Fast finite volume simulation of 3D electromagnetic problems with highly discontinuous coefficients
Fast finite volume simulation of 3D electromagnetic problems with highly discontinuous coefficients
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DOI：
10.1137/s1064827599360741
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发表时间：
2001-04-16
影响因子：
3.1
通讯作者：
Ascher, UM
中科院分区：
文献类型：
--
作者：
Haber, E;Ascher, UM
我们考虑解决三维电磁问题的参数制度，准静态近似适用的磁导率，介电常数和电导率可能会有很大的变化。所遇到的困难包括处理解在界面上的不连续性和加速传统迭代方法的收敛性，这些方法用于求解在频域中离散麦克斯韦方程时出现的线性代数方程组。哈伯，美国Ascher，D. Aruliah和D. Oldenburg，J.物理、163（2000），pp. 150-171; D.阿鲁利亚，美国Ascher，E. Haber和D. Oldenburg，数学模型方法应用科学，出现）。还可以处理渗透率是可变的并且可能包含显著的跳跃不连续性的问题。为了解决收敛速度慢的问题，我们重新制定麦克斯韦方程的潜力，应用亥姆霍兹分解的电场或磁场。旋度算子的零空间可以通过增加一个稳定化项，使用规范条件来消除，从而得到一个强椭圆微分算子。交错网格有限体积离散随后应用到重新制定的PDE系统。该方案适用于各种类型的源，即使在电导率和磁导率都存在强材料不连续性的情况下。所得到的离散系统是服从ILU预处理Krylov方法的快速收敛性。我们用几个数值例子来测试我们的方法，并证明了它的鲁棒效率。我们还比较它的经典Yee方法使用类似的迭代技术所产生的代数系统，我们表明，我们的方法是显着更快，特别是对电源。
We consider solving three-dimensional electromagnetic problems in parameter regimes where the quasi-static approximation applies and the permeability, permittivity, and conductivity may vary significantly. The difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing Maxwell's equations in the frequency domain.The present article extends methods we proposed earlier for constant permeability [E. Haber, U. Ascher, D. Aruliah, and D. Oldenburg, J. Comput. Phys., 163 ( 2000), pp. 150-171; D. Aruliah, U. Ascher, E. Haber, and D. Oldenburg, Math. Models Methods Appl. Sci., to appear.] to handle also problems in which the permeability is variable and may contain significant jump discontinuities. In order to address the problem of slow convergence we reformulate Maxwell's equations in terms of potentials, applying a Helmholtz decomposition to either the electric field or the magnetic field. The null space of the curl operators can then be annihilated by adding a stabilizing term, using a gauge condition, and thus obtaining a strongly elliptic differential operator. A staggered grid finite volume discretization is subsequently applied to the reformulated PDE system. This scheme works well for sources of various types, even in the presence of strong material discontinuities in both conductivity and permeability. The resulting discrete system is amenable to fast convergence of ILU-preconditioned Krylov methods.We test our method using several numerical examples and demonstrate its robust efficiency. We also compare it to the classical Yee method using similar iterative techniques for the resulting algebraic system, and we show that our method is significantly faster, especially for electric sources.