论文标题
Hodge-Helmholtz操作员
Coupled Domain-Boundary Variational Formulations For Hodge-Helmholtz Operators
论文作者
论文摘要
我们将普遍的Hodge-Helmholtz或Hodge-Laplace方程的混合变异问题与在有界的三维LIPSCHITZ域上提出的杂物 - 宽面条方程，而当没有结合的补体中假设恒定系数在恒定系数中引起，而后者是由后者产生的第一类边界积分方程。最近开发的针对相关边界积分运算符的Calderon投影仪用于执行对称耦合。我们通过建立广泛的花园不平等（T-COCERCERIVE）证明了耦合问题的稳定性。所得的方程式系统描述了在有界的不均匀各向同性体内单色电磁波的散射，可能具有“粗糙”的表面。麦克斯韦方程的潜在公式的低频鲁棒性使该模型成为盖尔金离散化的有希望的起点。
We couple the mixed variational problem for the generalized Hodge-Helmholtz or Hodge-Laplace equation posed on a bounded three-dimensional Lipschitz domain with the first-kind boundary integral equation arising from the latter when constant coefficients are assumed in the unbounded complement. Recently developed Calderon projectors for the relevant boundary integral operators are used to perform a symmetric coupling. We prove stability of the coupled problem away from resonant frequencies by establishing a generalized Garding inequality (T-coercivity). The resulting system of equations describes the scattering of monochromatic electromagnetic waves at a bounded inhomogeneous isotropic body possibly having a "rough" surface. The low-frequency robustness of the potential formulation of Maxwell's equations makes this model a promising starting point for Galerkin discretization.
