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The quasistatic normal-compliance contact problem of isotropic homogeneous linear visco-elastic bodies with Coulomb friction at small strains in Kelvin-Voigt rheology is considered. The discretization is made by a semi-implicit formula in…
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the…
This paper presents and proves an equation for the time horizon of symmetric trajectories with zero boundary conditions and bounded derivatives of arbitrary order. This equation holds regardless of the number of phases comprising the…
Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…
The Stochastic Green Function (SGF) algorithm is able to simulate any Hamiltonian that does not suffer from the so-called "sign problem". We propose a new global space-time update scheme for the SGF algorithm which, in addition to being…
We review some recent progress on the research of the periodic orbits of the N-body problem,and propose a numerical scheme to determine the spatial doubly-symmetric periodic orbits (SDSPs for short). Both comet- and lunar-type SDSPs in the…
The 3-level leapfrog time integration algorithm is an attractive choice for numerical relativity simulations since it is time-symmetric and avoids non-physical damping. In Newtonian problems without velocity dependent forces, this method…
We design an accurate orbital integration scheme for the general N-body problem preserving all the conserved quantities but the angular momentum.This scheme is based on the chain concept (Mikkola & Aarseth 1993) and is regarded as an…
We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…
A recently proposed method for computer simulations in the isothermal-isobaric (NPT) ensemble, based on Langevin-type equations of motion for the particle coordinates and the ``piston'' degree of freedom, is re-derived by straightforward…
This paper proposes a control algorithm for stable implementation of asynchronous parallel quadratic programming (PQP) through dual decomposition technique. In general, distributed and parallel optimization requires synchronization of data…
Quantum spectroscopy with single two level systems has considerably improved our ability to detect weak signals. Recently it was realized that for classical signals, precision and resolution of quantum spectroscopy is limited mainly by…
A systolic algorithm rhythmically computes and passes data through a network of processors. We investigate the performance of systolic algorithms for implementing the gravitational N-body problem on distributed-memory computers. Systolic…
This paper focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of $f$…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
This work is devoted to the numerical simulation of nonlinear Schr\"odinger and Klein-Gordon equations. We present a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency.…
We revisit second-order-in-time space-time discretizations of the linear and semilinear wave equations by establishing precise equivalences with first-order-in-time formulations. Focusing on schemes using continuous piecewise-polynomial…
The application of renormalization group methods to microscopic nuclear many-body calculations is discussed. We present the solution of the renormalization group equations in the particle-hole channels for neutron matter and the application…
A time-stepping scheme with adaptivity in both the step size and the integration order is presented in the context of non-equilibrium dynamics described via Kadanoff-Baym equations. The accuracy and effectiveness of the algorithm are…