3-D computation of E fields by the volume-surface integral equation (VSIE) method in comparison with the finite-integration theory (FIT) method (clinical hyperthermia application)

An algorithm has been developed for calculation of 3-D electric (E) fields by the volume-surface integral equation (VSIE) method. Integration over surface elements is performed using elementary analytical formulas, assuming a linear interpolation of surface charges. Grid points at electrical interfaces are split off, taking into account the E field behavior at these contours, specifically at sharp bends and multimedia junctions. Averaging procedures are utilized in order to avoid undefined or infinite values at critical points. The VSIE is solved by iteration using the GMRES (general minimum residuum) solver on a SUN workstation SPARC-IPX or Cray XMP, whereby convergence speed decreases considerably as the heterogeneity of the problem increases. Results for 3-D test cases (plane wave illuminating a layered cylinder) generally agree well with the finite-integration-theory (FIT) method if high E field gradients occur perpendicular to electrical boundaries. The VSIE method predicts slightly higher E fields only in critical regions. On the other hand, the FIT method at present is more efficient with respect to computation time for large domains with high cell numbers (>100000 cells).