Consistent infinitesimal finite-element cell method for diffusion equation in unbounded medium Original Research Article

To calculate the unit-step response matrix of an unbounded medium for use in a time-domain analysis of unbounded medium-structure interaction for the diffusion equation, the consistent infinitesimal finite-element cell method is developed for the three-dimensional case. Its derivation is based on the finite-element formulation and on similarity. The discretization is only performed on the structure-medium interface, yielding a reduction of the spatial dimension by 1. The procedure is rigorous in the radial direction and exact in the finite-element sense in the circumferential directions. In contrast to the boundary-element procedure, the consistent infinitesimal finite-element cell method does not require a fundamental solution and incorporates interfaces extending from the structure-medium interface to infinity compatible with similarity without any additional computational effort. A general anisotropic material can be processed.