Related papers: Convergence of a Fast Explicit Operator Splitting …
We develop two variance-reduced fast operator splitting methods to approximate solutions of a class of generalized equations, covering fundamental problems such as \rvs{minimization}, minimax problems, and variational inequalities as…
In this paper, we propose a time-fractional molecular beam epitaxy (MBE) model with slope selection and its efficient, accurate, full discrete, linear numerical approximation. The numerical scheme utilizes the fast algorithm for the Caputo…
It is common in classical mechanics to encounter systems whose Hamiltonian $H$ is the sum of an often exactly integrable Hamiltonian $H_0$ and a small perturbation $\epsilon H_1$ with $\epsilon\ll1$. Such near-integrability can be exploited…
This work introduces and rigorously analyzes a novel operator-splitting finite element scheme for approximating viscosity solutions of a broad class of constrained second-order partial differential equations. By decoupling the primary PDE…
Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and prior terms. This global EPS approach shows better smoothing performance than a local one that typically has a form of weighted…
We develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for…
Operator splitting methods solve composite optimization problems by breaking them into smaller sub-problems that can be solved sequentially or in parallel. In this paper, we propose a unified framework for certifying both linear and…
Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…
The pencil-beam model is valid only when elementary Gaussian beams are small enough with respect to lateral heterogeneity of a medium, which is not always the case in heavy charged particle radiotherapy. This work addresses a solution for…
We propose and analyze a versatile and general algorithm called nonlinear forward-backward splitting (NOFOB). The algorithm consists of two steps; first an evaluation of a nonlinear forward-backward map followed by a relaxed projection onto…
Euler's elastica model has a wide range of applications in Image Processing and Computer Vision. However, the non-convexity, the non-smoothness and the nonlinearity of the associated energy functional make its minimization a challenging…
A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…
Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…
We present a detailed convergence analysis for an operator splitting scheme proposed in [C. Liu et al.,J. Comput. Phys., 436, 110253, 2021] for a reaction-diffusion system with detailed balance. The numerical scheme has been constructed…
Variational level set method has become a powerful tool in image segmentation due to its ability to handle complex topological changes and maintain continuity and smoothness in the process of evolution. However its evolution process can be…
The forward-backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward-backward envelope (FBE).…
Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for a rigid…
Quasiperiodic elliptic operators (QEOs) serve as fundamental models in both mathematics and physics, as exemplified by their role in the numerical modeling of one-dimensional photonic quasicrystals. However, distinct from periodic elliptic…
The analytic continuation of imaginary-time quantum Monte Carlo data to extract real-frequency spectra remains a key problem in connecting theory with experiment. Here we present a fast and efficient stochastic optimization method (FESOM)…