The computational performance of a high-order coupled FEM/BEM procedure inelectropotential problems

This paper presents a thorough analysis of the computational performance of a coupled cubic Hermite boundary element/finite element procedure. This C- 1 (i.e., value and derivative continous) method has been developed specific ally for electropotential problems, and has been previously applied to tors o and skull problems. Here, the behavior of this new procedure is quantifie d by solving a number of dipole in spheres problems. A detailed set of resu lts generated with a wide range of the various input parameters (such as di pole orientation, location, conductivity, and solution method used in each spherical shell [either finite element or boundary elements]) is presented. The new cubic Hermite boundary element procedure shows significantly bette r accuracy and convergence properties and a significant reduction in CPU ti me than a traditional boundary element procedure which uses linear or const ant elements. Results using the high-order method are also compared with ot her computational methods which have had quantitative results published for electropotential problems. In all cases, the high-order method offered a s ignificant improvement in computational efficiency by increasing the soluti on accuracy for the same, or fewer, solution degrees of freedom.