An explicit marching-on-in-time scheme for solving the time domain Kirchhoff integral equation.

Area of Science:

• Computational physics
• Acoustics
• Numerical analysis

Background:

• Transient acoustic scattering analysis is crucial for understanding wave interactions with objects.
• Existing methods for solving time-domain integral equations often require computationally expensive implicit schemes.
• Developing efficient explicit solvers is essential for advancing real-time acoustic simulations.

Purpose of the Study:

• To present a fully explicit marching-on-in-time (MOT) scheme for the time-domain Kirchhoff integral equation.
• To analyze transient acoustic scattering from rigid objects using this novel explicit MOT solver.
• To demonstrate the accuracy and efficiency of the proposed method compared to implicit counterparts.

Main Methods:

• Spatial discretization using a higher-order Nyström method.
• Time marching employing a PE(CE)m-type ordinary differential equation integrator.
• Implementation of a fully explicit marching-on-in-time (MOT) scheme.

Main Results:

• The explicit MOT scheme achieves the same time step size as implicit methods without compromising accuracy or stability.
• Numerical results confirm the accuracy of the proposed solver for transient acoustic scattering.
• The efficiency and applicability of the explicit MOT solver are demonstrated.

Conclusions:

• The presented explicit MOT scheme offers an accurate and efficient alternative for analyzing transient acoustic scattering.
• The method's ability to use the same time step as implicit schemes enhances its practical utility.
• This work contributes to the advancement of numerical methods in computational acoustics.