Boundary element method for domains whose Green's function is not available

2022 Fiscal Year Final Research Report

• Project/Area Number: 21K19764
• Research Category: Grant-in-Aid for Challenging Research (Exploratory)
• Allocation Type: Multi-year Fund
• Review Section: Medium-sized Section 60:Information science, computer engineering, and related fields
• Research Institution: Keio University
• Principal Investigator: Isakari Hiroshi 慶應義塾大学, 理工学部(矢上), 講師 (50638773)
• Project Period (FY): 2021-07-09 – 2023-03-31
• Keywords: グリーン関数 / キャビティ散乱 / 境界要素法 / 共鳴

Outline of Final Research Achievements

In this study, we investigated a novel boundary element method (BEM) that is capable of solving the wave scattering problem defined in a domain with boundaries of infinite measure (e.g. semi-infinite and layered domains, etc). The proposed method is applicable even when the underlying Green's function is not available. Specifically, based on the recently proposed indirect BEM that utilises both the layer potential and the Sommerfeld integral, we developed a new BEM that circumvents the fictitious eigenvalue problem. It is found that our method equips higher reliability and provides more accurate solutions than the original one. In addition, we modified our formulation to deal with the case where the semi-infinite boundary is locally perturbed (so-called cavity scattering) and applied the modified BEM to open resonance simulation. We think that our study paved a new way to design devices that realises novel wave controlling.

Free Research Field

計算科学

Academic Significance and Societal Importance of the Research Achievements

境界要素法の古くから続く研究の主流は、個々の問題に対する適切なグリーン関数の解析的な評価・高速な数値計算を基礎とする各々の問題に特化した高度な算法を構築するというものである。本研究は、グリーン関数が求まらない場合においても利用可能な汎用可能な方法の構築をおこなった。特に、キャビティ散乱問題を高精度・高速に解くことのできるシンプルな境界要素法の開発に成功したことは計算科学の分野において学術的に意義深い。また、同問題はセンシングなどの分野において多くの応用を有することから、本研究で開発した新しい境界要素法は工学的にも利用価値の高いものであると考えられる。