交替方向隐式高阶有限元法模拟非规则生物组织中不定常电磁波的传播
Alternating directions implicit higher-order finite element method for simulations of time-dependent electromagnetic wave propagation in non-regular biological tissues
摘要：
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。
英文摘要：
We focus on non-stationary Maxwell equations defined on a regular patch of elements as considered in the isogeometric analysis (IGA). We apply the time-integration scheme following the ideas developed by the finite difference community [M. Hochbruck, T. Jahnke, R. Schnaubelt, Convergence of an ADI splitting for Maxwell's equations, Numerishe Mathematik, 2015] to derive a weak formulation resulting in discretization with Kronecker product matrices. We take the tensor product structure of the computational patch of elements from the IGA framework as an advantage, allowing for linear computational cost factorization in every time step. We design our solver to target simulations of electromagnetic waves propagations in non-regular biological tissues. We show that the linear cost of the alternating direction solver is preserved when we arbitrarily vary material data coefficients across the computational domain. We verify the solver using the manufactured solution and the problem of propagation of electromagnetic waves on the human head.
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