The second edition of Computational Physics by Rubin Landau, Manuel Paez and Cristian C. Bordeianu (published by Wiley) hit bookshelves in 2007, and is steadily making its way into physics classrooms across the United States. Your reviewer first encountered the book at the Stanford Campus Book Store, where it is presumably being put to good use by students and faculty. The first edition was published in 1997 with Landau and Paez as authors [Computational Physics, 1st edn, Wiley, New York, 1997]. Rubin Landau is a very experienced computational physicist and staff member of the Oregon State University in Corvallis, where he directs the Computational Physics for Undergraduates course and teaches using this book. Landau is an incredibly active teacher to put it mildly &#x2013; the code for the book is supplied in an accompanying DVD and he also posts applets and video lectures for his courses on his web page (http://www.physics.orst.edu/&#x7e;rubin/).

Adrian Brown

Book Review

A template-based generic programming approach was presented in Part I of this series of papers [Sci. Program. 20 (2012), 197&#x2013;219] that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertainty quantification results for a 3D PDE application.

Roger P. Pawlowski

Eric T. Phipps

Andrew G. Salinger

Steven J. Owen

Christopher M. Siefert

Matthew L. Staten

Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part II: Application to Partial Differential Equations

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary &#x201c;Scalar&#x201d; type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.

Eric Bavier

Mark Hoemmen

Sivasankaran Rajamanickam

Heidi Thornquist

Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

Sundance is a package in the Trilinos suite designed to provide high-level components for the development of high-performance PDE simulators with built-in capabilities for PDE-constrained optimization. We review the implications of PDE-constrained optimization on simulator design requirements, then survey the architecture of the Sundance problem specification components. These components allow immediate extension of a forward simulator for use in an optimization context. We show examples of the use of these components to develop full-space and reduced-space codes for linear and nonlinear PDE-constrained inverse problems.

Kevin Long

Paul T. Boggs

Bart G. van Bloemen Waanders

Sundance: High-Level Software for PDE-Constrained Optimization

Michael A. Heroux

Damian Rouson

Special Issue on the Trilinos Project, Part 2 of 2

Dan Nagle

This paper introduces Playa, a high-level user interface layer for composing algorithms for complex multiphysics problems out of objects from other Trilinos packages. Among other features, Playa provides very high-performance overloaded operators implemented through an expression template mechanism. In this paper, we give an overview of the central Playa objects from a user's perspective, show application to a sequence of increasingly complex solver algorithms, provide timing results for Playa's overloaded operators and other functions, and briefly survey some of the implementation issues involved.

Victoria E. Howle

Robert C. Kirby

Brian Brennan

Kimberly Kennedy

Playa: High-Performance Programmable Linear Algebra

PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of the underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.

William F. Spotz

PyTrilinos: Recent Advances in the Python Interface to Trilinos

MueLu is a library within the Trilinos software project [An overview of Trilinos, Technical Report SAND2003-2927, Sandia National Laboratories, 2003] and provides a framework for parallel multigrid preconditioning methods for large sparse linear systems. While providing efficient implementations of modern multigrid methods based on smoothed aggregation and energy minimization concepts, MueLu is designed to be customized and extended. This article gives an overview of design considerations for the MueLu package: user interfaces, internal design, data management, usage of modern software constructs, leveraging Trilinos capabilities, linear algebra operations and advanced application.

J&#xe9;r&#xe9;mie Gaidamour

Jonathan Hu

Chris Siefert

Ray Tuminaro

Design Considerations for a Flexible Multigrid Preconditioning Library

We present the first three-dimensional, partial differential equation solver to be built atop the recently released, open-source ForTrilinos package (http://trilinos.sandia.gov/packages/fortrilinos). ForTrilinos currently provides portable, object-oriented Fortran 2003 interfaces to the C++ packages Epetra, AztecOO and Pliris in the Trilinos library and framework [ACM Trans. Math. Softw.31(3) (2005), 397&#x2013;423]. Epetra provides distributed matrix and vector storage and basic linear algebra calculations. Pliris provides direct solvers for dense linear systems. AztecOO provides iterative sparse linear solvers. We demonstrate how to build a parallel application that encapsulates the Message Passing Interface (MPI) without requiring the user to make direct calls to MPI except for startup and shutdown. The presented example demonstrates the level of effort required to set up a high-order, finite-difference solution on a Cartesian grid. The example employs an abstract data type (ADT) calculus [Sci. Program.16(4) (2008), 329&#x2013;339] that empowers programmers to write serial code that lower-level abstractions resolve into distributed-memory, parallel implementations. The ADT calculus uses compilable Fortran constructs that resemble the mathematical formulation of the partial differential equation of interest.

Karla Morris

Damian W.I. Rouson

M. Nicole Lemaster

Salvatore Filippone

Exploring Capabilities within ForTrilinos by Solving the 3D Burgers Equation

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Scientific Programming provides a forum for research results in, and practical experience with, software engineering environments, tools, languages, and models of computation aimed specifically at supporting scientific and engineering computing.

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Scientific Programming

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Scientific Programming

A New Overview of the Trilinos Project – Part 2

A New Overview of the Trilinos Project – Part 2

Articles

Book Review

Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part II: Application to Partial Differential Equations

Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

Sundance: High-Level Software for PDE-Constrained Optimization

Special Issue on the Trilinos Project, Part 2 of 2

Book Review

Playa: High-Performance Programmable Linear Algebra

PyTrilinos: Recent Advances in the Python Interface to Trilinos

Design Considerations for a Flexible Multigrid Preconditioning Library

Exploring Capabilities within ForTrilinos by Solving the 3D Burgers Equation