Thermoacoustic tomography forward modeling with the spectral element method

A thermoacoustic tomography (TAT) forward solver based on the spectral element method (SEM) with perfectly matched layer absorbing boundary condition has been developed. The TAT forward solver is intended to model acoustically inhomogeneous media with high accuracy in the frequency domain. The high-order basis functions used in the SEM are Gauss-Lobatto-Legendre (GLL) polynomials. Due to the orthogonality of the GLL basis functions and GLL quadrature integration, the mass matrix is diagonal and the stiffness matrix is sparse. Thus, the proposed method greatly reduces the memory requirement and computational time in comparison with the conventional finite element method (FEM). Numerical results show that the high-order SEM is able to achieve the same accuracy as the FEM but with a much smaller number of unknowns. Therefore, the TAT forward solver based on SEM is able to simulate a large-scale and realistic TAT problem.