Fourier transform-based methods enable accurate, dispersion-free simulations of time-domain scattering problems by evaluating solutions to the Helmholtz equation at a discrete set of frequencies sufficient to approximate the inverse Fourier transform. However, in the case of scattering by trapping obstacles, the Helmholtz solution exhibits nearly-real complex resonances -- which significantly slows the convergence of numerical inverse transform. To address this difficulty this paper introduces a frequency-domain singularity subtraction technique that regularizes the integrand of the inverse transform and efficiently computes the singularity contribution via a combination of a straightforward and inexpensive numerical technique together with a large-time asymptotic expansion. Crucially, all relevant complex resonances and their residues are determined via rational approximation of integral equation solutions at real frequencies. An adaptive algorithm is employed to ensure that all relevant complex resonances are properly identified.

翻译：基于傅里叶变换的方法通过在一组离散频率上求解亥姆霍兹方程，并以此近似逆傅里叶变换，实现了时域散射问题的高精度、无频散模拟。然而，在涉及俘获型障碍物的散射场景中，亥姆霍兹解会呈现近似实数的复共振现象——这显著降低了数值逆变换的收敛速度。为解决此难题，本文提出一种频域奇异性减法技术，通过对逆变换被积函数进行正则化处理，并结合一种简单廉价的数值方法与长时间渐近展开，高效计算奇异性贡献。关键之处在于，所有相关复共振及其留数均通过实频率下积分方程解的有理逼近确定。采用自适应算法确保所有相关复共振被准确识别。