Currently, there is a need for the computational handling of near-singularities that arise in many branches of physics, particularly for handling near-strong singularities. An example of such singularities is presented by the case of gradients of Newton-type potentials and modified Newton-type potentials. Currently, practitioners resort to multiple methods that do not work well, suffer from accuracy issues, or work only for very specialized cases. Accuracy issues provide results that cannot be trusted. Using codes that work only for specialized cases results in either misapplication of the code, and hence reduced accuracy, or failed attempts at a solution or infrequent and expensive code modifications to handle new cases.
This innovation comprises a method and computer code to improve machine efficiency in the computation of nearly singular integrals that arise in many branches of physics. Resulting efficiency increases permit computational modeling of more complex structures and increased detail. The simplicity of this method and computer code has long been sought since it addresses many problems associated with the existing art. For example, the method disclosed herein handles a wide span of nearly singular integrals that up to now have been addressed with a variety of special-case algorithms. To date, the method and computer code have been applied to computational electromagnetics (CEM) problems; however, the method is general and is expected to find use in a variety of computational modeling disciplines.
This work was done by Patrick Fink and Michael Khayat of Johnson Space Center. MSC-25640-1