README

This directory contains source code to solve systems of linear equations
arising from a particular sparse approximation to the Jacobian matrix that
arises when solving for spun-up ocean tracers with the Newton-Krylov
method. The actual solve is performed in an external sparse solver
library. The current implementation uses the distributed memory version
of SuperLU.

The work flow to solve the system of linear equations is
1) create the sparse matrix, saving the matrix to a file
2) read the matrix and solve the linear systems of equations

Step 1 assumes some details of the ocean GCM discretizations, but is
primarily independent of the sparse solver library. (The only dependency
is the use of a typedef for long integers, int_t.) The matrix is stored
compressed row storage format, described in matrix.c.

Step 2 depends on the API of the sparse solver library being used, but
is is primarily independent of the GCM. (The only dependency is the
functionality of reading/writing ocean tracers from/to a file.) For
SuperLU, there are 2 solver programs, one in which the matrix and
vectors are are globally available on all processes (solve_ABglobal.c),
and another where they are distributed (solve_ABdist.c).