A mathematical model is developed based on the application of permeable and impermeable breakwaters utilizing the mild slope equation (MSE) to analyze the wave amplification in an arbitrary shaped harbor with variable bathymetry. Finite element method (FEM) coupled with analytical approximation is described as Hybrid FEM, which is used to solve the MSE and Helmholtz equation in bounded and unbounded domains (open Sea region), respectively. The validation of the present numerical scheme is conducted by comparing the simulation results with the existing studies and the convergence analysis is also conducted to verify the accuracy of the numerical scheme. The effects of energy dissipation, bottom friction, and variable wave transmission through impermeable and permeable breakwaters are investigated to understand the resonance phenomenon in rectangular port. In addition, the current numerical scheme is implemented on a real Paradip port, Odisha, India at six different key locations, and for the first time the effect of breakwaters placed at the entrance and in the bounded region, along with bottom friction, and partially reflecting port boundary are investigated. The breakwaters with small permeability/transmission coefficient have high efficiency to reduce the wave resonance inside the port.

基于可渗透性和不可渗透性防波堤的应用，利用温和坡度方程（MSE）来开发数学模型，以分析具有可变测深的任意形状港口中的波浪放大。有限元方法（FEM）与解析逼近相结合称为混合FEM，用于分别求解有界和无界域（开阔海域）中的MSE和Helmholtz方程。通过将仿真结果与现有研究进行比较，对当前数值方案进行验证，并进行收敛性分析，以验证数值方案的准确性。能量耗散，底部摩擦，研究了通过不透水和透水防波堤的可变波传播，以了解矩形端口的共振现象。此外，当前的数值方案是在印度奥里萨邦的一个真实Paradip港口的六个不同关键位置实施的，这是首次在入口和边界区域设置防波堤的影响，以及底部摩擦以及部分影响。反映港口边界。渗透/透射系数小的防波堤具有很高的效率，可以减少端口内部的波谐振。研究部分反映港口边界的情况。渗透/透射系数小的防波堤具有很高的效率，可减少端口内部的波谐振。研究部分反映港口边界的情况。渗透/透射系数小的防波堤具有很高的效率，可减少端口内部的波谐振。