In this work, a method for the simulation of guided wave propagation in solids defined by implicit surfaces is presented. The method employs structured grids of spectral elements in combination with a fictitious domain approach to represent complex geometrical features through signed distance functions. A novel approach, based on moment fitting, is introduced to restore the diagonal mass matrix property in elements intersected by interfaces, thus enabling the use of explicit time integrators. Since this approach can lead to significantly decreased critical time steps for intersected elements, a “leap-frog” algorithm is employed to locally comply with this condition, thus introducing only a small computational overhead. The resulting method is tested through a series of numerical examples of increasing complexity, where it is shown that it offers increased accuracy compared to other similar approaches. Due to these improvements, components of interest for structural health monitoring-related tasks can be effectively discretized, while maintaining a performance comparable or only slightly worse than the standard spectral element method.

在这项工作中，提出了一种模拟由隐式表面定义的固体中导波传播的方法。该方法采用光谱元素的结构化网格与虚拟域方法相结合，通过有符号距离函数表示复杂的几何特征。引入了一种基于矩拟合的新方法来恢复与界面相交的元素中的对角质量矩阵属性，从而能够使用显式时间积分器。由于这种方法可以显着减少相交元素的关键时间步长，因此采用“跨越式”算法来局部遵守该条件，从而仅引入少量计算开销。由此产生的方法通过一系列复杂度增加的数值示例进行测试，结果表明，与其他类似方法相比，它提供了更高的准确性。由于这些改进，结构健康监测相关任务的相关组件可以有效地离散化，同时保持与标准谱元方法相当或仅略差的性能。