Hybrid Method for Energy flow in Mid-High Frequency Acoustics: Applications in Robust Shape Optimization for Complex Cavities

We present an efficient method for computing acoustic energy within complex-shaped geometries and cavities with obstacles in the mid-high frequency range. This method is based on the Simplified Energy Method (MES), known for its accuracy in such frequency ranges but traditionally limited to simple cavity shapes. The proposed hybrid method integrates the techniques of ray and triangle intersection with the MES formulation to address these limitations. By calculating the intersection points of the rays, we identify the obstructing elements before computing the energy transfer between the boundary elements. A primary intersection state matrix, containing direct view information between elements, is integrated into a modified MES equation to eliminate unnecessary computations and ensure precise calculations of energy transfer for obstructed elements. This hybrid approach is applied to both direct and reverberant fields to determine the total energy density. Numerical simulations conducted within a complex domain enclosure demonstrate the precision of the proposed algorithms when compared to traditional MES calculations. In addition, we propose applying this method to robust shape optimization, effectively balancing competing criteria to achieve optimized acoustic performance. This refined and computationally feasible tool significantly advances computational acoustics, providing accurate and efficient design solutions for complex environments.