this jacobian.

Feel++ Keyword

Math Object

Description

detJ()

\(\det(J)\)

Determinant of jacobian matrix

invJT()

\((J^{-1})^T\)

Transposed inverse of jacobian matrix