Computational Mechanics using High Performance Computing
Chapter 11
R.E. Bank+ and P.K. Jimack*+Department of Mathematics, University of California at San Diego, United States of America *School of Computer Studies, University of Leeds, Leeds, United Kingdom Adaptive algorithms are of great importance in computational mechanics codes since they can allow both reliability, through the satisfaction of error tolerances, and efficiency, by ensuring that the total number of degrees of freedom present is as small as possible. Unfortunately, the successful incorporation of adaptivity into most software is a complex programming task, and this is especially true for parallel codes. This chapter introduces a new parallel domain decomposition preconditioner which is ideally suited for use in an adaptive framework. Unlike conventional domain decomposition approaches, this technique requires each process to work on the entire domain but with a coarse mesh which has been locally refined only in the subdomain for which that process is responsible. In order to justify the proposed preconditioner it is presented as a natural development of existing domain decomposition and subspace iteration algorithms, and its implementation as part of a parallel mesh adaptivity algorithm, due to Bank and Holst, is also outlined. The paper concludes with the presentation and discussion of a number of provisional numerical results. | ||||||||||
