Development of a method of moment based on discontinuous Galerkin method and Hdiv inner products

• Project/Area Number: 15K13418
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Computational science
• Research Institution: Kyoto University
• Principal Investigator: Nishimura Naoshi 京都大学, 情報学研究科, 教授 (90127118)
• Co-Investigator(Kenkyū-buntansha): 新納 和樹 京都大学, 情報学研究科, 助教 (10728182)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: Maxwell 方程式 / 積分方程式 / 不連続Galerkin法 / Hdiv内積 / 数値計算手法 / モーメント法 / Maxwell方程式

Outline of Final Research Achievements

We have investigated methods of moments for Maxwell's equations using the discontinuous Galerkin (DG) method, with relaxed continuity requirements for interpolation functions for unknowns. Particular attentions have been paid to issues such as the accuracy, preconditioning and prevention of the low frequency breakdown with the help of discretization using Hdiv inner products. We have concluded the effectiveness of the DG method using rooftop functions. Also, we could successfully formulate a DG method using Hdiv inner product which does not require dual bases. As for preconditioning, we have concluded that standard methods such as the tri-diagonal preconditioners work, but that the Calderon preconditioners are not effective with the proposed DG method.