210 citations · 533 across the 14 of their papers we have counts for
7 papers · 1 filter
Gradient-based Monte Carlo methods for relaxation approximations of hyperbolic conservation laws
Giulia Bertaglia, Lorenzo Pareschi, Russel E. Caflisch
Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes, inspired by vortex methods for the N…
Adjoint DSMC for Nonlinear Spatially-Homogeneous Boltzmann Equation With a General Collision Model
Yunan Yang, Denis Silantyev, Russel Caflisch
We derive an adjoint method for the Direct Simulation Monte Carlo (DSMC) method for the spatially homogeneous Boltzmann equation with a general collision law. This generalizes our…
Adjoint DSMC for nonlinear Boltzmann equation constrained optimization
Russel Caflisch, Denis Silantyev, Yunan Yang
Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the…
Projection to the Set of Shift Orthogonal Functions
Farzin Barekat, Rongjie Lai, Ke Yin +3
This paper presents a fast algorithm for projecting a given function to the set of shift orthogonal functions (i.e. set containing functions with unit norm that are orthogona…
Simulation with Fluctuating and Singular Rates
Farzin Barekat, Russel Caflisch
In this paper we present a method to generate independent samples for a general random variable, either continuous or discrete. The algorithm is an extension of the acceptance-reje…
Compressed Modes for Variational Problems in Mathematics and Physics
Vidvuds Ozoliņš, Rongjie Lai, Russel Caflisch +1
This paper describes a general formalism for obtaining localized solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems.…
Sparse Dynamics for Partial Differential Equations
Hayden Schaeffer, Stanley Osher, Russel Caflisch +1
We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at ever…