论文标题
一个准螺旋托投影仪稳定了包含涡流状态的全波求解器
A Quasi-Helmholtz Projector Stabilized Full Wave Solver Encompassing the Eddy Current Regime
论文作者
论文摘要
尽管有多种品质,但Poggio-Miller-Chang-Harrington-wu-tsai(PMCHWT)制剂用于模拟电介质的散射,但在低频下遭受了数值不稳定性和严重的不良条件。尽管这种缺点是用于散射问题的标准低频故障制度中进行了许多解决方案尝试的对象,但涡流状态需要特定的治疗方法。 In this contribution, we present an extension of the recently introduced quasi-Helmholtz projectors based preconditioning of the PMCHWT to obtain an equation stable at low frequencies and specifically in three regimes relevant for eddy currents analyses: (i) when the frequency decreases with a constant conductivity, (ii) when the conductivity increases at fixed frequency and (iii) when the frequency decreases while keeping the product of the frequency and the conductivity constant.基于准Helmholtz投影仪,我们的新策略不会进一步降低原始方程的条件,并且与现有的快速求解器兼容。所得的全波公式能够平稳地从高频的模拟过渡到尤其是涡流应用程序的不同低频制度。数值结果证明了我们在所有制度中的有效性,并特别强调了涡流。
Despite its several qualities, the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation for simulating scattering by dielectric media suffers from numerical instabilities and severe ill-conditioning at low frequencies. While this drawback has been the object of numerous solution attempts in the standard low-frequency breakdown regime for scattering problems, the eddy-current regime requires a specific treatment. In this contribution, we present an extension of the recently introduced quasi-Helmholtz projectors based preconditioning of the PMCHWT to obtain an equation stable at low frequencies and specifically in three regimes relevant for eddy currents analyses: (i) when the frequency decreases with a constant conductivity, (ii) when the conductivity increases at fixed frequency and (iii) when the frequency decreases while keeping the product of the frequency and the conductivity constant. Being based on quasi-Helmholtz projectors our new strategy does not further degrade the conditioning of the original equation and is compatible with existing fast solvers. The resulting full-wave formulation is capable of smoothly transitioning from simulations at high frequencies to the different low-frequency regimes which encompass, in particular, eddy currents applications. Numerical results demonstrate the validity of our approach in all the regimes with a special emphasis given to eddy currents.