#### Filter Results:

- Full text PDF available (44)

#### Publication Year

1999

2016

- This year (0)
- Last 5 years (17)
- Last 10 years (37)

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

- TRIANGULAR MESHES, JIANLIANG QIAN, YONG-TAO ZHANG, HONG-KAI ZHAO
- 2007

The original fast sweeping method, which is an efficient iterative method for stationary Hamilton–Jacobi equations, relies on natural ordering provided by a rectangular mesh. We propose novel ordering strategies so that the fast sweeping method can be extended efficiently and easily to any unstructured mesh. To that end we introduce multiple reference… (More)

We design an Eulerian Gaussian beam summation method for solving Helmholtz equations in the high-frequency regime. The traditional Gaussian beam summation method is based on Lagrangian ray tracing and local ray-centered coordinates. We propose a new Eulerian formulation of Gaussian beam theory which adopts global Cartesian coordinates, level sets, and… (More)

- Yong-Tao Zhang, Hongkai Zhao, Jianliang Qian
- J. Sci. Comput.
- 2006

We construct high order fast sweeping numerical methods for computing viscosity solutions of static Hamilton-Jacobi equations on rectangular grids. These methods combine high order weighted essentially non-oscillatory (WENO) approximation to derivatives, monotone numerical Hamiltonians and Gauss Seidel iterations with alternating-direction sweepings. Based… (More)

- Shingyu Leung, Jianliang Qian
- J. Comput. Physics
- 2009

We propose Gaussian-beam based Eulerian methods to compute semi-classical solutions of the Schrödinger equation. Traditional Gaussian beam type methods for the Schrödinger equation are based on the Lagrangian ray tracing. We develop a new Eulerian framework which uses global Cartesian coordinates, level-set based implicit representation and Liouville… (More)

The geometric optics approximation to high frequency anisotropic wave propagation reduces the anisotropic wave equation to a static Hamilton–Jacobi equation. This equation is known as the anisotropic eikonal equation and has three different coupled wave modes as solutions. We introduce here a level set-based Eulerian approach that captures all three of… (More)

- Jianliang Qian, Yong-Tao Zhang, Hongkai Zhao
- SIAM J. Numerical Analysis
- 2007

The original fast sweeping method, which is an efficient iterative method for stationary Hamilton-Jacobi equations, relies on natural ordering provided by a rectangular mesh. We propose novel ordering strategies so that the fast sweeping method can be extended efficiently and easily to any unstructured mesh. To that end we introduce multiple reference… (More)

- Jianliang Qian, Plamen Stefanov, Gunther Uhlmann, Hongkai Zhao
- SIAM J. Imaging Sciences
- 2011

We present an efficient algorithm for reconstructing an unknown source in Thermoacoustic and Photoacoustic Tomography based on the recent advances in understanding the theoretical nature of the problem. We work with variable sound speeds that might be also discontinuous across some surface. The latter problem arises in brain imaging. The algorithmic… (More)

- Songting Luo, Jianliang Qian
- J. Comput. Physics
- 2011

In the high frequency regime, the geometrical-optics approximation for the Helmholtz equation with a point source results in an eikonal equation for traveltime and a transport equation for amplitude. Because the point-source traveltime field has an upwind singularity at the source point, all formally high-order finite-difference eikonal solvers exhibit… (More)

- Songting Luo, Jianliang Qian
- J. Sci. Comput.
- 2012

The viscosity solution of static Hamilton-Jacobi equations with a point-source condition has an upwind singularity at the source, which makes all formally high-order finite-difference scheme exhibit first-order convergence and relatively large errors. To obtain designed high-order accuracy, one needs to treat this source singularity during computation. In… (More)

- Songting Luo, Jianliang Qian, Robert Burridge
- SIAM J. Numerical Analysis
- 2014

The solution for the eikonal equation with a point-source condition has an upwind singularity at the source point as the eikonal solution behaves like a distance function at and near the source. As such, the eikonal function is not differentiable at the source so that all formally high-order numerical schemes for the eikonal equation yield first-order… (More)