Global Element Method Research Articles

An abstract data-type technique for scientific software

Numerical computation forms a substantial part of the total of world computing, and, as a result, large amounts of money are spent on the production, modification and maintenance of scientific software. A methodology based on an abstract data-type technique for algorithmic design has the potential to reduce numerical software development costs. This paper describes the abstract data-type development of GEM2, a package for solving two-dimensional single/coupled real/complex elliptic partial differential equations using the global-element method. We show that the abstract design of the GEM2 package, together with the use of an extensible implementation language (Algol 68), yields a family of packages able to handle a variety of problems but based on a single source code. Development and maintenance costs are reduced by this approach; we show that, at least in this case, run time efficiency is unimpaired.

The global element method applied to a discontinuous nuclear potential

A new variational technique, the Global Element Method (GEM), is applied to a well-known nuclear physics problem. The GEM enables the solution region to be divided into physically meaningful subregions and appropriate expansion functions to be used in each of these subregions. The continuity of the trial functions (and their derivatives) at the subregion interfaces, together with the prescribed boundary conditions is enforced by the variational principle. It is demonstrated that for the bound-state and scattering problems for a typical discontinuous nuclear potential, the GEM obtains significantly faster convergence rates than previous variational methods. Moreover this new approach will enable the major components of existing computer programs, using conventional global variational methods, to be reused after suitable modification. The GEM, with the possibility of high convergence rates, should hopefully prove to be a useful computational tool in many areas of computational physics.