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Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N~^), is independent of dimension, which shows Monte Carlo to be very robust but also slow. Thisâ€¦ (More)

- William J. Morokoff, Russel E. Caflisch
- SIAM J. Scientific Computing
- 1994

Quasi-random (also called low discrepancy) sequences are a deterministic alternative to random sequences for use in Monte Carlo methods, such as integration and particle simulations of transportâ€¦ (More)

The initial value problem for the linearized spatially-homogeneous equation has the form ~ + L f = 0 with f({, t = 0) given. Boltzmann The linear operator L operates only on the ~ variable and isâ€¦ (More)

- Russel E. Caflisch, SHI JIN
- 1997

We develop high-resolution shock-capturing numerical schemes for hyperbolic systems with relaxation. In such systems the relaxation time may vary from order-1 to much less than unity. When theâ€¦ (More)

Shock waves in gas dynamics can be described by the Euler Nav ie r Stokes, or Boltzmann equations. We prove the existence of shock profile solutions of the Boltzmann equation for shocks which areâ€¦ (More)

For the Broadwell model of the nonlinear Boltzmann equation, there are shock profile solutions, i.e. smooth traveling waves that connect two equilibrium states. For weak shock waves, we proveâ€¦ (More)

- WILLIAM J. MOROKOFFt, Russel E. Caflisch

The convergence of the Monte Carlo method for numerical integration can often be improved by replacing random numbers with more uniformly distributed numbers known as quasi-random. In this paper theâ€¦ (More)

For the space homogeneous Boltzmann equation, we formulate a hybrid Monte Carlo method that is robust in the fluid dynamic limit. This method is based on an analytic representation of the solutionâ€¦ (More)

- Christian Ratsch, Mark F. Gyure, +5 authors Dimitri D. Vvedensky
- 2002

A level-set model for the simulation of epitaxial growth is described. In this model, the motion of island boundaries of discrete atomic layers is determined by the time evolution of a continuousâ€¦ (More)

- FrÃ©dÃ©ric Gibou, Ronald Fedkiw, Russel E. Caflisch, Stanley Osher
- J. Sci. Comput.
- 2003

In this paper, we present a level set approach for the modeling of dendritic solidification. These simulations exploit a recently developed second order accurate symmetric discretization of theâ€¦ (More)