Related papers: Fast integrators for dynamical systems with severa…
We develop algorithms built around properties of the transfer operator and Koopman operator which 1) test for possible multiscale dynamics in a given dynamical system, 2) estimate the magnitude of the time-scale separation, and finally 3)…
We present {\sc Venice}, an operator splitting algorithm to integrate a numerical model on a hierarchy of timescales. {\sc Venice} allows a wide variety of different physical processes operating a different scales to be coupled on…
Force-gradient decomposition methods are used to improve the energy preservation of symplectic schemes applied to Hamiltonian systems. If the potential is composed of different parts with strongly varying dynamics, this multirate potential…
The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…
In some recent works [G. Dimarco, L. Pareschi, Hybrid multiscale methods I. Hyperbolic Relaxation Problems, Comm. Math. Sci., 1, (2006), pp. 155-177], [G. Dimarco, L. Pareschi, Hybrid multiscale methods II. Kinetic equations, SIAM…
This paper discusses the multiscale approach and the convergence of the time-dependent Maxwell-Schr\"{o}dinger system with rapidly oscillating discontinuous coefficients arising from the modeling of a heterogeneous nanostructure with a…
In this work, we apply the finite element heterogeneous multiscale method to a class of dispersive first-order time-dependent Maxwell systems. For this purpose, we use an analytic homogenization result, which shows that the effective system…
We present a new class of integrators for stiff PDEs. These integrators are generalizations of FLow AVeraging integratORS (FLAVORS) for stiff ODEs and SDEs introduced in [Tao, Owhadi and Marsden 2010] with the following properties: (i)…
We propose a fast bivariate smoothing approach for symmetric surfaces that has a wide range of applications. We show how it can be applied to estimate the covariance function in longitudinal data as well as multiple additive covariances in…
We consider a numerical scheme for Hamilton-Jacobi equations based on a direct discretization of the Lax-Oleinik semi-group. We prove that this method is convergent with respect to the time and space stepsizes provided the solution is…
This paper investigates a time-stepping procedure of the Newmark type for dynamic analyses of viscoelastic structures characterized by a generalized Maxwell model. We depart from a scheme developed for a three-parameter model by Hatada et…
In this paper we apply implicit two-derivative multistage time integrators to viscous conservation laws in one and two dimensions. The one dimensional solver discretizes space with the classical discontinuous Galerkin (DG) method, and the…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
We construct an efficient integrator for stochastic differential systems driven by Levy processes. An efficient integrator is a strong approximation that is more accurate than the corresponding stochastic Taylor approximation, to all orders…
We propose two new classes of time integrators for stiff DEs: the implicit-explicit exponential (IMEXP) and the hybrid exponential methods. In contrast to the existing exponential schemes, the new methods offer significant computational…
It was recently demonstrated that a simple Monte Carlo (MC) algorithm involving the swap of particle pairs dramatically accelerates the equilibrium sampling of simulated supercooled liquids. We propose two numerical schemes integrating the…
We present VegasFlow, a new software for fast evaluation of high dimensional integrals based on Monte Carlo integration techniques designed for platforms with hardware accelerators. The growing complexity of calculations and simulations in…
Many recently introduced enhanced sampling techniques are based on biasing coarse descriptors (collective variables) of a molecular system on the fly. Sometimes the calculation of such collective variables is expensive and becomes a…
The stationarity is assumed in vanilla Hawkes process, which reduces the model complexity but introduces a strong assumption. In this paper, we propose a fast multi-resolution segmentation algorithm to capture the time-varying…
High order methods have shown great potential to overcome performance issues of simulations of partial differential equations (PDEs) on modern hardware, still many users stick to low-order, matrix-based simulations, in particular in porous…