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Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
This paper devises a novel lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick is to view a generic polygon $K$ as a new one…
A new algorithm is introduced to integrate the equations of rotational motion. The algorithm is derived within a leapfrog framework and the quantities involved into the integration are mid-step angular momenta and on-step orientational…
In this paper, the convergence of an algorithm for recovering the unknown kinematic viscosity of a two-dimensional incompressible, viscous fluid is studied. The algorithm of interest is a recursive feedback control-based algorithm that…
This article describes two independent developments aimed at improving the Particle Tracking Method for measurements of flow or particle velocities. First, a stereoscopic multicamera calibration method that does not require any optical…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…
We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to devise an inversion procedure which has the…
In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…
We point out that two of Milne's fourth-order integrators are well-suited to bit-reversible simulations. The fourth-order method improves on the accuracy of Levesque and Verlet's algorithm and simplifies the definition of the velocity $v$…
The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A recent development in computational fluid dynamics is to modify the linear transport equation…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
This paper introduces a novel model-free approach to synthesize virtual sensors for the estimation of dynamical quantities that are unmeasurable at runtime but are available for design purposes on test benches. After collecting a dataset of…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
In this paper, we discuss a novel higher-order stabilization-free virtual element method for general second-order elliptic eigenvalue problems. Optimal a priori error estimates are derived for both the approximate eigenspace and…
We describe and summarize a class of minimal numerical models emerged from recent development of simulation methods for dense particle suspensions in overdamped linear flows. The main ingredients include (i) a frame-invariant, short-range…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
In recent years, algorithms aiming at learning models from available data have become quite popular due to two factors: 1) the significant developments in Artificial Intelligence techniques and 2) the availability of large amounts of data.…