The presented doctoral thesis aims at development a new efficient tool for optimization of uniformity of point samples. One of use-cases of these point sets is the usage as optimized sets of integration points in statistical analyses of computer models using Monte Carlo type integration. It is well known that the pursuit of uniformly distributed sets of integration points is the only possible way of decreasing the error of estimation of an integral over an unknown function. The tasks of the work concern a survey of currently used criteria for evaluation and/or optimization of uniformity of point sets. A critical evaluation of their properties is presented, leading to suggestions towards improvements in spatial and statistical uniformity of resulting samples. A refined variant of the general formulation of the phi optimization criterion has been derived by incorporating the periodically repeated design domain along with a scale-independent behavior of the criterion. Based on a notion of a physical analogy between a set of sampling points and a dynamical system of mutually repelling particles, a hyper-dimensional N-body system has been selected to be the driver of the developed optimization tool. Because the simulation of such a dynamical system is known to be a computationally intensive task, an efficient solution using the massively parallel GPGPU platform Nvidia CUDA has been developed. An intensive study of properties of this complex architecture turned out as necessary to fully exploit the possible solution speedup.
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:390276 |
| Creators | Mašek, Jan |
| Contributors | Šejnoha,, Jiří, Kruis,, Jaroslav, Vořechovský, Miroslav |
| Publisher | Vysoké učení technické v Brně. Fakulta stavební |
| Source Sets | Czech ETDs |
| Language | Czech |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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