Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Review Article Homology in Electromagnetic Boundary Value Problems | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 381953 18 pages doi 2010 381953 Review Article Homology in Electromagnetic Boundary Value Problems Matti Pellikka Saku Suuriniemi and Lauri Kettunen Tampere University of Technology Electromagnetics . Box 692 33101 Tampere Finland Correspondence should be addressed to Matti Pellikka Received 4 March 2010 Revised 2 July 2010 Accepted 14 July 2010 Academic Editor Veli Shakhmurov Copyright 2010 Matti Pellikka et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We discuss how homology computation can be exploited in computational electromagnetism. We represent various cellular mesh reduction techniques which enable the computation of generators of homology spaces in an acceptable time. Furthermore we show how the generators can be used for setting up and analysis of an electromagnetic boundary value problem. The aim is to provide a rationale for homology computation in electromagnetic modeling software. 1. Introduction Setting up a well-posed electromagnetic boundary value problem encompasses setting up constraints that are related to the problem domain the boundary conditions field sources and material parameters. These constraints usually surreptitiously involve the topology of the field problem domain. The division of the domain boundary to be governed by different boundary conditions imposed source fields or circuit quantities the division of the domain to conducting and nonconducting subdomains and the use of field potentials bring up topological aspects that cannot be overlooked when defining the boundary value problem 1-6 . Failure to provide the above information in a consistent manner often leads to an over-or underdetermined system and worse than that the user as well as the software .
