Andrew G. Salinger

An overview of the Trilinos project

The Trilinos Project is an effort to facilitate the design, development, integration, and ongoing support of mathematical software libraries within an object-oriented framework for the solution of large-scale, complex multiphysics engineering and scientific problems. Trilinos addresses two fundamental issues of developing software for these problems: (i) providing a streamlined process and set of tools for development of new algorithmic implementations and (ii) promoting interoperability of independently developed software.Trilinos uses a two-level software structure designed around collections of packages. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common look-and-feel, including configuration, documentation, licensing, and bug-tracking.Here we present the overall Trilinos design, describing our use of abstract interfaces and default concrete implementations. We discuss the services that Trilinos provides to a prospective package and how these services are used by various packages. We also illustrate how packages can be combined to rapidly develop new algorithms. Finally, we discuss how Trilinos facilitates high-quality software engineering practices that are increasingly required from simulation software.

Bifurcation and stability analysis of laminar isothermal counterflowing jets

We present a numerical study of the structure and stability of laminar isothermal flows formed by two counterflowing jets of an incompressible Newtonian fluid. We demonstrate that symmetric counterflowing jets with identical mass flow rates exhibit multiple steady states and, in certain cases, time-dependent (periodic) steady states. Two geometric configurations were studied based on the inlet jet shapes: planar and axisymmetric. Stagnation flows formed by planar counterflowing jets exhibit both steady-state multiplicity and time-dependent behaviour, while axisymmetric jets exhibit only a steady-state multiplicity. A linearized bifurcation and stability analysis based on the continuity and Navier–Stokes equations revealed transitions between a single (symmetric) steady state and multiple steady states or periodic steady states. The dimensionless quantities forming the parameter space of this system are the inlet Reynolds number (Re) and a geometric aspect ratio (α), equal to the jet inlet characteristic length (used for calculating Re) divided by the jet separation. The boundaries separating different flow regimes have been identified in the (Re, α) parameter space. The resulting flow maps are useful for the design and operation of counterflow jet reactors.

Numerical challenges in the application of density functional theory to biology and nanotechnology

This paper summarizes our efforts to develop fast algorithms for density functional theory (DFT) calculations of inhomogeneous fluids. Our goal is to apply DFTs to a variety of problems in nanotechnology and biology. To this end we have developed DFT codes to treat both atomic fluid models and polymeric fluids. We have developed both three-dimensional real space and Fourier space algorithms. The former rely on a matrix-based Newtons method while the latter couple fast Fourier transforms with a matrix-free Newtons method. Efficient computation of phase diagrams and investigation of multiple solutions is facilitated with phase transition tracking algorithms and arclength continuation algorithms. We have explored the performance that can be obtained by application of massively parallel computing, and have begun application of the codes to a variety of two-and three-dimensional systems. In this paper, we summarize our algorithm development work as well as briefly discuss a few applications including adsorption and transport in ion channel proteins, capillary condensation in disordered porous media and confinement effects in a diblock copolymer fluid.

BIFURCATION TRACKING ALGORITHMS AND SOFTWARE FOR LARGE SCALE APPLICATIONS

We present the set of bifurcation tracking algorithms which have been developed in the LOCA software library to work with large scale application codes that use fully coupled Newtons method with iterative linear solvers. Turning point (fold), pitchfork, and Hopf bifurcation tracking algorithms based on Newtons method have been implemented, with particular attention to the scalability to large problem sizes on parallel computers and to the ease of implementation with new application codes. The ease of implementation is accomplished by using block elimination algorithms to solve the Newton iterations of the augmented bifurcation tracking systems. The applicability of such algorithms for large applications is in doubt since the main computational kernel of these routines is the iterative linear solve of the same matrix that is being driven singular by the algorithm. To test the robustness and scalability of these algorithms, the LOCA library has been interfaced with the MPSalsa massively parallel finite element reacting flows code. A bifurcation analysis of an 1.6 Million unknown model of 3D Rayleigh–Benard convection in a 5 × 5 × 1 box is successfully undertaken, showing that the algorithms can indeed scale to problems of this size while producing solutions of reasonable accuracy.

