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ACM Transactions on Mathematical Software (TOMS), Volume 39 Issue 1, November 2012

Graph-Based Software Design for Managing Complexity and Enabling Concurrency in Multiphysics PDE Software
Patrick K. Notz, Roger P. Pawlowski, James C. Sutherland
Article No.: 1
DOI: 10.1145/2382585.2382586

Multiphysics simulation software is plagued by complexity stemming from nonlinearly coupled systems of Partial Differential Equations (PDEs). Such software typically supports many models, which may require different transport equations,...

Families of Algorithms for Reducing a Matrix to Condensed Form
Field G. Van Zee, Robert A. van de Geijn, Gregorio Quintana-Ortí, G. Joseph Elizondo
Article No.: 2
DOI: 10.1145/2382585.2382587

In a recent paper it was shown how memory traffic can be diminished by reformulating the classic algorithm for reducing a matrix to bidiagonal form, a preprocess when computing the singular values of a dense matrix. The key is a reordering of the...

PyDEC: Software and Algorithms for Discretization of Exterior Calculus
Nathan Bell, Anil N. Hirani
Article No.: 3
DOI: 10.1145/2382585.2382588

This article describes the algorithms, features, and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as...

Computing the Crosscap Number of a Knot Using Integer Programming and Normal Surfaces
Benjamin A. Burton, Melih Ozlen
Article No.: 4
DOI: 10.1145/2382585.2382589

The crosscap number of a knot is an invariant describing the nonorientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers are difficult to compute and no general algorithm is known....

Algorithm 924: TIDES, a Taylor Series Integrator for Differential EquationS
Alberto Abad, Roberto Barrio, Fernando Blesa, Marcos Rodríguez
Article No.: 5
DOI: 10.1145/2382585.2382590

This article introduces the software package TIDES and revisits the use of the Taylor series method for the numerical integration of ODEs. The package TIDES provides an easy-to-use interface for standard double precision integrations, but also for...

Algorithm 925: Parallel Solver for Semidefinite Programming Problem having Sparse Schur Complement Matrix
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata
Article No.: 6
DOI: 10.1145/2382585.2382591

A SemiDefinite Programming (SDP) problem is one of the most central problems in mathematical optimization. SDP provides an effective computation framework for many research fields. Some applications, however, require solving a large-scale SDP...