Geometry

MagTense Parameters

integer :: tileType
real :: r0, theta0, z0, dr, dtheta, dz
real :: a, b, c
real,dimension(3,4) :: vert

real,dimension(3) :: offset
real,dimension(3) :: rotAngles

With the mentioned parameters a tile can be arbitrarily defined in the global coordinate system. For each tile an individual local coordinate system is created.

Tile Types

• 1 = cylindrical tile

• 2 = prism

• 3 = circular piece

• 4 = inverted circular piece

• 5 = tetrahedron

• 6 = sphere

• 7 = spheroid

• 8 = avgPrism, i.e. a prism whose demagnetization tensor is averaged over the volume of the receiving tile rather than evaluated at its centre

• 101 = planar coil

The tile types are defined as parameters in TileNComponents.f90. The micromagnetic model uses type 2 or type 8 for prismatic cells - selected with useAvgN, see Cell-averaged versus point-evaluated tensor - and type 5 for a tetrahedral mesh.

Offset

The offset is a three-dimensional displacement vector, from the origin of the global coordinate system to origin of the local coordinates. Thus the offset vectors give the center positions of each tile

Rotation Angles

The rotation angles [radians] define the rotation of a tile in its local coordinate system. A tile can be rotated around its local axis with yaw (rotation around local z-axis, \(\psi\)), pitch (rotation around local y-axis, \(\theta\)) and roll (rotation around local x-axis, \(\phi\)).

Rotations of a tile are performed in its local coordinate system. Firstly, the tile is rotated with \(\phi\) around its local x-axis. Secondly, the local y-axis is rotated by \(\theta\). Finally, the angle \(\psi\) is performed around the local z-axis.

Set geometric dimensions

Cylindrical Tile

The cylindrical tile is defined in cylindrical coordinates with respect to its local coordinate system. The center point is located at \((r_0, \theta_0, z_0)\). The extensions in each direction are given with \(dr, d\theta\) and \(dz\), respectively.

Examples of how to compute the magnetic field from such a tile are given in Matlab and python.

Prism

The prism is defined by the side lengths \(a, b\) and \(c\). Its center coordinate is \((x_{off}, y_{off}, z_{off})\) in the global coordinate system. (Note that this is opposed to the definition in the original publication which uses side lengths of [2a, 2b, 2c])

Examples of how to compute the magnetic field from such a tile are given in Matlab and python.

Circular Piece

The circular piece is defined by its center point (\(r_0, \theta_0, z_0\)) in the local coordinate system. The midpoint of the outer circular edge is given with a translation of \(\frac{dr}{2}\) from the center point. The extensions in the others directions are given with \(d\theta\) and \(dz\). In contrast to the cylindrial tile, the inner edges are parallel to the local x-axis and y-axis and from a right angle.

Examples of how to compute the magnetic field from such a tile are given in python.

Inverted Circular Piece

The midpoint of the inner circular edge is located at (\(r_0 + \frac{dr}{2}, \theta_0, z_0\)) in the local coordinate system. The angular extension in each direction is \(\frac{d\theta}{2}\) extensions and the height of such a tile is \(dz\). The outer edges are parallel to the local x-axis and y-axis and from a right angle. Therefore, its naming is “inverted circular piece”.

Examples of how to compute the magnetic field from such a tile are given in python.

Tetrahedron

A tetrahedron is specified by its four vertices in the global coordinate system.

Examples of how to compute the magnetic field from such a tile are given in Matlab and python.

Sphere

A sphere is fully defined by its radius \(a\). Its center coordinate is \((x_{off}, y_{off}, z_{off})\) in the global coordinate system.

Examples of how to compute the magnetic field from such a tile are given in Matlab and python.

Spheroid

Its center coordinate is \((x_{off}, y_{off}, z_{off})\) in the global coordinate system. The axial radii can be specified with \(a, b\) and \(c\), whereas two radii must have the same length.
If \(b < a\), then we have a oblate spheroid.
If \(b > a\), then a prolate spheroid is constructed.
In praxis, any of the axial radii can be chosen to differ from the others.

As a specialty of this geometry, rotation may be also defined as a rotation axis pointing in a given direction. One can either choose the symmetry axis (axis with a radius different to the other ones) or the c-axis. The arguments are defined in the interfaces and are translated to the corresponding rotation angles in the local coordinate system.

Examples of how to compute the magnetic field from such a tile are given in Matlab and python.