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This paper investigates the application of the Red-Black Half-Sweep Gauss-Seidel (HSGS-RB) method by using the half-sweep triangle finite element approximation equation based on the Galerkin scheme to solve two-dimensional Poisson equations. Formulations of the full-sweep and half-sweep triangle finite element approaches in using this scheme are also derived. Some numerical experiments are conducted to show that the HSGS-RB method is superior to the Full-Sweep method.

Red-Black Half-Sweep Iterative Method Using Triangle Finite Element Approximation for 2D Poisson Equations