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ACM Transactions on Mathematical Software (TOMS), Volume 32 Issue 3, September 2006

N-body simulations: The performance of some integrators
Philip W. Sharp
Pages: 375-395
DOI: 10.1145/1163641.1163642
We describe four challenging N-body test problems involving the Sun and planets and use them to compare the performance of nine nonsymplectic and two symplectic integrators. Each problem has a long interval of integration and two have non-Newtonian...

An object-oriented framework for the development of scalable parallel multilevel preconditioners
Marzio Sala
Pages: 396-416
DOI: 10.1145/1163641.1163643
We present the design of a high-performance object-oriented framework that enables the rapid development and usage of efficient, scalable, and portable implementations of multilevel preconditioners for distributed sparse real matrices, in both serial...

A compiler for variational forms
Robert C. Kirby, Anders Logg
Pages: 417-444
DOI: 10.1145/1163641.1163644
As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the FEniCS...

An out-of-core sparse symmetric-indefinite factorization method
Omer Meshar, Dror Irony, Sivan Toledo
Pages: 445-471
DOI: 10.1145/1163641.1163645
We present a new out-of-core sparse symmetric-indefinite factorization algorithm. The most significant innovation of the new algorithm is a dynamic partitioning method for the sparse factor. This partitioning method results in very low I/O traffic...

Algorithm 855: Subroutines for the computation of Mathieu characteristic numbers and their general orders
Fayez A. Alhargan
Pages: 472-484
DOI: 10.1145/1163641.1163646
A continued fraction function algorithm is developed to evaluate general-order Mathieu characteristic numbers, and a new technique is presented for evaluating the Mathieu determinant which can be used to compute the order directly. Approximate...

Algorithm 856: APPSPACK 4.0: asynchronous parallel pattern search for derivative-free optimization
Genetha A. Gray, Tamara G. Kolda
Pages: 485-507
DOI: 10.1145/1163641.1163647
APPSPACK is software for solving unconstrained and bound-constrained optimization problems. It implements an asynchronous parallel pattern search method that has been specifically designed for problems characterized by expensive function evaluations....