Abstract : Sparse linear solvers are a basic component in the tool chain for scientific applications; solution of spa
rse linear systems is indeed one of the main computational kernels in physics-driven models for numer
ical simulation and, more recently, also in data-driven models. The current challenge of exascale requir
es to rethink numerical algorithms for efficient exploitation of heterogeneous massively parallel comput
ers, embedding multi/many-core processors. In this MS we bring together some very active researcher
s in this field to discuss recent advancements in the development of highly scalable algorithms and sof
tware for solving and preconditioning sparse linear systems on modern high-end supercomputers.
[04144] Scalable domain decomposition solvers for cardiac reaction-diffusion cell-by-cell models
Format : Talk at Waseda University
Author(s) :
Luca Franco Pavarino (University of Pavia)
Ngoc Mai Monica Huynh (University of Pavia)
Simone Scacchi (University of Milano)
Fatemeh Chegini (Zuse Institute Berlin)
Martin Weiser (Zuse Institute Berlin)
Abstract : Scalable preconditioners are constructed and analyzed for the iterative solution of composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. These models lead to large-scale ill-conditioned discrete systems which have discontinuous global solutions across cells (subdomains) boundaries. A scalable convergence rate bound is proved for dual-primal cell-by-cell preconditioned operators. Numerical tests validate this bound and investigate its dependence on the discretization parameters.
[04292] Adapting Patch-based Relaxation to Generalized MHD Systems Within An Algebraic Multigrid Solver
Format : Talk at Waseda University
Author(s) :
Raymond Tuminaro (Sandia National LaboratoriesWe discuss a multigrid algorithm for generalized magnetohydrodynamics (GMHD). This GMHD system has two different PDE terms that can each generate a large near null space, complicating the linear solution process. One expre)
Michael Crockatt (Sandia National Laboratories)
Graham Harper (Sandia National Laboratories)
Allen Robinson (Sandia National Laboratories)
Abstract : We discuss multigrid solvers for generalized magnetohydrodynamics. This system has two PDE terms that each generate a large near null space. One expression contains the curl operator while the other arises from generalized Ohm's law. We propose a geometric multigrid algorithm based on Arnold-Falk-Winther relaxation. We then adapt the Rietzinger/Schoberl AMG scheme to the generalized system. We apply the resulting preconditioner to two test problems to illustrate its effectiveness.
[04198] An immersed approach to fluid-structure-contact interaction
Format : Talk at Waseda University
Author(s) :
Patrick Zulian (Università della Svizzera italiana)
Maria Giuseppina Chiara Nestola (Università della Svizzera italiana)
Rolf Krause (Università della Svizzera italiana)
Abstract : We presents an immersed technique for solving fluid-structure interaction (FSI) problems using dual Lagrange multipliers, which enables the resampling of discrete fields with standard matrix-vector multiplication within the nonlinear solution procedure. The fluid and structure are coupled in the overlapping volume, while different structures in contact are coupled on the surface using mortar-based techniques.
[02685] GMRES+AMG Navier-Stokes Pressure Projection Solvers with RAS and ORAS Smoothers
Format : Online Talk on Zoom
Author(s) :
Stephen Thomas (Advanced Micro Devices)
Amik St-Cyr (Shell)
Erika Strakova (IT4-innovations Ostrava)
Allison Baker (National Center for Atmospheric Research)
Abstract : PeleLM is a Navier-Stokes combustion model. Extremely ill-conditioned
problems arise for incompressible and reacting flows in the low Mach flow
regime, particularly for cut-cell meshes in complex geometries, Prenter (2020)
improved convergence rates for cut-cells by employing PCG-AMG
with Schwarz smoothers. We combine ILU smoothers
using iterative triangular solves with RAS and ORAS smoothers adapted to hypre
for a new low-synch MGS-CGS GMRES. The iteration counts
tend to remain constant and these smoothers reduce run times
on many-core GPU's in the strong-scaling limit.
Pasqua D'Ambra (Institute for Applied Computing (IAC)-National Research Council of Italy (CNR))
Salvatore Filippone (University of Rome "Tor Vergata")
Abstract : In this talk, we will describe a software framework for solving large and sparse linear systems on hybrid architectures, from small servers to high-end supercomputers, embedding multi-core CPUs and Nvidia GPUs. The framework has a tripartite modular structure, which separates basic functionalities for distributed sparse matrices and sparse matrix computations involved in Krylov methods, eventually exploiting multi-threading and CUDA-based programming models, from the setup and application of different types of preconditioners.
[04611] Recent Developments in Two-level Schwarz Domain Decomposition Preconditioners in Trilinos
Format : Talk at Waseda University
Author(s) :
Ichitaro Yamazaki (Sandia National Labs)
Alexander Heinlein (Delft University of Technology (TU Delft))
Sivasankaran Rajamanickam (Sandia National Labs)
Abstract : Domain decomposition methods are used to build a class of effective parallel solvers for sparse linear systems arising from the discretization of partial differential equations. FROSch is a software package, which implements GDSW type Two-level Schwarz Domain Decomposition preconditioners in Trilinos. In this talk, we present several recent developments made in FROSch.
[05152] Preparing Algebraic Multigrid Solvers in hypre for Exascale Computers
Format : Talk at Waseda University
Author(s) :
Rui Peng Li (LLNL)
Abstract : The emerging exascale computers provide opportunities to perform much larger scale simulations to obtain more accurate solutions than ever before. The increasing complexities of heterogeneous accelerators on such platforms have made the development of sparse linear solvers challenging to achieve high performance. In this talk, we will discuss the porting strategies, new developments and performance optimizations of the multigrid solvers in hypre in preparation for the exascale computers with the results from real application codes.
[04535] JXPAMG: an auto-tuning parallel AMG solver for extreme‑scale numerical simulations
Format : Online Talk on Zoom
Author(s) :
Xiaowen Xu (IAPCM)
Silu Huang (IAPCM)
Xiaoqiang Yue (Xiangtan University)
Runzhang Mao (IAPCM)
Abstract : JXPAMG is a parallel algebraic multigrid (AMG) solver for solving the extreme-scale sparse linear systems on modern supercomputers. It is designed follows the auto-tuning mechanisms allow JXPAMG to use different AMG strategies for different application features and architecture features, and thereby JXPAMG becomes aware of changes in these features. This talk introduces the algorithms, implementation techniques, auto-tuning mechanisms and applications of JXPAMG.
