Wust P, Nadobny J, Seebass M, Dohlus J M, John W, Felix R
Strahlenklinik und Poliklinik des Klinikum Rudolf Virchow, Freie Universität Berlin, Germany.
IEEE Trans Biomed Eng. 1993 Aug;40(8):745-59. doi: 10.1109/10.238459.
An algorithm has been developed for calculation of 3-dimensional E fields by the volume-surface integral equation (VSIE) method. Integration over surface elements is performed by elementary analytical formulas, assuming a linear interpolation of surface charges. Grid points at electrical interfaces are split off, well considering 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 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. Computation time (e.g., 20 min on a supercomputer for approximately 30,000 cells) needs to be reduced by further code development. 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 (> 100,000 cells).
已经开发出一种算法，用于通过体积-表面积分方程（VSIE）方法计算三维电场。假设表面电荷呈线性插值，通过基本解析公式对表面单元进行积分。将电界面处的网格点分离出来，充分考虑这些轮廓处的电场行为，特别是在尖锐弯曲和多媒体交界处。采用平均程序以避免临界点处出现未定义或无限值。在SUN工作站SPARC-IPX或Cray XMP上，使用GMRES（“广义最小残差”）求解器通过迭代求解VSIE，随着问题异质性的增加，收敛速度会显著降低。需要通过进一步的代码开发来减少计算时间（例如，在超级计算机上对大约30,000个单元进行计算需要20分钟）。如果在垂直于电边界处出现高电场梯度，三维测试案例（平面波照射分层圆柱体）的结果通常与有限积分理论（FIT）方法非常吻合。VSIE方法仅在关键区域预测的电场略高。另一方面，对于具有高单元数量（>100,000个单元）的大区域，目前FIT方法在计算时间方面更高效。
