CONSTRUCTING DIMENSION-ADAPTIVE SPARSE GRID INTERPOLANTS USING PARALLEL FUNCTION EVALUATIONS
Abstract
Dimension-adaptive sparse grid interpolation is a powerful tool to obtain surrogate functions of smooth, medium to high-dimensional objective models. In case of expensive models, the efficiency of the sparse grid algorithm is governed by the time required for the function evaluations. In this paper, we first briefly analyze the inherent parallelism of the standard dimension-adaptive algorithm. Then, we present an enhanced version of the standard algorithm that permits, in each step of the algorithm, a specified number (equal to the number of desired processes) of function evaluations to be executed in parallel, thereby increasing the parallel efficiency.
References
- Acta Numerica 13, 147 (2004). Crossref, Google Scholar
M. Griebel , Multigrid Methods III,Internat. Ser. Numer. Math. 98 (Birkhäuser, Basel, 1991) pp. 211–221. Crossref, Google Scholar- Parallel Processing Letters 2, 61 (1992), DOI: 10.1142/S0129626492000180. Link, Google Scholar
- Parallel Comput. 24(7), 1081 (1998), DOI: 10.1016/S0167-8191(98)00043-X. Crossref, ISI, Google Scholar
J. Garcke , M. Hegland and O. Nielsen ,Lecture Notes in Computer Science 2659 (Springer, 2003) pp. 683–692. Google Scholar- H.-J. Bungartz, Dünne Gitter und deren Anwendung bei der adaptiven Lösung der dreidimensionalen Poissongleichung, PhD thesis, Technische Universität München, Germany, 1992 . Google Scholar
-
H.-J. Bungartz , Finite Elements of Higher Order on Sparse Grids ( Shaker , 1998 ) . Google Scholar - Adv. Comput. Math. 12(4), 273 (2000), DOI: 10.1023/A:1018977404843. Crossref, ISI, Google Scholar
- Computing 71, 65 (2003), DOI: 10.1007/s00607-003-0015-5. Crossref, ISI, Google Scholar
- A. Klimke, Uncertainty modeling using fuzzy arithmetic and sparse grids, PhD thesis, Universität Stuttgart, Shaker Verlag, Aachen, 2006 . Google Scholar
- ACM Transactions on Mathematical Software 31(4), 561 (2005), DOI: 10.1145/1114268.1114275. Crossref, ISI, Google Scholar


