Related papers: Substructured formulations of nonlinear structure …
We analyse a class of nonoverlapping domain decomposition preconditioners for nonsymmetric linear systems arising from discontinuous Galerkin finite element approximation of fully nonlinear Hamilton--Jacobi--Bellman (HJB) partial…
In the paper, a variant of the \ssstar Newton method is developed for the numerical solution of generalized equations, in which the multi-valued part is a so-called SCD (subspace containing derivative) mapping. Under a rather mild…
Inspired by rational canonical forms, we introduce and analyze two decompositions of dynamic programming (DP) problems for systems with linear dynamics. Specifically, we consider both finite and infinite horizon DP problems in which the…
A Koopman decomposition is a powerful method of analysis for fluid flows leading to an apparently linear description of nonlinear dynamics in which the flow is expressed as a superposition of fixed spatial structures with exponential time…
Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…
We study a quadratic nonlocal variational problem on a hybrid domain formed by a compact interval and finitely many discrete points. The associated energy splits into continuous, discrete, and interface contributions. Our main estimate…
The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g. in soil layers in contact with the atmosphere)…
We propose V--cycle multigrid methods for vector field problems arising from the lowest order hexahedral N\'{e}d\'{e}lec finite element. Since the conventional scalar smoothing techniques do not work well for the problems, a new type of…
We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the…
In this paper we prove existence and uniqueness of viscosity solutions of elliptic systems associated to fully nonlinear operators for minimization problems that involve interconnected obstacles. This system appears, among other, in the…
We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides…
The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…
In this work, a combined strategy of domain decomposition and the direct-line method is implemented to solve the forward and inverse linear elasticity problems of composite materials in general domains with multiple singularities. Domain…
We present an adaptive space-time mesh refinement approach based a domain decomposition approach (Singh and Wheeler, 2018) that allows different time-step sizes and mesh refinements in different subdomains. Our numerical experiments…
The study deals with the parallelization of finite element based Navier-Stokes codes using domain decomposition and state-ofart sparse direct solvers. There has been significant improvement in the performance of sparse direct solvers.…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely…
In this paper we consider optimal control of nonlinear time-dependent fluid structure interactions. To determine a time-dependent control variable a BFGS algorithm is used, whereby gradient information is computed via a dual problem. To…
In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global…
In this paper, we propose a novel overlapping domain decomposition method that can be applied to various problems in variational imaging such as total variation minimization. Most of recent domain decomposition methods for total variation…