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"Efficient representation of high-order finite element operators"

Abstract:
We present an extensible low-level library that provides a versatile algebraic interface and optimized implementations suitable for high-order operators: libCEED. This library aims to overcome the challenges in high-order methods that use global sparse matrices as operator representations. In fact, one of the challenges with high-order methods is that a global sparse matrix is no longer a good representation of a high-order operator, both with respect to the FLOPs needed for its evaluation, as well as the memory transfer needed for simple matrix-vector multiplies. Thus, high-order methods require a new "format" that represents a linear (or more generally non-linear) operator, not associated with a sparse matrix. The goal of libCEED is to propose such a format, as well as supporting implementations and data structures, that enable efficient operator evaluation and composition, on a variety of computational device types (CPUs, GPUs, etc.) and enables portable performance through nearly optimal memory transfers and FLOPs for operator evaluation. We investigate operator composition and design of coupled solvers in the context of atmospheric modeling, providing examples of the usage of libCEED with PETSc. We will show examples of solutions of the advection equation and the full compressible Navier-Stokes equations, to investigate the dynamics of density currents in the stratified atmosphere.

For the remainder of the talk, I am going to show some of my past research in the field of computational fluid dynamics, regarding numerical simulations of the dynamics of free-boundary/interfacial flows of thin viscoelastic liquid films and membranes of Maxwell and Jeffreys type.