ON THE COMPATIBILITY OF FINITE ELEMENT‐BOUNDARY ELEMENT COUPLING IN FIELD PROBLEMS Available to Purchase

A technique combining finite elements and boundary elements is promising for unbounded field problems. A hypothetical boundary is assumed in the unbounded domain, and the usual finite element method is applied to the inner region, while the boundary element method is applied to the outer infinite region. On the coupling boundary, therefore, both potential and flux must be compatible. In the finite element method, the flux is defined as the derivative of the potential for which a trial function is defined. In the boundary element method, on the other hand, the same polynomial function is chosen for the potential and the flux. Thus, the compatibility cannot be satisfied unless a special device is considered. In the present paper, several compatibility conditions are discussed concerning the total flux or energy flow continuity across the coupling boundary. Some numerical examples of Poisson and Helmholtz problems are demonstrated.