High-Performance Implementations for High-Order Finite-Element Discretizations of PDEs

Explore high-performance implementations for high-order finite-element discretizations of partial differential equations in this NHR PerfLab Seminar talk. Delve into recent developments in matrix-free finite-element algorithms for solving PDEs on complex geometries, focusing on on-the-fly computation of integrals. Discover how performance engineering has made this approach faster than assembling global sparse matrices for high-order discretizations with curvilinear unstructured hexahedral mesh elements or variable coefficients. Examine node-level performance results for high-order continuous and discontinuous Galerkin discretizations, including adaptively refined meshes with hanging nodes. Learn about loop fusion techniques to increase data locality, benefiting CPUs with large L2 and L3 caches. Gain insights from speaker Martin Kronbichler, Professor at the University of Augsburg, on matrix-free implementations, efficient numerical linear algebra, and parallel high-performance implementation on emerging exascale hardware.