DOUG components

The idea of a component is to abstract operations and define an interface, so that the code can be used without knowing which implementation is underneath - polymorphism.

This allows for code reuse and is a part of Object Oriented Programming (OOP) principles. The Fortran 95 support for OOP is very poor, which caused to create artificial polymorhpism. See for example A Simplified Method for Implementing Run-Time Polymorphism in Fortran95 by Viktor K. Decyk and Charles D. Norton.

There are currently several components that define different parts of DOUG:

1. Distribution - creates fine grid (mesh), reads in data and distributes original matrix and vector
2. Partitioning - creates fine and coarse partitionings of the mesh
3. Preconditioner - creates fine and coarse grid preconditioners using the partitionings, which comes in two subcomponents
   • FinePreconditioner - first level preconditioner: additive Schwarz with overlapping subdomains
   • CoarsePreconditioner - second level preconditioner: coarse space based preconditioner

Note:

Several other components may be created in the future, like Solver, or existing may be split, e.g. Distribution into DataInput and MeshRefinement

Every component has one or several implementations - modules, listed below. These implementations may just delegate interface subroutines to actual implementations.

Distribution component modules

The two primary modules are Distribution_mod and Distribution_base_mod.

• Distribution_elem_mod - reads, distributes, and assembles finite element data: elemental matrices, coordinates, ...
• Distribution_assm_mod - reads and distributes an assembled matrix
• Distribution_struct_mod - generates grid and local matrices on each process using Laplace equation and its logical distribution

Partitioning component modules

The primary module is Partitioning_mod, others are:

• Partitioning_aggr_mod - uses aggregation algorithm to create partitions, either or both coarse and fine;
• Partitioning_full_mod - takes the whole process region as one coarse partition;
• Partitioning_metis_mod - uses METIS library to create coarse partitions using fine aggregates.

Note:

Currently, the implementation is not very flexible, e.g. METIS partitioning requires fine aggregates created by Partitioning_aggr_mod module, although partitioning from any module should be suitable.

Partitioning component modules

The primary modules are Preconditioner_mod and Preconditioner_base_mod

Note:

Again, implementation may use aggregates instead of partitions, although they are almost equivalent.

FinePreconditioner modules

Fine preconditioner uses coarse partitions as subdomains. Fine preconditioner modules are:

• FinePreconditioner_complete_mod - completely solves local problems on subdomains
• FinePreconditioner_sgs_mod - Symmetric Gauss-Seidel preconditioner

CoarsePreconditioner modules

Coarse preconditioner uses fine partitions as coarse space basis function support.

• CoarsePreconditioner_geometric_mod - uses geometric coarse grid
• CoarsePreconditioner_smooth_mod - uses smoothing on fine partitions to create coarse problem
• CoarsePreconditioner_robust_mod - uses Robust Coarse Spaces