Related papers: Semi-implicit method of high-index saddle dynamics…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
The problem of computing saddle points is important in certain problems in numerical partial differential equations and computational chemistry, and is often solved numerically by a minimization problem over a set of mountain passes. We…
Quasi-linear hyperbolic systems with source terms introduce significant computational challenges due to the presence of a stiff source term. To address this, a finite volume Nessyahu-Tadmor (NT) central numerical scheme is explored and…
In this paper, we derive a randomized version of the Mirror-Prox method for solving some structured matrix saddle-point problems, such as the maximal eigenvalue minimization problem. Deterministic first-order schemes, such as Nesterov's…
Recently, saddle point problems have received much attention due to their powerful modeling capability for a lot of problems from diverse domains. Applications of these problems occur in many applied areas, such as robust optimization,…
Describing the complex landscape of infinite-dimensional free energy is generally a challenging problem. This difficulty arises from the existence of numerous minimizers and, consequently, a vast number of saddle points. These factors make…
We introduce a new family of high order accurate semi-implicit schemes for the solution of non-linear hyperbolic partial differential equations on unstructured polygonal meshes. The time discretization is based on a splitting between…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
We consider (stochastic) convex-concave saddle point (SP) problems with high-dimensional decision variables, arising in various applications including machine learning problems. To contend with the challenges in computing full gradients, we…
This study concerns numerical methods for efficiently solving the Richards equation where different weak formulations and computational techniques are analyzed. The spatial discretizations are based on standard or mixed finite element…
In this paper we propose a novel and general approach to design semi-implicit methods for the simulation of fluid-structure interaction problems in a fully Eulerian framework. In order to properly present the new method, we focus on the…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
In this work, we propose a novel framework for the numerical solution of time-dependent conservation laws with implicit schemes via primal-dual hybrid gradient methods. We solve an initial value problem (IVP) for the partial differential…
We present strongly convergent explicit and semi-implicit adaptive numerical schemes for systems of stiff stochastic differential equations (SDEs) where both the drift and diffusion are non-globally Lipschitz continuous. This stiffness may…
Active contour models have been widely used in image segmentation, and the level set method (LSM) is the most popular approach for solving the models, via implicitly representing the contour by a level set function. However, the LSM suffers…
In this paper, we provide some analysis on the asymptotic escape of strict saddles in manifold optimization using the projected gradient descent (PGD) algorithm. One of our main contributions is that we extend the current analysis to…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of…
We propose the nullspace-preserving high-index saddle dynamics (NPHiSD) method for degenerating multiple solution systems in constrained and unconstrained settings. The NPHiSD efficiently locates high-index saddle points and provides parent…
This paper focuses on the distributed optimization of stochastic saddle point problems. The first part of the paper is devoted to lower bounds for the centralized and decentralized distributed methods for smooth (strongly) convex-(strongly)…