David A. Hopkins

Integration rules and time domain integral equation stability

Because the mathematical analysis of time domain integral equations is fraught with difficulty, researchers are often forced to use experimental means to characterize the stability of their approaches. The difficulty inherent in this approach is that the variables affecting the success or failure of an experiment necessarily depend on a computer implementation of potentially hundreds of thousands of lines of instructions hiding unknown assumptions and even errors. In this work, the importance of different integration orders for near and far basis functions is investigated, and demonstrated to have an enormous effect on the stability of the implementation. Methods previously thought unstable for difficult problems are shown reliable with tiny changes over broad choices of parameter values.

Integration rules and experimental evidence for the stability of time domain integral equations

Because the analysis of the time domain integral equations of electromagnetics is complicated and cannot easily take into account all sources of error in any given implementation, judgements of stability tend to rest on experience. While such an approach eliminates the worst methods immediately, subtle implementation issues may affect the stability of more promising approaches. In this work, we examine the effects of integration rules on stability. Numerical results demonstrate that increasing accuracy does not always increase stability.

Development of an Object-Oriented Program With Adaptive Mesh Refinement for Heat Transfer Simulations

A 2D/3D object-oriented program with h-type adaptive mesh refinement method is developed for finite element analysis of the multi-physics applications including heat transfer. A framework with some basic classes that enable the code to be built accordingly to the type of problem to be solved is proposed. The program consists of different modules and classes, which ease code development for large-scale complex systems, code extension and program maintenance. The developed program can be used as a “test-bed” program for testing new analysis techniques and algorithms with high extensibility and flexibility. The overall mesh refinement causes the CPU time cost to greatly increase as the mesh is refined. However, the CPU time cost does not increase very much with the increase of the level of h-adaptive mesh refinement. The CPU time cost can be saved by up to 90%, especially for the simulated system with a large number of elements and nodes.Copyright