Fundamental models of the metalorganic vapor-phase epitaxy of gallium nitride and their use in reactor design

A fundamental reaction-transport model describing the metalorganic vapor-phase epitaxy (MOVPE) of GaN from trimethyl-gallium (TMG) and ammonia has been developed. This model has been tested against experimental data from research-scale and industrial-scale reactors, A simplified version of the model that includes only transport phenomena and a unity sticking coefficient of the limiting film precursor (TMG) to the surface of the growing film was found to accurately capture observed film deposition variations in an early variant of the Thomas Swan close-coupled-showerhead 3 × 2 reactor. Modifications of the Thomas Swan reactor, in line with the findings suggested by this work, enabled state-of-the-art thickness uniformity to be achieved. The model has been used to develop performance diagrams for conceptual multi-aperture MOVPE reactors and for the Thomas Swan system. These performance diagrams identify regions of the parameter space of the reactor which correspond to minimal variations in film growth rate across large-area substrates. Published by Elsevier Science B.V.

Efficient parallel computation of unstructured finite element reacting flow solutions

Abstract A parallel unstructured finite element (FE) reacting flow solver designed for message passing MIMD computers is described. This implementation employs automated partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global FE equations, and parallel Krylov subspace iterative solvers. In this paper, a number of issues related to the efficient implementation of parallel unstructured mesh applications are presented. These issues include the differences between structured and unstructured mesh parallel applications, major communication kernels for unstructured Krylov iterative solvers, automatic mesh partitioning algorithms, and the influence of mesh partitioning metrics and single-node CPU performance on parallel performance. Results are presented for example FE heat transfer, fluid flow and full reacting flow applications on a 1024 processor nCUBE 2 hypercube and a 1904 processor Intel Paragon. Results indicate that very high computational rates and high scaled efficiencies can be achieved for large problems despite the use of sparse matrix data structures and the required unstructured data communication.

Automating embedded analysis capabilities and managing software complexity in multiphysics simulation, Part I: Template-based generic programming

An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++ language to transform a given calculation into one that can compute a variety of additional quantities that are necessary for many state-of-the-art simulation and analysis algorithms. An approach for incorporating these ideas into complex simulation codes through general graph-based assembly is also presented. These ideas have been implemented within a set of packages in the Trilinos framework and are demonstrated on a simple problem from chemical engineering.

LOCA 1.0 Library of Continuation Algorithms: Theory and Implementation Manual

LOCA, the Library of Continuation Algorithms, is a software library for performing stability analysis of large-scale applications. LOCA enables the tracking of solution branches as a function of a system parameter, the direct tracking of bifurcation points, and, when linked with the ARPACK library, a linear stability analysis capability. It is designed to be easy to implement around codes that already use Newtons method to converge to steady-state solutions. The algorithms are chosen to work for large problems, such as those that arise from discretizations of partial differential equations, and to run on distributed memory parallel machines. This manual presents LOCAs continuation and bifurcation analysis algorithms, and instructions on how to implement LOCA with an application code. The LOCA code is being made publicly available at www.cs.sandia.gov/loca.

A Comparison of Mesh Morphing Methods for 3D Shape Optimization

The ability to automatically morph an existing mesh to conform to geometry modifications is a necessary capability to enable rapid prototyping of design variations. This paper compares six methods for morphing hexahedral and tetrahedral meshes, including the previously published FEMWARP and LBWARP methods as well as four new methods. Element quality and performance results show that different methods are superior on different models. We recommend that designers of applications that use mesh morphing consider both the FEMWARP and a linear simplex based method.

Density functional theory for inhomogeneous polymer systems. I. Numerical methods

We present a new real space Newton-based computational approach to computing the properties of inhomogeneous polymer systems with density functional theory (DFT). The DFT is made computationally efficient by modeling the polymers as freely jointed chains and obtaining direct correlation functions from polymer reference interaction site model calculations. The code we present can solve the DFT equations in up to three dimensions using a parallel implementation. In addition we describe our implementation of an arc-length continuation algorithm, which allows us to explore the phase space of possible solutions to the DFT equations. These numerical tools are applied in this paper to hard chains near hard walls and briefly to block copolymer systems. The method is shown to be accurate and efficient. Arc-length continuation calculations of the diblock copolymer systems illustrate the care required to obtain a complete understanding of the structures that may be found with this polymer-DFT approach.