Related papers: Efficient implementation of the hybridized Raviart…
For elliptic interface problems in two- and three-dimensions, this paper establishes a priori error estimates for Crouzeix-Raviart nonconforming, Raviart-Thomas mixed, and discontinuous Galerkin finite element approximations. These…
We propose a low-dimensional interface reduction method for elliptic interface problems based on conservative flux reconstruction. The approach combines a fitted $P_1$ finite element discretization with a flux recovery procedure following…
We present the hybridization of flux reconstruction methods for advection-diffusion problems. Hybridization introduces a new variable into the problem so that it can be reduced via static condensation. This allows the solution of implicit…
We consider approximations to the solutions of differential Riccati equations in the context of linear quadratic regulator problems, where the state equation is governed by a multiscale operator. Similarly to elliptic and parabolic…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…
Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices which are used to represent dense data in an optimized form by applying low-rank…
This work is on constrained large-scale non-convex optimization where the constraint set implies a manifold structure. Solving such problems is important in a multitude of fundamental machine learning tasks. Recent advances on Riemannian…
A new technique of residual-type a posteriori error analysis is developed for the lowest-order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed…
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…
This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…
This paper is concerned with the development and testing of advanced time-stepping methods suited for the integration of time-accurate, real-world applications of computational fluid dynamics (CFD). The performance of several time…
In this note, we propose a symplectic algorithm for the stable manifolds of the Hamilton-Jacobi equations combined with an iterative procedure in [Sakamoto-van~der Schaft, IEEE Transactions on Automatic Control, 2008]. Our algorithm…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve…
The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier-Stokes equations. We develop a separation of variables representation for this equation in polar…
In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first…
This paper introduces a novel data-driven convergence booster that not only accelerates convergence but also stabilizes solutions in cases where obtaining a steady-state solution is otherwise challenging. The method constructs a…
In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic…
We consider systems of nonlinear magnetostatics and quasistatics that typically arise in the modeling and simulation of electric machines. The nonlinear problems, eventually obtained after time discretization, are usually solved by…