2013 Fiscal Year Final Research Report
Studies on preconditioning and basis functions in periodic fast multipole methods for Maxwell's equations
| Project/Area Number |
23560068
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIKAWA Hitoshi 京都大学, 情報学研究科, 講師 (90359836)
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| Project Period (FY) |
2011 – 2013
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| Keywords | Maxwell方程式 / 周期境界値問題 / 高速多重極法 / 前処理法 / 基底関数 |
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| Research Abstract |
This study aims at further accelerating the periodic FMM, which is a fast method for solving electromagnetic scattering problems for periodic structures, by improving preconditioners for linear equations, basis functions and integral equation formulations. The square of certain integral operators in electromagnetic scattering problems are well-conditioned, and so are their numerical counterparts as one uses the right basis functions. We were able to obtain an efficient solver of periodic scattering problems using this idea. We also investigated other well-conditioned integral equation formulations and developed a solution method for almost periodic structures found in photonic crystal applications, as well as an efficient preconditioner for volume integral equations.
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