Related papers: High-Order Implicit Low-Rank Method with Spectral …
We introduce novel dynamical low-rank methods for solving large-scale matrix differential equations, motivated by algorithms from randomized numerical linear algebra. In terms of performance (cost and accuracy), our methods overperform…
This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the…
We develop two new sets of stable, rank-adaptive Dynamically Orthogonal Runge-Kutta (DORK) schemes that capture the high-order curvature of the nonlinear low-rank manifold. The DORK schemes asymptotically approximate the truncated singular…
The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time variant of the well-known Differential Dynamic Programming (DDP) technique with a Gauss-Newton Hessian approximation. This family of methods has gained popularity in the…
Efficient time integration schemes are necessary to capture the complex processes involved in atmospheric flows over long periods of time. In this work, we propose a high-order, implicit-explicit numerical scheme that combines Multi-Level…
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…
The numerical method of dynamical low-rank approximation (DLRA) has recently been applied to various kinetic equations showing a significant reduction of the computational effort. In this paper, we apply this concept to the linear…
An implicit high-order discontinuous Galerkin (DG) method is developed to find steady-state solution of rarefied gas flow described by the Boltzmann equation with full collision operator. In the physical space, velocity distribution…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction…
Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…
We introduce a new class of arbitrary-order exponential time differencing methods based on spectral deferred correction (ETDSDC) and describe a simple procedure for initializing the requisite matrix functions. We compare the stability and…
Dynamical low-rank (DLR) approximation has gained interest in recent years as a viable solution to the curse of dimensionality in the numerical solution of kinetic equations including the Boltzmann and Vlasov equations. These methods…
We construct a high-order adaptive time stepping scheme for vesicle suspensions with viscosity contrast. The high-order accuracy is achieved using a spectral deferred correction (SDC) method, and adaptivity is achieved by estimating the…
This paper develops a high-order selective discontinuous Galerkin (SDG) method for solving elliptic interface problems on interface-unfitted Cartesian meshes. This method applies the discontinuous Galerkin (DG) formulation on interface…
This paper aims to present a local discontinuous Galerkin (LDG) method for solving backward stochastic partial differential equations (BSPDEs) with Neumann boundary conditions. We establish the $L^2$-stability and optimal error estimates of…
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…
Dynamical low-rank approximation (DLRA) is an emerging tool for reducing computational costs and provides memory savings when solving high-dimensional problems. In this work, we propose and analyze a semi-implicit dynamical low-rank…
In this study, we address the challenge of low-rank model compression in the context of in-memory computing (IMC) architectures. Traditional pruning approaches, while effective in model size reduction, necessitate additional peripheral…
We introduce a dynamical low-rank method to reduce the computational complexity for solving the multi-scale multi-dimensional linear transport equation. The method is based on a macro-micro decomposition of the equation. The proposed…