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**FEMSTER**: An object-oriented class library of high-order discrete differential forms

Paul Castillo, Robert Rieben, Daniel White

Pages: 425-457

DOI: 10.1145/1114268.1114269

FEMSTER is a modular finite element class library for solving three-dimensional problems arising in electromagnetism. The library was designed using a modern geometrical approach based on differential forms (or *p*-forms) and can be used for...

**A differentiation-enabled Fortran 95 compiler**

Uwe Naumann, Jan Riehme

Pages: 458-474

DOI: 10.1145/1114268.1114270

The availability of first derivatives of vector functions is crucial for the robustness and efficiency of a large number of numerical algorithms. An upcoming new version of the differentiation-enabled NAGWare Fortran 95 compiler is described that...

**DFTI---a new interface for Fast Fourier Transform libraries**

Ping Tak Peter Tang

Pages: 475-507

DOI: 10.1145/1114268.1114271

The Fast Fourier Transform (FFT) algorithm that calculates the Discrete Fourier Transform (DFT) is one of the major breakthroughs in scientific computing and is now an indispensable tool in a vast number of fields. Unfortunately, software...

**PDE.Mart**: A network-based problem-solving environment for PDEs

Mo Mu

Pages: 508-531

DOI: 10.1145/1114268.1114272

*PDE.Mart* is a network-based problem-solving environment (PSE) for solving partial differential equations (PDEs) in numerical simulations and academic research, as well as in educational settings. The client-server protocol consists of a...

**MATSLISE**: A MATLAB package for the numerical solution of Sturm-Liouville and Schrödinger equations

V. Ledoux, M. Van Daele, G. Vanden Berghe

Pages: 532-554

DOI: 10.1145/1114268.1114273

MATSLISE is a graphical MATLAB software package for the interactive numerical study of regular Sturm-Liouville problems, one-dimensional Schrödinger equations, and radial Schrödinger equations with a distorted Coulomb potential. It allows...

**Algorithm 846**: MixedVol: a software package for mixed-volume computation

Tangan Gao, T. Y. Li, Mengnien Wu

Pages: 555-560

DOI: 10.1145/1114268.1114274

MixedVol is a C++ software package that computes the mixed volume of *n* finite subsets of ℤ^{n} or the support of a system of *n* polynomials in *n* variables. The software produces the mixed volume as...

**Algorithm 847**: Spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB

Andreas Klimke, Barbara Wohlmuth

Pages: 561-579

DOI: 10.1145/1114268.1114275

To recover or approximate smooth multivariate functions, sparse grids are superior to full grids due to a significant reduction of the required support nodes. The order of the convergence rate in the maximum norm is preserved up to a logarithmic...

**Algorithm 848**: A recursive fixed-point algorithm for the infinity-norm case

Spencer Shellman, K. Sikorski

Pages: 580-586

DOI: 10.1145/1114268.1114276

We present the PFix algorithm for approximating a fixed point of a function f that has arbitrary dimensionality, is defined on a rectangular domain, and is Lipschitz continuous with respect to the infinity norm with constant 1. PFix has applications...

**Algorithm 849**: A concise sparse Cholesky factorization package

Timothy A. Davis

Pages: 587-591

DOI: 10.1145/1114268.1114277

The LDL software package is a set of short, concise routines for factorizing symmetric positive-definite sparse matrices, with some applicability to symmetric indefinite matrices. Its primary purpose is to illustrate much of the basic theory of...