Numerics of acoustical 2D tomography based on the conservation laws
Sergey Kabanikhin, Dmitriy Klyuchinskiy, Nikita S. Novikov, Maxim Shishlenin
Abstract
Abstract We investigate the mathematical modeling of the 2D acoustic waves propagation, based on the conservation laws. The hyperbolic first-order system of partial differential equations is considered and solved by the method of S. K. Godunov. The inverse problem of reconstructing the density and the speed of sound of the medium is considered. We apply the gradient method to reconstruct the parameters of the medium. The gradient of the functional is obtained. Numerical results are presented.
Topics & Concepts
Conservation lawInverse problemPartial differential equationHyperbolic partial differential equationAcousticsAcoustic theoryTomographyMathematical analysisMathematicsComputer sciencePhysicsApplied mathematicsOpticsNumerical methods in inverse problemsPhotoacoustic and Ultrasonic ImagingMicrowave Imaging and Scattering Analysis