Interface Splitting Algorithm: A Parallel Solution to Diagonally Dominant Tridiagonal Systems

We present an interface-splitting algorithm (ITS) for solving diagonally dominant tridiagonal systems in parallel. The construction of the ITS algorithm profits from bidirectional links in modern networks, and it only needs one synchronization step to solve the system. The algorithm trades some necessary accuracy for better parallel performance. The accuracy and the performance of the ITS algorithm are evaluated on four different parallel machines of up to 2048 processors. The proposed algorithm scales very well, and it is significantly faster than the algorithm used in ScaLAPACK. The applicability of the algorithm is demonstrated in the three-dimensional simulations of turbulent channel flow at Reynolds number 41,430.