A new technique for boundary element analyses of 2D potential problems to quickly obtain the solution only in a target region was developed. This technique takes advantage of diffusion effects in Laplace fields. In fields governed by diffusion equations, high-frequency disturbances of boundary conditions on non-target boundaries far from the target region give little influence to the target region. In this technique, boundary conditions on non-target boundaries are transformed into the Fourier series, and only their low-frequency terms are utilized by using special weight functions for boundary integral equations. When the solutions only in a target region are needed, especially in large size boundary value problems, this technique enables us to obtain them quickly and precisely. The present method can be extended not only to Laplace equations but also to any kind of diffusive systems such as elastostatics. © 2004 Elsevier Ltd. All rights reserved.
Onishi, Y., & Amaya, K. (2004). A new technique for high-speed boundary element analyses of Laplace equations to obtain solutions in target regions. Engineering Analysis with Boundary Elements, 28(7), 791–799. https://doi.org/10.1016/j.enganabound.2003.12.008