A Cubic-Hole Finite Element for 3-D Resistivity Modeling
We have developed a new 3-D finite element for a cubic block with a vertical hole. The cubic-hole element, which has 24 nodes, is tailored to 3-D finite-element modeling of dc flow in formations penetrated by a borehole. It improves the condition number of the finite-element matrix by representing the borehole directly and avoiding elements with a large ratio of length to width. The new element assembles easily with conventional cubic elements and is suitable for domain decomposition and parallelization. We have incorporated this element into an iterative resistivity imaging algorithm.