210 citations · 533 across the 14 of their papers we have counts for
15 papers
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…
Complex singularities and PDEs
R. E. Caflisch, F. Gargano, M. Sammartino +1
In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tr…
Compressed Wannier modes found from an regularized energy functional
Farzin Barekat, Ke Yin, Russel E. Caflisch +3
We propose a method for calculating Wannier functions of periodic solids directly from a modified variational principle for the energy, subject to the requirement that the Wannier…
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…
PDEs with Compressed Solutions
Russel E. Caflisch, Stanley J. Osher, Hayden Schaeffer +1
Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted t…
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…
Multilevel Monte Carlo simulation of Coulomb collisions
M. S. Rosin, L. F. Ricketson, A. M. Dimits +2
We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the f…
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.…
An entropy based thermalization scheme for hybrid simulations of Coulomb collisions
L. F. Ricketson, M. S. Rosin, R. E. Caflisch +1
We formulate and test a hybrid fluid-Monte Carlo scheme for the treatment of elastic collisions in gases and plasmas. While our primary focus and demonstrations of applicability ar…
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…
Direct simulation Monte Carlo schemes for Coulomb interactions in plasmas
Giacomo Dimarco, Russell Caflisch, Lorenzo Pareschi
We consider the development of Monte Carlo schemes for molecules with Coulomb interactions. We generalize the classic algorithms of Bird and Nanbu-Babovsky for rarefied gas dynamic…
Anisotropic step stiffness from a kinetic model of epitaxial growth
Dionisios Margetis, Russel E. Caflisch
Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs-Thomson type formula and the associated step stiffness as a function of the ste…
Level Set Approach to Reversible Epitaxial Growth
M. Petersen, C. Ratsch, R. E. Caflisch +1
We generalize the level set approach to model epitaxial growth to include thermal detachment of atoms from island edges. This means that islands do not always grow and island disso…