Related papers: Fast integrators for dynamical systems with severa…
We develop a multiscale hybrid scheme for simulations of soft condensed matter systems, which allows one to treat the system at the particle level in selected regions of space, and at the continuum level elsewhere. It is derived…
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
An energetically balanced, implicit integrator for non-hydrostatic vertical atmospheric dynamics on the sphere is presented. The integrator allows for the exact balance of energy exchanges in space and time for vertical atmospheric motions…
In this paper we present an extension of standard iterative splitting schemes to multiple splitting schemes for solving higher order differential equations. We are motivated by dynamical systems, which occur in dynamics of the electrons in…
A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions obtained from a basic…
In the framework of a Particle-In-Cell scheme for some 1D Vlasov-Poisson system depending on a small parameter, we propose a time-stepping method which is numerically uniformly accurate when the parameter goes to zero. Based on an…
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
Hamiltonian systems with multiple timescales arise in molecular dynamics, classical mechanics, and theoretical physics. Long-time numerical integration of such systems requires resolving fast dynamics with very small time steps, which…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…
This article illustrates the application of multiple scales analysis to two archetypal quasilinear systems; i.e. to systems involving fast dynamical modes, called fluctuations, that are not directly influenced by fluctuation--fluctuation…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
We present a new mixed variable symplectic (MVS) integrator for planetary systems, that fully resolve close encounters. The method is based on a time regularisation that allows keeping the stability properties of the symplectic integrators,…
We consider in this paper a challenging problem of simulating fluid flows, in complex multiscale media possessing multi-continuum background. As an effort to handle this obstacle, model reduction is employed. In \cite{rh2}, homogenization…
Scaling up hardware systems has become an important tactic for improving performance as Moore's law fades. Unfortunately, simulations of large hardware systems are often a design bottleneck due to slow throughput and long build times. In…
This paper proposes a hierarchical adaptive sampling scheme for passivity characterization of large-scale linear lumped macromodels. Here, large-scale is intended both in terms of dynamic order and especially number of input/output ports.…
We introduce and analyze a family of heterogeneous multiscale methods for the numerical integration of highly oscillatory systems of delay differential equations with constant delays. The methodology suggested provides algorithms of…
Phase-field simulations are a practical but also expensive tool to calculate microstructural evolution. This work aims to compare explicit time integrators for a broad class of phase-field models involving coupling between the phase-field…
We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These…