This paper is focused on a fast and reliable estimate of anchor energy losses from a Micro-Electro-Mechanical System resonator, working at pressure in the order of the microbar, due to the scattering of elastic waves from the resonator into the substrate to which it is attached. The proposed numerical method is based on the fundamentals of the analytical procedure employed to estimate quality factors of resonators in the literature and consists in the modeling of the resonator by Finite Elements and of the radiated waves dissipation into the substrate by collocation Boundary Element Method. In order to simulate as quickly as possible an accurate response of the substrate in real time, we further consider $\mathcal{H}$-matrix$/$vector product in the Boundary Element Method. The proposed numerical approach results in a very small elapsed computational time and it will therefore allow applications to real life engineering problems, targeted as future investigations.

本文着重于快速，可靠地估算微机电系统谐振器产生的锚定能量损失，由于谐振器中的弹性波会散射到谐振器所处的基板上，因此该谐振器在压力为微巴的情况下工作被附上。所提出的数值方法基于文献中用于估计谐振器品质因数的分析程序的基础，并且包括通过有限元对谐振器进行建模以及通过并置边界元法对进入基板的辐射波进行建模。为了尽可能快地实时模拟基材的准确响应，我们进一步考虑$\mathcal{H}$-矩阵$/$边界元素方法中的向量乘积。所提出的数值方法所花费的计算时间非常小，因此将允许将其应用于现实生活中的工程问题，作为未来的研究目标。