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Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

Journal of Computational Physics

Lin, Paul T.; Shadid, John N.; Sala, Marzio; Tuminaro, Raymond S.; Hennigan, Gary L.; Hoekstra, Robert J.

In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system is obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 108 unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system. © 2009 Elsevier Inc. All rights reserved.

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TYPE Journal Article YEAR 2009
ScopusOSTI

Highly scalable linear solvers on thousands of processors

Siefert, Christopher S.; Tuminaro, Raymond S.; Domino, Stefan P.; Robinson, Allen C.

In this report we summarize research into new parallel algebraic multigrid (AMG) methods. We first provide a introduction to parallel AMG. We then discuss our research in parallel AMG algorithms for very large scale platforms. We detail significant improvements in the AMG setup phase to a matrix-matrix multiplication kernel. We present a smoothed aggregation AMG algorithm with fewer communication synchronization points, and discuss its links to domain decomposition methods. Finally, we discuss a multigrid smoothing technique that utilizes two message passing layers for use on multicore processors.

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TYPE SAND Report YEAR 2009
OSTIDOI

A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations

Journal of Computational Physics

Elman, Howard; Howle, Victoria E.; Shadid, John N.; Shuttleworth, Robert R.; Tuminaro, Raymond S.

In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible Navier-Stokes equations based on preconditioned Krylov methods. These include physics-based methods, such as SIMPLE, and purely algebraic preconditioners based on the approximation of the Schur complement. All these techniques can be represented as approximate block factorization (ABF) type preconditioners. The goal is to decompose the application of the preconditioner into simplified sub-systems in which scalable multi-level type solvers can be applied. In this paper we develop a taxonomy of these ideas based on an adaptation of a generalized approximate factorization of the Navier-Stokes system first presented in [A. Quarteroni, F. Saleri, A. Veneziani, Factorization methods for the numerical approximation of Navier-Stokes equations, Computational Methods in Applied Mechanical Engineering 188 (2000) 505-526]. This taxonomy illuminates the similarities and differences among these preconditioners and the central role played by efficient approximation of certain Schur complement operators. We then present a parallel computational study that examines the performance of these methods and compares them to an additive Schwarz domain decomposition (DD) algorithm. Results are presented for two and three-dimensional steady state problems for enclosed domains and inflow/outflow systems on both structured and unstructured meshes. The numerical experiments are performed using MPSalsa, a stabilized finite element code. © 2007 Elsevier Inc. All rights reserved.

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TYPE SAND Report YEAR 2008
ScopusOSTIDOI

Algebraic multilevel preconditioners for nonsymmetric PDEs on stretched grids

Lecture Notes in Computational Science and Engineering

Sala, Marzio; Lin, Paul L.; Shadid, John N.; Tuminaro, Raymond S.

We report on algebraic multilevel preconditioners for the parallel solution of linear systems arising from a Newton procedure applied to the finite-element (FE) discretization of the incompressible Navier-Stokes equations. We focus on the issue of how to coarsen FE operators produced from high aspect ratio elements.

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TYPE Conference YEAR 2007
ScopusOSTI
Results 126–150 of 170
Results 126–150 of 170