Boundary Integral Equations for Calculating Complex Eigenvalues of Transmission Problems
Boundary Integral Equations for Calculating Complex Eigenvalues of Transmission Problems
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DOI：
10.1137/16m1087436
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
Ryota Misawa;K. Niino;N. Nishimura
中科院分区：
文献类型：
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作者：
Ryota Misawa;K. Niino;N. Nishimura
谐振频率是复特征值，在该复特征值处齐次传输问题具有非平凡解。这些频率是令人感兴趣的，因为即使频率是真实的，它们也会影响解的行为。共振频率的问题，可以有效地解决与边界积分方程法（BIEM）的无限域。因此，我们考虑一个数值方法确定共振频率与快速BIEM和樱井-杉浦投影法。然而，BIEM可能有虚构的特征值，即使当一个使用穆勒或PMCHWT公式，这是已知的谐振自由时，频率是真实的值。在本文中，我们提出了新的边界积分方程的传输问题，其中一个可以区分真正的和虚构的特征值容易。具体来说，我们考虑波导问题的亥姆霍兹方程在二维和标准散射问题的麦克斯韦方程在三维。我们在数字上验证了th...
Resonance frequencies are complex eigenvalues at which the homogeneous transmission problems have nontrivial solutions. These frequencies are of interest because they affect the behavior of the solutions even when the frequency is real. The resonance frequencies are related to problems for infinite domains which can be solved efficiently with the boundary integral equation method (BIEM). We thus consider a numerical method for determining resonance frequencies with fast BIEM and the Sakurai--Sugiura projection method. However, BIEM may have fictitious eigenvalues even when one uses Muller or PMCHWT formulations which are known to be resonance free when the frequency is real valued. In this paper, we propose new BIEs for transmission problems with which one can distinguish true and fictitious eigenvalues easily. Specifically, we consider waveguide problems for the Helmholtz equation in two dimensions and standard scattering problems for Maxwell's equations in three dimensions. We verify numerically that th...