On A Comparative Study of Direct Solution Methods of the Discrete Poisson’s Equation on A Rectangle

The solution of systems of algebraic equations arising from the 5-point discretization of Poisson’s equation on a rectangle with Dirichlet boundary conditions is analyzed by direct solution methods. Special emphasis is given for block direct methods, such as block elimination, block decomposition and block cyclic reduction methods. For this purpose block elimination algorithms, orthogonal block decomposition algorithms, cyclic odd even reduction method, (CORF) algorithm and Buneman version of the CORF algorithm is also studied. A test problem is constructed for the Laplace equation and solved by these block methods for the mesh size 1 4 h  . Comparisons are given based on the computational complexity of the methods. Keywords: Block elimination methods, block cyclic reduction method, block decomposition methods, Thomas algorithm, discrete Poisson’s equation, 5-point scheme.