Q-tensor 3D

"Q-tensor 3D" is an implementation of the Landau-de Gennes Q-tensor model for liquid crystals.

Saves

To use qtensor3d, a save folder needs to be created. The easiest way to do this is to use qsave in the following manner:

qsave -b <savepath>

where <savepath> is the save folder. This will create a save folder with the default settings, cosntants, and uflexpr files.

Settings configuration

Settings files are in the '.yml' format. Visit PyYAML for more information.

• mesh:
  • source - builtin, local, global, or legacy
  • name - See "Choosing a mesh" for more info
  • refs - How many refinements of the mesh to complete
• options:
  • strong_boundary - May be given as a number or a list of numbers; specifies those boundaries where Dirichlet conditions will be enforced
  • weak_boundary - May be given as a number or a list of numbers; specifies those boundaries where weak conditions will be enforced
• pde:
  • formulation - default or lavrentovich
  • grad_desc - If true, will use gradient descent to solve PDE
  • gd_ls - backtrack, exact1, exact2, or none - Chooses the line search type of the gradient descent
  • solver - dynamic, newton, or builtin_nonlinear
  • tol_u - lower tolerance for dynamic solver
  • tol_l - upper tolerance for dynamic solver
  • tol - tolerance for finding a solution
• solver:
  • ksp_type - Krylov subspace method
  • pc_type - Preconditioner type
• time:
  • num - Number of time steps
  • save_every - Number of time steps at which to save the simulation
  • step - The step size
• vis:
  • normal - upward or outwrd - which direction the normal vector is pointing

Choosing a mesh

To choose a mesh, we go into our settings.yml file and edit the settings listed under mesh. We begin with the source setting. We may choose builtin, local, global, or legacy.

Builtin

If using a builtin mesh, the only mesh implemented at the moment is the Box Mesh. Let's say we want to create a Box Mesh of length, width and height x, y, and z respectively. Moreover, let's let xn, yn, and zn be the number of nodes along the length, width, and height repectively. To do this, we set source to builtin, and set name to BoxMesh xn yn zn x y z. For example, for a slab with a 10 x 10 base and a height of 0.2, with a mesh size of 0.1, we would implement it as follows:

mesh:
  source: builtin
  name: BoxMesh 10 10 2 1 1 0.2

Local

To use a local mesh, simply save a .msh file inside of the save folder. For example, if we want to use a mesh named mesh.msh located in our save folder, we implement the following settings:

mesh:
  source: local
  name: mesh.msh

Global

To use a mesh saved at an absolute file path, specify the absolute path. For example, if we have a mesh located at /scratch/username/meshes/mesh.msh, we would implement is as follows:

mesh:
  source: global
  name: /scratch/username/meshes/mesh.msh

Legacy

Mainly used for the old mesh format. For instance, we would specify /scratch/username/meshes/meshX.msh, where X is the refinement number. For example, the following implementation will cycle through 3 refinement levels of the mesh named as above:

mesh:
  source: legacy
  name: /scratch/username/meshes/mesh
  refs: 0-2