Roadmap

[v0.6.0] - coming soon

Features

• PlanarMesh file I/O
  • save and load PlanarMesh objects to/from file
  • convert svg files to meshes
• new system for defining Edge objects
  • curve type: line
  • curve type: spline
  • curve type: quadratic Bézier
  • curve type: cubic Bézier
  • curve type: symbolic (using sympy)
• Solver improvments
  • option to select preconditioner
  • option to select verbosity level/depth
  • construct global function space if none provided

Examples

• Example 3.1: Finding eigenmodes

Documentation

• update examples and tutorials to reflect new edge system
• tutorials
  • 2: Local function spaces
    • 2.1: Polynomials
    • 2.3: Local Poisson functions
    • 2.4: Local Poisson spaces
  • 3: Finite elements
    • 3.1 Global function spaces (simpler version of Example 2.1)
    • 3.2 Global boundary conditions
  • 4: Advanced topics
    • 4.1 Nystrom solvers

Maintenance

• GlobalFunctionSpace improvements:
  • compute EdgeSpace objects only on reference edges
  • compute quantities of interest only on reference cells
• PlanarMesh improvements:
  • deprecate mesh builder functions in favor of file I/O system
  • automatic identification of repeated edges
  • automatic identification of repeated cells in a mesh (up to scaling and rigid motion)
• refactor Quad:
  • should be named Quadrature with sensible names for attributes
  • use Quadrature class to store all three types of quadrature rules
  • deprecate QuadDict class and get_quad_dict() function
  • the casual user should not need to touch Quadrature objects directly
• MeshPlot improvements:
  • change: initialize with either a list of Edge objects, a MeshCell, or a PlanarMesh
  • add: plot interior points with draw_interior_points() method
  • add: plot interior point triangulation with draw_interior_triangulation() method
• LocalFunctionPlot improvements:
  • add: 'skeleton' option to draw() method, which plots only values on the edges

Project Management

• add sympy to dependencies

Other Planned Features and Improvements

Features

• global boundary conditions
  • define trace of a global function with DirichletTrace class
  • mixed Dirichlet/Neumann boundary conditions
  • nonhomogeneous boundary conditions
• a posteriori error estimation
• BilinearForm improvements
  • piecewise constant coefficients, load function
  • advection terms
  • diffusion terms
• \(p\)-refinement: different polynomial degree on different cells/edges
• \(h\)-refinement: algorithm to split cells

Examples

• "subdivision refinement"
• eigenvalue problem

Documentation

• add: mathematical background

Maintenance

• fix disabled pylint messages
• Polynomial improvements:
  • allow for Floatlike output from eval() method
  • use sets instead of lists of Monomial objects in Polynomial class
  • deprecate barycentric_products() function
  • allow barycentric_coordinates() to accept a list of Vert objects
  • use binary exponentiation algorithm for Polynomial.pow()
  • weighted normal derivative of Polynomial objects in separate module
• Monomial improvements:
  • replace eval() method with __call__() method
  • allow for Floatlike output from eval() method
  • deprecate is_zero() method
• MultiIndex improvements:
  • use Tuple instead of List to set multi-index
• PlanarMesh improvements
  • set vertex and edge indices automatically
  • rename vertex and edge indices to something more descriptive (global mesh properties, not local to a cell)
  • use set instead of list for vertex and cell indices class
• MeshCell improvements
  • optimize computation of interior points and triangulation

Project Management

• add: .github/workflows/ directory for CI/CD
  • add: format.yml for formatting with black and isort
  • add: lint.yml for linting with pylint and mypy
  • add: test.yml for running tests with pytest
  • add: doc.yml for building documentation with mkdocs
• git hooks
  • add: pre-commit hook for formatting
    • isort
    • black
  • add: pre-push hook for linting and testing
    • pylint
    • mypy
    • pydocstyle
    • pytest
• update CONTRIBUTING.md with how to use git hooks and CI/CD

Known bugs

• Polynomial not recognized as a callable map when passed to is_Func_R2_R()
• case with xy2 < TOL near corners on distinct edges in double layer operator can result in nan entries for large values of the discretization parameter n
• DirichletTrace does not recompute traces when function changes

Tentative Features

Features

• \(H\)(div)-conforming spaces
• \(H\)(curl)-conforming spaces
• surface elements
• 3D elements

Examples

• time-dependent problems
• nonlinear problems
• Stokes flow
• Maxwell's equations
• shape optimization

Maintenance

• automatic identification of cells (user does not need to specify cell indices when creating an Edge object)
• allow sampling parameter n to have different values for different edges
• type validation with pydantic
• add logging with logging module
• modify LocalFunctionSpace to treat a split edge as a single edge
• add batch processing for multiple LocalFunctions
• use multiprocessing to speed up computation