We use the method of dimensional continuation to isolate singularities in integrals containing products of Green's functions or their derivatives. Rules for the extraction of the finite part of so-called hypersingular integrals are developed, which should be useful in methods based on boundary integral techniques in science and engineering. In applications to potential theory, electromagnetic scattering, and crack dynamics in continuum mechanics, boundary integrals now can be readily evaluated using computational techniques without recourse to complex analysis or contour distortions since the hypersingularities occurring in intermediate steps of the computations can be isolated and ignored while taking the finite parts of the integrals into account in a consistent manner.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Li, Zehao

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-062111-122949

Advisor

• Ram-Mohan, L. Ramdas
• Heinricher, Arthur C.

Year

• 2011

Date created

• 2011-06-21

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences
• Physics

Rights statement

• In Copyright

Last modified

• 2021-02-02