# Matrix Solver Options

There are two main approaches to the solution of the system of equations – direct solutions and iterative solutions. The iterative solutions can be split into ones that involve the full system matrix and element by element (EBE) methods.

For the direct (matrix) solutions there a number of options available. The general equation to be solver in GSS is

The fact that the matrix is symmetric and relatively sparse is exploited in the solution.

Once the matrix is factorized the solution of the equations is a straightforward back substitution in two passes.

# Sparse Parallel Direct Solver

The sparse parallel direct solver makes use of the 'Pardiso' solver from Intel Math Kernel Library. Pardiso uses METIS based reordering for reducing fill-in and employs Bunch-Kauffman based pivoting for a sparse LDLT factorization.