Thermoacoustic tomography forward modeling with the spectral element method.

Area of Science:

• Computational physics
• Medical imaging
• Acoustics

Background:

• Thermoacoustic tomography (TAT) requires accurate forward modeling for image reconstruction.
• Conventional methods like the finite element method (FEM) can be computationally intensive for large-scale problems.

Purpose of the Study:

• To develop a highly accurate and computationally efficient forward solver for thermoacoustic tomography.
• To model acoustically inhomogeneous media in the frequency domain using the spectral element method (SEM).

Main Methods:

• Implementation of a spectral element method (SEM) forward solver.
• Utilized Gauss-Lobatto-Legendre (GLL) polynomials as high-order basis functions.
• Incorporated a perfectly matched layer (PML) absorbing boundary condition for accurate wave propagation modeling.

Main Results:

• The SEM approach resulted in a diagonal mass matrix and a sparse stiffness matrix due to GLL properties.
• Achieved high accuracy comparable to FEM but with significantly fewer unknowns.
• Demonstrated substantial reductions in memory requirements and computational time compared to FEM.

Conclusions:

• The developed SEM-based TAT forward solver offers a computationally efficient and accurate solution for modeling complex acoustic media.
• This method enables the simulation of large-scale and realistic thermoacoustic tomography problems.