An APL2 tool box investigating Schwarz methods

ABSTRACT

A Schwarz method is an iterative algorithm for aggregating the solution of an elliptic PDE on some domain &OHgr; from repeated solutions on overlapping sub-domains. This general definition incorporates many algorithms which differ in the sequence of sub-domain solutions and the way this information is aggregated. This calls for a tool for investigating and comparing these different algorithms at least for a model problem without the tedious work of programming. The idea is to have simple building blocks for formulating the algorithm in terms of sub-domain solutions. On the other hand this tool should give the user as much freedom as possible, still maintaining ease of use. APL2 was chosen as the base of the tool box because of the interactive environment, the graphics facilities, and the hot spot and run time analysis ready at hand. For maintaining performance, the CPU intensive parts are taken from the ESSL library or coded directly in Vector Assembler.

REFERENCES

• 1: Pierre Louis Lions. On the schwarz alternating method. In Roland Glowinski, Gene H. Golub, G6rard A. Meurant, and Jacques P6riaux, editors, First International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 1-43, SIAM, Philadelphia, 1988.
• 2: Christoph Pospiech. Comparison of Schwavz methods for two subdomains. Technical Report 75.91.15, IBM Scientific Center, Heidelberg, 1991.
• 3: Christoph Pospiech and Jens Weidner. Modified Schwarz algorithms. Technical Report, IBM Scientitle Center, Heidelberg, to appear.
• 4: ttermann A. Schwarz. Gesammelte Mathematische Abhandlungen, pages 133-143. Volume 2, Springer, Berlin/Heidelberg/New York, 1890.
• 5: Jens Weidner. Remarks on the Schwarz alterhating principle. Technical Report, IBM Scientific Center, Heidelberg, to appear.

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms, Languages, Performance