Collisional processes are critical in the understanding of non-Maxwellian plasmas. The Landau form of the Fokker-Planck equation is the gold standard for modeling collisions in most plasmas, however$\mathcal{O}(N^{2})$work complexity inhibits its widespread use. We show that with advanced numerical methods and GPU hardware this cost can be effectively mitigated. This paper extends previous work on a conservative, high order accurate, finite element discretization with adaptive mesh refinement of the Landau operator, with extensions to GPU hardware and implementations in both the CUDA and Kokkos programming languages. This work focuses on the Landau kernels and on NVIDIA hardware, however preliminary results on AMD and Fujitsu/ARM hardware, as well as end-to-end performance of a velocity space model of a plasma thermal quench, are also presented. Both the fully implicit Landau time integrator and the plasma thermal quench model are publicly available in PETSc (Portable, Extensible, Toolkit for Scientific computing).

Charm++ and MPI embody two distinct perspectives for writing parallel programs. While MPI provides a process-centric, user-driven model for developing parallel codes, Charm++ supports work-centric, system-driven parallel programming. One of them might be a better or more natural fit for individual modules that constitute a parallel application. In this paper, we present a framework that enables hybrid parallel programming with Charm++ and MPI, and allows programmers to develop different modules of a parallel application in these two languages while facilitating smooth interoperation. We describe the challenges in enabling interoperation between Charm++ and MPI, and present techniques for managing the control flow and resource sharing between the two. Finally, we demonstrate the benefits of interoperation between Charm++ and MPI through several case studies that use production applications and libraries, including CHARM/Chombo, EpiSimdemics, NAMD, FFTW, MPI-IO and ParMETIS.

The solution of elliptic diffusion operators is the computational bottleneck in many simulations in a wide range of engineering and scientific disciplines. We present a truly scalable-ultrascalable-algebraic multigrid (AMG) linear solver for the diffusion operator in unstructured elasticity problems. Scalability is demonstrated with speedup studies of a non-linear micro-finite element analyses of a human vertebral body with over a half of a billion degrees of freedom on up to 4088 processors on the ACSI White machine. This work is significant because in the domain of unstructured implicit finite element analysis in solid mechanics with complex geometry, this is the first demonstration of a highly parallel and efficient application of a mathematically optimal linear solution method on a common large scale computing platform — the IBM SP Power3.

Accurate micro-finite element analyses of whole bones require the solution of large sets of algebraic equations. Multigrid has proven to be an effective approach to the design of highly scalable linear solvers for solid mechanics problems. We present some of the first applications of scalable linear solvers, on massively parallel computers, to whole vertebral body structural analysis. We analyze the performance of our algebraic multigrid (AMG) methods on problems with over 237 million degrees of freedom on IBM SP parallel computers. We demonstrate excellent parallel scalability, both in the algorithms and the implementations, and analyze the nodal performance of the important AMG kernels on the IBM Power3 and Power4 architectures.

Gauss-Seidel is a popular multigrid smoother as it is provably optimal on structured grids and exhibits superior performance on unstructured grids. Gauss-Seidel is not used to our knowledge on distributed memory machines as it is not obvious how to parallelize it effectively. We, among others, have found that Krylov solvers preconditioned with Jacobi, block Jacobi or overlapped Schwarz are effective on unstructured problems. Gauss-Seidel does however have some attractive properties, namely: fast convergence, no global communication (ie, no dot products) and fewer flops per iteration as one can incorporate an initial guess naturally. This paper discusses an algorithm for parallelizing Gauss-Seidel for distributed memory computers for use as a multigrid smoother and compares its performance with preconditioned conjugate gradients on unstructured linear elasticity problems with up to 76 million degrees of freedom.