amg4psblas/samples

Samples

This folder contains several example for the AMG4PSBLAS library. After having compiled (and if needed installed) the library these example can be compiled and run to become familiar with the use of the library and the preconditioners implemented in it.

Simple

pdegen

This folder contains three main examples

• amg_dexample_ml.f90
• ``
• ``

Example amg_dexample_ml.f90

This sample program solves a linear system obtained by discretizing a PDE with Dirichlet boundary conditions. The solver used is Flexible Conjugate Gradient (FCG), coupled with one of the following multi-level preconditioners, as explained in Section 4.1 of the AMG4PSBLAS User's and Reference Guide:

Available Preconditioner Choices:

• Choice = 1 (Default multi-level preconditioner):
  V-cycle with decoupled smoothed aggregation, 1 hybrid forward/backward Gauss-Seidel sweep as pre/post-smoother, and UMFPACK as the coarsest-level solver.
  (See Section 4.1, Listing 1)

• Choice = 2:
  V-cycle preconditioner with 1 block-Jacobi sweep (using ILU(0) on the blocks) as pre/post-smoother, and 8 block-Jacobi sweeps (with ILU(0) on the blocks) as the coarsest-level solver.
  (See Section 4.1, Listing 2)

• Choice = 3:
  W-cycle preconditioner based on coupled aggregation relying on matching, with:

  • Maximum aggregate size of 8
  • Smoothed prolongators
  • 2 hybrid forward/backward Gauss-Seidel sweeps as pre/post-smoother
  • A distributed coarsest matrix
  • Preconditioned Flexible Conjugate Gradient as the coarsest-level solver
    (See Section 4.1, Listing 3)

Input Data

The matrix and the right-hand side (RHS) are read from files. If an RHS is not available, a unit RHS is set.

The PDE Formulation

The PDE is a general second-order equation in 3D:

- \left( a_1 \frac{d^2 u}{dx^2} + a_2 \frac{d^2 u}{dy^2} + a_3 \frac{d^2 u}{dz^2} \right) 
+ \left( b_1 \frac{du}{dx} + b_2 \frac{du}{dy} + b_3 \frac{du}{dz} \right) 
+ c u = f

with Dirichlet boundary conditions:

u = g

on the unit cube:

0 \leq x,y,z \leq 1

Special Case: Laplace Equation

If b_1 = b_2 = b_3 = c = 0, the PDE reduces to the Laplace equation.

Computational Domain and Data Distribution

In this sample program:

1. The index space of the discretized computational domain is numbered sequentially in a standard way.
2. The corresponding vector is then distributed according to a BLOCK data distribution.