Jakub Gałecki, ZA MEiL PW, Efficient and Scalable Application of the Lest-Squares Spectral/hp Element Method to Incompressible Flow Problems

The least-squares finite element method (LSFEM) is a numerical method for the solution of partial differential equations, offering several advantages compared to the classic Galerkin formulation. The presentation will discuss the application of the LSFEM to incompressible flow problems, with a strong focus on the computational efficiency of the approach. A pressure-correction-type splitting scheme for the solution components will be reviewed and extended to include open boundary conditions. Strategies for the evaluation of the algebraic operators arising from the application of a high-order discretization to the least-squares formulation will be presented, notably including the sum-factorization technique. A systematic analysis of the different approaches will be shown, along with a corresponding computational study. Part of the seminar will be dedicated to L3STER, the open-source numerical code within which the methods and algorithms discussed have been implemented. Finally, examples of applications of the solver will be presented, including time convergence studies, a direct numerical simulation of flow past a cylinder at Re=400, and fracture flow.

Keywords: least-squares finite element method, spectral/hp element method, incompressible flow, matrix-free operator evaluation, sum-factorization, high-performance computing.