AIP Publishing

A new, operator-based algorithm for the calculation of Clebsch–Gordon coefficients for the group SU3 is introduced, and an ansi c program for its implementation is described. The algorithm involves the use of raising and lowering operators in analogy to a standard pedagogical approach to the more familiar SU2 Clebsch–Gordon coefficients. The nature of the approach makes the sign conventions utilized and the rules for resolution of the outer degeneracy explicit, and therefore allows straightforward changes to adapt the program to other choices. The program is written to allow its execution on personal computers of modest memory size, but also to take advantage of available memory allowing more complex results to be obtained on larger computing systems.

An efficient serial algorithm for finite temperature, quenched Potts model simulations of domain evolution has been developed. This ‘‘n-fold way’’ algorithm eliminates unsuccessful spin flip attempts a priori by flipping sites with a frequency proportional to their site activity, defined as the sum of the probability of success for every possible spin flip at that site. Finite temperature efficiency for high-spin degeneracy systems is achieved by utilizing a new, analytical expression for the portion of the site activity due to flips to non-neighbor spin values. Hence, to determine the activity of a site, only flips to the nearest neighbor spin values need be considered individually; all other flips are evaluated in a single expression. A complexity analysis of this algorithm gives the dependence of computing time on system parameters and on simulation progress. While a conventional Potts model algorithm has a constant computing time per simulation timestep, the n-fold way algorithm increases in efficiency as domain coarsening progresses. Computer experiments confirm the complexity analysis results and indicate that the n-fold way algorithm is much more efficient than the conventional algorithm even at high fractions of the critical temperature.

In this article the principles of the field operation and manipulation (FOAM) C++ class library for continuum mechanics are outlined. Our intention is to make it as easy as possible to develop reliable and efficient computational continuum-mechanics codes: this is achieved by making the top-level syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Object-orientation techniques enable the creation of data types that closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modeling in a FOAM computational-fluid-dynamics code is discussed, and calculations performed on a standard test case, that of flow around a square prism, are presented. To demonstrate the flexibility of the FOAM library, codes for solving structures and magnetohydrodynamics are also presented with appropriate test case results given. © 1998 American Institute of Physics.