Coupling interface method and its applications
I shall briefly review the coupling interface method (CIM) that Yu-Chen Shu and I proposed in 2007 [1] for solving elliptic complex interface problems in arbitrary dimensions, where the coecients, the source terms, and the solutions may be discontinuous or singular across the interfaces. The main part of this talk will be on its applications, including (1) solving the electrocstatic potential for macromolecules in ionic solvent, (2) simulating the tumor growth using a continuum model, and (3) solving guided wave modes in plasmonic crystals [2]. These applications demonstrate that CIM is capable to handle some moving interface problems and some elliptic eigenvalue problems with complex geometry. Reference
Determining whether a new software development technique is useful and usable is a challenging taste. Various flavors of empirical study may be used to help with this task, including surveys, case studies, and experiments. Little guidance is available within the software engineering community to help choose among these alternatives when assessing a new and evolving software development technique within some cost bounds. We faced this challenge when assessing a new programming technique called aspect-oriented programming. To assess the technique, we chose to apply both a case study approach and a series of four experiments because we wanted to understand and characterize the kinds of information that each approach might provide. We describe and critique the evaluation methods we employed, and discuss the lessons we have learned. These lessons are applicable to other researchers attempting to assess new programming techniques that are in an early stage of development.