Domain Integral Reduction In Bem: The Foundations
Foundations of a new BEM algorithm, called Domain Integral Reduction (DIRA), are discussed. DIRA concerns situations in which an exact fundamental solution is not available, for example in many nonlinear, inhomogeneous and dynamic problems. Commonly, an approximate fundamental solution is used from, say, a corresponding linear, homogeneous or static problem. Doing so gives rise to a residual domain integral at variance with the boundary-only character of BEM. Current methods for domain integrals include Dual Reciprocity Algorithms, domain cells, and Monte Carlo integration methods, all involving calculations at points throughout the domain. Some dependence of accuracy and efficiency is expected on the number and positions of the internal points. DIRA exploits relations reminiscent of the Helmholtz decomposition to eliminate domain integrals exactly in favor of surface integrals. It avoids domain function evaluations in computing, say, the surface displacements.
Number of Pages
Article; Proceedings Paper
Source API URL
Nicholson, D. W.; Kassab, A. J.; and Ionescu, I., "Domain Integral Reduction In Bem: The Foundations" (2001). Scopus Export 2000s. 22.