A stable volume integral equation (VIE) solver based on polarization/magnetization currents is presented, for the accurate and efficient computation of the electromagnetic scattering from highly inhomogeneous and high contrast objects.We employ the Galerkin Method of Moments to discretize the formulation with discontinuous piecewise linear basis functions on uniform voxelized grids, allowing for the acceleration of the associated matrix-vector products in an iterative solver, with the help of FFT. Numerical results illustrate the superior accuracy and more stable convergence properties of the proposed framework, when compared against standard low order (piecewise constant) discretization schemes and a more conventional VIE formulation based on electric flux densities. Finally, the developed solver is applied to analyze complex geometries, including realistic human body models, typically used in modeling the interactions between electromagnetic waves and biological tissue.
High-performance Parallel Solver for Integral Equations of Electromagnetics Based on Galerkin Method
SUNY New Paltz（纽约州立大学新帕尔茨分校）；Faculty of Computational Mathematics and Cybernetics, Lomonosov MSU（莫斯科国立大学计算数学与控制论系）；Institute of Geophysics, ETH Zurich（苏黎世联邦理工学院地球物理研究所）
Alternating directions implicit higher-order finite element method for simulations of time-dependent electromagnetic wave propagation in non-regular biological tissues
我们专注于非平稳麦克斯韦方程组定义在一个定期补丁的元素考虑在等几何分析（IGA）。我们采用时间积分方案的思想发展的有限差分社区[M。Hochbruck，T.扬克河，巴西-地Schnaubelt，Convergence of an ADI splitting for Maxwell's equations，Numerishe Mathematik，2015]，以导出导致Kronecker乘积矩阵离散化的弱公式。我们采取的张量积结构的计算补丁的元素从IGA框架作为一个优势，允许在每个时间步长的线性计算成本因式分解。我们设计我们的求解器，以模拟电磁波在不规则的生物组织中的传播。我们表明，交替方向求解器的线性成本被保存时，我们任意改变材料的数据系数在整个计算域。我们验证求解器使用制造的解决方案和电磁波在人的头部的传播问题。
Proxy-surface-based fast direct solver for TE-mode scattering problems on distributed memory systems
Center for Information Infrastructure, Institute of Science Tokyo（科学技术研究所信息基础设施中心）；Institute of Integrated Research, Institute of Science Tokyo（科学技术研究所综合研究机构）
Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；Nanyang Technological University（南洋理工大学）；KTH Royal Institute of Technology（皇家理工学院）；University of Michigan（密歇根大学）
