Development of uncertainty analysis methods for numerical analysis of partial differential equations

2016 Fiscal Year Final Research Report

• Project/Area Number: 26630451
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Naval and maritime engineering
• Research Institution: Yokohama National University
• Principal Investigator: Kawamura Yasumi 横浜国立大学, 大学院工学研究院, 教授 (50262407)
• Co-Investigator(Renkei-kenkyūsha): HINO Takanori 横浜国立大学, 大学院工学研究院, 教授 (60373429)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 不確定性解析 / 材料・構造力学 / 流体力学 / 応答曲面 / 多項式カオス展開

Outline of Final Research Achievements

In order to evaluate the uncertainty of response for the problem with inherent uncertainties, Monte Carlo simulation (MCS) is usually used in which many deterministic analyses should be carried out by changing the inherent uncertainty parameters. However, as the problem becomes more complicated, the cost of the analysis becomes high so that application of MCS for the uncertainty analysis becomes difficult. In this study, by applying response surface methodology with polynomial chaos expansion (PCE) to the partial differential equations directly, the stochastic analysis formulation is developed which is a natural extension of the deterministic problem to the space of random variables. The effectiveness and validity of the stochastic formulation is investigated for the structural problems (elastostatics and eigenvalue problem) and the fluid problems (compressible quasi-1D flow).

Free Research Field

船舶海洋工学、構造力学、CAE