Andrey Prokopenko

Andrey Prokopenko, Raymond S. Tuminaro

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points. Specifically, we investigate a $Q_2-Q_1$ mixed finite element discretization of the incompressible Navier-Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees-of-freedom (dofs) are defined at spatial locations where there are no corresponding pressure dofs. Thus, AMG approaches leveraging this co-located structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocity dof relationships of the $Q_2-Q_1$ discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity dofs resembles that on the finest grid. To define coefficients within the inter-grid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier-Stokes problems.

Piyush Sao, Andrey Prokopenko, Damien Lebrun-Grandié

This paper presents \pandora, a novel parallel algorithm for efficiently constructing dendrograms for single-linkage hierarchical clustering, including \hdbscan. Traditional dendrogram construction methods from a minimum spanning tree (MST), such as agglomerative or divisive techniques, often fail to efficiently parallelize, especially with skewed dendrograms common in real-world data. \pandora addresses these challenges through a unique recursive tree contraction method, which simplifies the tree for initial dendrogram construction and then progressively reconstructs the complete dendrogram. This process makes \pandora asymptotically work-optimal, independent of dendrogram skewness. All steps in \pandora are fully parallel and suitable for massively threaded accelerators such as GPUs. Our implementation is written in Kokkos, providing support for both CPUs and multi-vendor GPUs (e.g., Nvidia, AMD). The multithreaded version of \pandora is 2.2$\times$ faster than the current best-multithreaded implementation, while the GPU \pandora implementation achieved 6-20$\times$ on \amdgpu and 10-37$\times$ on \nvidiagpu speed-up over multithreaded \pandora. These advancements lead to up to a 6-fold speedup for \hdbscan on GPUs over the current best, which only offload MST construction to GPUs and perform multithreaded dendrogram construction.

Seth R. Johnson, Andrey Prokopenko, Katherine J. Evans

Although many active scientific codes use modern Fortran, most contemporary scientific software "libraries" are implemented in C and C++. Providing their numerical, algorithmic, or data management features to Fortran codes requires writing and maintaining substantial amounts of glue code. This article introduces a tool that automatically generates native Fortran 2003 interfaces to C and C++ libraries. The tool supports C++ features that have no direct Fortran analog, such as templated functions and exceptions. A set of simple examples demonstrate the utility and scope of the tool, and timing measurements with a mock numerical library illustrate the minimal performance impact of the generated wrapper code.