Improvement of Preconditioner by means of Incomplete Cholesky Decomposition: Development of Scheme Suitable for Vector Calculating Machine

The supercomputer allows us to analyze the large-scale problem which can not have been carried out because of the limitation of calculation time so far. In the FDM, we can extract the peak performance of the supercomputer efficiently because a scheme based on the FDM is suitable for the hardware of the supercomputer. On the other hand, the FEM, which can treat arbitrary shapes and boundary conditions, is not suitable for the vector calculating machine because the finite-element subdivision is often irregular. In the present study, we develop a preconditioner suitable for a vector calculating machine in the ICCG method. The usual preconditioner by means of Incomplete Cholesky Decomposition is not suitable for a vector calculating machine because many recursions occur in a preconditioning procedure. Then, we use a finite element which has another node at a center of gravity in the usual serendipity element. Using this element, we could reduce the number of recursions in the precondition