The traditional Born series (TBS) and convergent Born series (CBS) methods to numerically solve the time-independent inhomogeneous photoacoustic (PA) wave equation are discussed. The performance of these algorithms is examined for a circular PA source (a disk of radius, $a = 5\,\,\unicode{x00B5}{\rm m}$) in two dimensions. The speed of sound within the source region was gradually decreased from ${v_s} = 1950$ to 1200 m/s, but the same quantity for the ambient medium was fixed to ${v_f} = 1500 \;{\rm m/s}$. The PA fields were calculated over a large frequency band from $f = 7.3$ to 2000 MHz. Accordingly, the wave number (${k_f} = 2\pi f/{v_f}$) varied from ${k_f} = 0.03$ to ${8.38}\;\unicode{x00B5}{{\rm m}^{- 1}}$. The TBS method does not offer converging solutions when ${k_f}a \ge 25$ for ${v_s} = 1950\; {\rm m/s}$ and ${k_f}a \ge 9$ for ${v_s} = 1200 \;{\rm m/s}$. These have been observed in both the near and far fields. However, the solutions for the CBS technique converge in all cases. Both methods facilitate accurate solutions if the computational domain contains a collection of monodisperse/polydisperse disks considered in this study. Our numerical results suggest that the CBS protocol can provide accurate solutions under various test conditions.

中文翻译：

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Born级数法求解与时间无关的非均匀光声波方程的数值解

讨论了传统的Born级数（TBS）和收敛性Born级数（CBS）方法，以数值方式求解与时间无关的非均匀光声（PA）波动方程。对于二维PA的圆形PA源（半径为$ a = 5 \，\，\ unicode {x00B5} {\ rm m} $的圆盘），检查了这些算法的性能。源区域内的声音速度从$ {v_s} = 1950 $逐渐降低到1200 m / s，但是对于环境介质，相同的量被固定为$ {v_f} = 1500 \; {\ rm m / s } $。在从$ f = 7.3 $到2000 MHz的较大频段上计算了PA字段。因此，波数（$ {k_f} = 2 \ pi f / {v_f} $）从$ {k_f} = 0.03 $到$ {8.38} \; \ unicode {x00B5} {{\ rm m} ^ {-1}} $。当$ {k_f} a \ ge 25 $ for $ {v_s} = 1950 \时，TBS方法不提供收敛解。{\ rm m / s} $和$ {k_f} a \ ge 9 $ for $ {v_s} = 1200 \; {\ rm m / s} $。这些都在近场和远场都被观察到。但是，CBS技术的解决方案在所有情况下都可以收敛。如果计算域包含本研究中考虑的单分散/多分散磁盘集合，则这两种方法都有助于精确求解。我们的数值结果表明，CBS协议可以在各种测试条件下提供准确的解决方案。