一种适用于高波数时谐Maxwell方程的绝对稳定hp-HDG方法
An absolutely stable $hp$-HDG method for the time-harmonic Maxwell equations with high wave number
AI总结：
本文提出并分析了一种混合不连续Galerkin方法，用于求解时谐Maxwell方程，通过强制电场的无散条件并引入拉格朗日乘子，得到混合curl-curl形式。该方法在高波数情况下具有绝对稳定性，并通过数值实验验证了理论分析。
摘要：
我们提出并分析了一种混合不连续Galerkin（HDG）方法，用于求解时谐Maxwell方程。通过强制电场的无散条件，引入拉格朗日乘子，问题转化为求解Maxwell问题的混合curl-curl形式。该方法被证明是对不定时谐Maxwell方程在高波数情况下具有绝对稳定性的HDG方法。通过利用对偶论证，得到了HDG方法的收敛性依赖于波数k、网格尺寸h和多项式阶数p的关系。给出了数值结果以验证理论分析。
英文摘要：
We present and analyze a hybridizable discontinuous Galerkin (HDG) method for the time-harmonic Maxwell equations. The divergence-free condition is enforced on the electric field, then a Lagrange multiplier is introduced, and the problem becomes the solution of a mixed curl-curl formulation of the Maxwell's problem. The method is shown to be an absolutely stable HDG method for the indefinite time-harmonic Maxwell equations with high wave number. By exploiting the duality argument, the dependence of convergence of the HDG method on the wave number k, the mesh size h and the polynomial order p is obtained. Numerical results are given to verify the theoretical analysis.
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