Maxwell 方程组自适应 PML 高阶棱元离散系统的快速算法

项目名称： Maxwell 方程组自适应 PML 高阶棱元离散系统的快速算法

项目编号： No.11201159

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 钟柳强

作者单位： 华南师范大学

项目金额： 22万元

中文摘要： 针对电磁场方程组自适应完全匹配层法的高阶棱有限元离散系统, 深入研究其快速迭代算法和高效预条件子, 并建立相关理论。本课题所涉及的模型问题具有很强的实际应用背景。自适应完全匹配层法能够很好地求解无界区域上的电磁场散射问题, 对其离散系统快速算法的研究是计算电磁场领域中的热点和难点。与已有工作相比, 我们将面临许多困难点，如模型问题的非正定性对算法的影响, 高阶棱元带来的计算复杂性，算法效率对完全匹配层方程中各向异性系数的强依赖性等等。解决上述困难，需要发展新的算法和理论分析工具。为此，我们已作了比较充分的准备工作。本课题的研究是一项既富有挑战性，又具有重要理论意义和实际应用价值的研究工作，其研究成果将对现有的无界区域上电磁场散射问题的数值模拟起到积极的作用。

中文关键词： 快速算法；高阶棱有限元；Maxwell方程组；完全匹配层；自适应

英文摘要： We will research the fast iterative methods and efficient preconditions as well as establish related theories for highe order edge finite element discretizations of adaptive perfectly matched methods for Maxwell equations. The proposed research and issues have been formulated for practical applications. Adaptive perfectly matched layer methods are suitable to handle the electromagnetic scattering problem in an unbounded domain, and the research for its fast solvers is a very active area today in scientific computing. Compared to the reported research, we are faced with the difficult which from the indefinite property of model, the reality of complexity in computation using the high-order edge finite element, the dependence of computational efficiency on the jump coefficient etc. Many new algorithms and theories have to be developed and explored in order to resolve the above problems. For these reasons, we are well prepared and equipped to achieve our goals. This research project is a challenging one, which is of significance on the theoretical ground and has important implications in practice. This research will advance our knowledge in the existing numerical simulation for the electromagnetic scattering problem in an unbounded domain.

英文关键词： Fast Solvers；High-oder Edge Finite Element；Maxwell Equations；Perfectly Matched Layer；Adaptive