Showing papers by "Hongkai Zhao published in 2008"
TL;DR: A second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations, built on a DG method developed recently.
68 citations
01 Jul 2008
TL;DR: In this paper, a hybrid approach that combines both Lagrangian and Eulerian formulations was proposed to solve the resulting inverse problem, which can take into account multiple arrival times naturally.
Abstract: We adopt a recent work in Chung, Qian, Uhlmann and Zhao (Inverse Problems, 23(2007) 309-329) to develop a phase space method for reconstructing pressure wave speed and shear wave speed of an elastic medium from travel time measurements. The method is based on the so-called Stefanov-Uhlmann identity which links two Riemannian metrics with their travel time information. We design a numerical algorithm to solve the resulting inverse problem. The algorithm is a hybrid approach that combines both Lagrangian and Eulerian formulations. In particular the Lagrangian formulation in phase space can take into account multiple arrival times naturally, while the Eulerian formulation for wave speeds allows us to compute the solution in physical space. Numerical examples are shown to validate the method.
6 citations