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- Yen-Hsi Richard Tsai, Li-Tien Cheng, Stanley Osher, Hongkai Zhao
- SIAM J. Numerical Analysis
- 2003

We derive a Godunov-type numerical flux for the class of strictly convex, homogeneous Hamiltonians that includes H(p, q) = âˆš ap2 + bq2 âˆ’ 2cpq, c < ab. We combine our Godunov numerical fluxes withâ€¦ (More)

- BjÃ¶rn Engquist, Yen-Hsi Richard Tsai
- Math. Comput.
- 2005

The heterogeneous multiscale methods (HMM) is a general framework for the numerical approximation of multiscale problems. It is here developed for ordinary differential equations containing differentâ€¦ (More)

- Gil Ariel, BjÃ¶rn Engquist, Yen-Hsi Richard Tsai
- Math. Comput.
- 2009

A multiscale method for computing the effective behavior of a class of stiff and highly oscillatory ordinary differential equations (ODEs) is presented. The oscillations may be in resonance with oneâ€¦ (More)

- Selim Esedoglu, Steven J. Ruuth, Yen-Hsi Richard Tsai
- J. Comput. Physics
- 2010

We describe a new class of algorithms for generating a variety of geometric interfacial motions by alternating two steps: Construction of the signed distance function (i.e. redistancing) to theâ€¦ (More)

- Yen-Hsi Richard Tsai, Yoshikazu Giga, Stanley Osher
- Math. Comput.
- 2003

We introduce two types of finite difference methods to compute the L-solution and the proper viscosity solution recently proposed by the second author for semi-discontinuous solutions to a class ofâ€¦ (More)

- Chiu-Yen Kao, Stanley Osher, Yen-Hsi Richard Tsai
- SIAM J. Numerical Analysis
- 2005

We propose a new sweeping algorithm which discretizes the Legendre transform of the numerical Hamiltonian using an explicit formula. This formula yields the numerical solution at a grid point usingâ€¦ (More)

We present two fast and simple algorithms for approximating the distance function for given isolated points on uniform grids. The algorithms are then generalized to compute the distance to piecewiseâ€¦ (More)

We develop a level set method for the computation of multivalued physical observables (density, velocity, etc.) for the semiclassical limit of the SchrÃ¶dinger equation in arbitrary number of spaceâ€¦ (More)

- Gil Ariel, BjÃ¶rn Engquist, Yen-Hsi Richard Tsai
- Multiscale Modeling & Simulation
- 2008

A multiscale method for computing the effective slow behavior of a system of weakly coupled general oscillators is presented. The oscillators may be either in the form of a periodic solution or aâ€¦ (More)