Reformulating a Boundary-Integral Equation in Three Dimensions as as Integral-Operator Problem in a Plane Region
| Author(s) | Dallas, A.G. | |
| Date Accessioned | 2005-02-17T18:46:38Z | |
| Date Available | 2005-02-17T18:46:38Z | |
| Publication Date | 2001 | |
| Abstract | Motivated by a desire to simplify the design of numerically stable and efficient approximation schemes for boundary-operator problems, we develop a framework in which an integral equation on the boundary of a domain ${I\kern-.30em R}^3$ can be systematically reformulated as an integral-operator problem set in a region in the plane; some geometric restrictions are imposed on the shape of the (smooth) boundary. When the plane region is chosen to be a rectangle, the necessary Sobolev-space structures can be handled numerically rather easily in the new simpler geometry, in contrast to the situation on the original boundary. Moreover, familiar trial- and test- functions can then be employed in the construction of approximate solutions of the reformulated problems. We show for two examples how a well-posed problem can be transferred from the domain-boundary setting to the plane-region setting. We describe a numerical implementation of these ideas to a lower-dimensional example involving the approximate solution of a first-kind integral equation associated with the Helmholtz equation that is originally set on the boundary of a domain in ${I\kern-.30em R}^2$. | en |
| Sponsor | This work was supported by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under Grant F49620-96-1-0039. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government. | en |
| Extent | 400499 bytes | |
| MIME type | application/pdf | |
| URL | http://udspace.udel.edu/handle/19716/342 | |
| Language | en_US | |
| Publisher | Department of Mathematical Sciences | en |
| Part of Series | technical Report: 2001-02 | |
| Title | Reformulating a Boundary-Integral Equation in Three Dimensions as as Integral-Operator Problem in a Plane Region | en |
| Type | Technical Report | en |