A study of a high accurate numerical method for the inverse problem in the wave equation

2015 Fiscal Year Final Research Report

• Project/Area Number: 23540152
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Aichi Prefectural University
• Principal Investigator: SHIROTA Kenji 愛知県立大学, 情報科学部, 准教授 (90302322)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Keywords: 非適切問題 / 高精度解法 / 波動場 / 数値的再構成手法 / 多倍長計算 / 密度型位相最適化問題 / 任意多点差分法 / H1勾配法

Outline of Final Research Achievements

In this research, we considered about the numerical method to get a high accurate approximated solutions to the initial-boundary value problem in scalar wave equation. We apply the lattice-free finite difference method and the spectral collocation method with the Gauss-Lobatto points to the discretization in space and time direction, respectively. We show the effectiveness of our method by some numerical experiments.
Moreover, we consider a high accurate method for SIMP type topology optimization problem. We adopt the H1 gradient method to solve our problem. In order to get high accurate solution of the partial differential equation in our algorithm, we use the lattice-free finite difference method. By the numerical experiments, we check the effectiveness, stability, and convergency of our algorithm.

Free Research Field

数値解析