相关论文: Crank-Nicolson-type iterative decoupled algorithms…

We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand it…

This paper proposes and analyzes a fully discrete scheme that discretizes space with an ultra-weak local discontinuous Galerkin scheme and time with the Crank--Nicolson method for the nonlinear biharmonic Schr\"odinger equation. We first…

We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs…

Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…

We propose a general strategy to discretize the Dyson series without applying direct numerical quadrature to high-dimensional integrals, and extend this framework to open quantum systems. The resulting discretization can also be interpreted…

The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix are presented. This method has the same complexity as…

Noise and decoherence are ubiquitous in the dynamics of quantum systems coupled to an external environment. In the regime where environmental correlations decay rapidly, the evolution of a subsytem is well described by a Lindblad quantum…

We consider the Cauchy problem for the 1D generalized Schr\"odinger equation on the whole axis. To solve it, any order finite element in space and the Crank-Nicolson in time method with the discrete transparent boundary conditions (TBCs)…

We present an efficient, accurate, and robust method for simulation of dense suspensions of deformable and rigid particles immersed in Stokesian fluid in two dimensions. We use a well-established boundary integral formulation for the…

In this dissertation, we investigate the issue of robust localization in swarms of heterogeneous mobile agents with multiple and time-varying sensing modalities. Our focus is the development of filter-based and decoupled estimators under…

We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or…

In this paper we design an iterative domain decomposition method for free boundary problems with nonlinear flux jump condition. Our approach is related to damped Newton's methods. The proposed scheme requires, in each iteration, the…

We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric…

Many scientific and engineering problems require to perform Bayesian inferences for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement,…

We propose a dictionary-matching-free pipeline for multi-parametric quantitative MRI image computing. Our approach has two stages based on compressed sensing reconstruction and deep learned quantitative inference. The reconstruction phase…

A novel distributed algorithm is proposed for finite-time converging to a feasible consensus solution satisfying global optimality to a certain accuracy of the distributed robust convex optimization problem (DRCO) subject to bounded…

This paper is concerned with the numerical integration in time of nonlinear Schr\"odinger equations using different methods preserving the energy or a discrete analog of it. The Crank-Nicolson method is a well known method of order 2 but is…

The main purpose of this paper is to present a new corrected decoupled scheme combined with a spatial finite volume method for chemotaxis models. First, we derive the scheme for a parabolic-elliptic chemotaxis model arising in embryology.…

TriCG is a short-recurrence iterative method recently introduced by Montoison and Orban [SIAM J. Sci. Comput., 43 (2021), pp. A2502--A2525] for solving symmetric quasi-definite (SQD) linear systems. TriCG takes advantage of the inherent…

This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward…