A k-space Green's function solution for acoustic initial value problems in homogeneous media with power law...

Area of Science:

• Acoustics
• Wave Propagation
• Computational Physics

Background:

• Acoustic initial value problems are crucial in various fields.
• Modeling power law absorption and dispersion in homogeneous media presents computational challenges.
• Existing methods often require time-stepping, leading to stability constraints and inefficiencies.

Purpose of the Study:

• To derive an efficient Green's function solution for acoustic initial value problems.
• To incorporate power law absorption and dispersion into the wave equation.
• To enable single-step computation of the pressure field without time-stepping.

Main Methods:

• Utilized the homogeneous wave equation with added terms for absorption and dispersion.
• Incorporated the fractional Laplacian to model power law effects.
• Employed Fourier transforms and an exact k-space time propagator for single-step calculation.
• Leveraged the fast Fourier transform for efficient computation on Cartesian grids.

Main Results:

• Developed a Green's function solution applicable to homogeneous media with power law absorption.
• The solution allows for direct calculation of the pressure field at any time t>0.
• Demonstrated efficient computation in one, two, or three dimensions without stability constraints.

Conclusions:

• The derived solution offers a computationally efficient alternative to time-stepping methods.
• This approach facilitates the accurate modeling of acoustic wave propagation with power law absorption and dispersion.
• The method is suitable for various dimensions and grid types, offering broad applicability.