ABSTRACT
The solution of the linear system that arises from the discretization of a partial differential equation (PDE) can be accomplished by direct or iterative methods. Direct methods can lead to high computational complexity and to considerable memory requirements, both of which limit the practical size of the discretization that can be used to solve the PDE. Iterative methods permit the maintenance of the sparsity pattern, reducing storage requirements while decreasing computation time as well. The primary purpose of using the preconditioner is to accelerate the convergence in the iterative phase of the computation. The chapter discusses the block structure inherent in the linear system that arises in discretizing the partial differential equation. The advantage of rowsum approach is that the operations in the iterative method with the preconditioner can be conducted as matrix-vector products rather than doing forward and backsolve steps involving the factorization.
