Fast Adaptive Finite Element Methods for Electromagnetic Applications

9812895TsukermanFinite有限元分析在各种工程应用中被广泛用于电磁场的计算机模拟。尽管在过去二十年中取得了重大进展，但仍存在相当大的计算困难。为了达到理想的精度，通常需要非常精细的有限元网格，单元数达到数十万或更多，而计算时间可能高得令人望而却步。在拟议的项目中，通过将带有多层预条件的自适应有限元方法应用于微磁学和地球物理中的各种电磁问题，将在电磁有限元分析方面取得质的进展。快速自适应方法将大大提高电磁场计算的速度和精度。该项目本质上是跨学科的，旨在弥合最先进的计算方法和电磁应用之间的差距。预条件分层基多重网格法将应用于磁记录问题，特别是多粒子系统(磁带、薄膜介质)和磁记录头。将模拟由Landau-Lifshitz-Gilbert方程描述的静磁场和动态过程。多层预处理器还将应用于地球物理中的静态和涡流问题。自适应网格加密将在多个应用领域系统地实施。在微磁学中，它将提供一种跟踪磁场壁运动的方法。在地球物理应用中，通常计算域很大，自适应网格加密应该在可管理的网格大小上产生合理的精度。四面体单元和其他类型的单元的网格加密策略将基于申请人提出的单元形状的精确先验特征来评估：通用的最大特征值准则和对于一阶四面体单元的最小奇异值条件。本项目将涉及两名研究生。对这些学生来说，一个明显的好处是他们接触到了现代计算方法、电磁场分析和各种实际应用。几家公司已经对申请者的研究表示了浓厚的兴趣。该项目很有可能与磁记录行业、石油勘探服务和有限元软件公司开展产业合作。人们认为，该项目的结果将具有理论和实践意义：它们将促进地球物理中磁记录介质和磁头、电偶和感应测井的快速三维场分析，并将对无损检测、优化和其他领域具有重要意义。

9812895TsukermanFinite Element (FE) analysis is very widely used for computer simulation of electromagnetic fields in various engineering applications. Although significant progress has been achieved over the last two decades, considerable computational difficulties remain. Very fine FE meshes, with hundreds of thousands of elements or more, are often needed to achieve a desirable accuracy, and the computational time may be prohibitively high.In the proposed project, a qualitative advancement in electromagnetic FE analysis will be achieved by applying adaptive finite element methods with multilevel preconditioners to a variety of electromagnetic problems in micromagnetics and geophysics. Fast adaptive methods will lead to a drastic increase in the speed and accuracy of electromagnetic field computation. The project is interdisciplinary in its nature and is intended to bridge the gap between state-of-the-art computational methods and electromagnetic applications.Preconditioned Hierarchical Basis Multigrid methods will be applied to magnetic recording problems, in particular to multiparticle systems (magnetic tapes, thin film media) and to magnetic recording heads. Magnetostatic ("demagnetizing") fields as well as dynamic processes described by the Landau-Lifshitz-Gilbert equation will be modeled. Multilevel Preconditioners will also be applied to static and eddy current problems in geophysics.Adaptive mesh refinement will be systematically implemented in several application areas. In micromagnetics, it will provide a way to trace the domain wall motion. In geophysical applications, for which very large computational domains are typical, adaptive mesh refinement should lead to a reasonable accuracy on meshes of manageable size.Mesh refinement strategies for tetrahedral elements and other types of elements will be evaluated on the basis of precise a priori characterization of element shapes proposed by the applicant: the general maximum eigenvalue criterion and, for first order tetrahedral elements, the minimum singular value condition for the element 'edge shape matrix'.Two graduate students are to be involved in the proposed project. An obvious benefit to these students will be their exposure to modern computational methods, electromagnetic field analysis and various practical applications.Several companies have already expressed significant interest in the applicant's research. Industrial collaboration with companies in magnetic recording industry, oil exploration services and finite element software is very likely to develop in the course of the proposed project.It is felt that the results of this project would be of both theoretical and practical significance: they would facilitate fast three-dimensional field analysis of magnetic recording media and heads, galvanic and induction logging in geophysics, and will have important implications for nondestructive testing, optimization, and in other areas.***