RIA: Algebro-Topological Methods for the Formulation and Numerical Solution of Three Dimensional Magnetoquasistatic Problems

RIA：三维磁准静态问题的公式化和数值求解的代数拓扑方法

• 批准号: 8909537
• 负责人: P. Robert Kotiuga
• 金额: $ 6万
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-15 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8909537&HistoricalAwards=false
• 关键词: RIA; Algebro; Topological; Methods; Formulation

The use of differential forms and algebraic topology have become indispensible in theoretical physics. Application of this mathematical formalism to boundary value problems of Maxwell's equations results in a clear articulation of topolocial problems in engineering electronmagnetics and gives general relationships between vector fields and lumped parameters. The calculation of three dimensional electromagnetic fields on the largest of computers is a challenging research area which also benefits from this mathematical formalism. This research will extend the state of computational engineering in this area by investigating o the implementation of algorithms which automatically find "cuts" for magnetic scalar potentials in multiply connected current free regions; o the practical use of variational principles which yield first order Euler- Lagrange equations of the magnetic field, thereby avoiding the use of a vector potential; o the algebraic topology of "Heegard Splitting of three dimensional homology spheres" in order to develop algorithms for handling topological aspects of three dimensional eddy current problems where a magnetic scalar potential is used in current free regions.

微分形式和代数拓扑的使用已经成为 在理论物理学中不可或缺。 适用本 麦克斯韦边值问题的数学形式 方程的结果在一个明确的衔接拓扑问题， 工程电磁学，并给出了一般的关系 向量场和集总参数。 计算三 最大的计算机上的三维电磁场是一个 具有挑战性的研究领域，也受益于这种数学 形式主义 这项研究将扩展计算的状态 在这一领域的工程调查 o实现自动找到“切割”的算法， 多连通无电流区中的磁标量势; 变分原理的实际应用， 欧拉-拉格朗日方程的磁场，从而避免了 使用 矢势 o三维Heegard分裂的代数拓扑 同源性 球体”，以便开发用于处理 三维涡流问题的拓扑方面， 在无电流区域中使用磁标量势。