A parallel time-space least-squares spectral element solver for incompressible flow problems

The least-squares spectral element method (LSQ-SEM) is a very promising numerical method which combines the least-squares formulation with the spectral element method. In this article, a parallel space-time implementation of a least-squares spectral element method for incompressible flows is presented. In the space-time formulation, time is included as an extra dimension, providing an efficient framework for handling time dependent independent multidimensional problems. The algebraic solver is based on the Shur complement method. Numerical experiments are performed for showing the capability and computational efficiency of the solver. Besides, the scalability of the code is tested.