Related papers: Efficient Time Domain Decomposition Algorithms for…
Parabolic optimal control problems arise in numerous scientific and engineering applications. They typically lead to large-scale coupled forward-backward systems that cannot be treated with classical time-stepping schemes and are…
The single-step one-shot method has proven to be very efficient for PDE-constrained optimization where the partial differential equation (PDE) is solved by an iterative fixed point solver. In this approach, the simulation and optimization…
We study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all…
We present here the classical Schwarz method with a time domain decomposition applied to unconstrained parabolic optimal control problems. Unlike Dirichlet-Neumann and Neumann-Neumann algorithms, we find different properties based on the…
This paper derives optimal coefficients for optimized Schwarz iterations for the time-dependent Stokes-Darcy problem using an innovative strategy to solve a nonstandard min-max problem. The coefficients take into account both physical and…
To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a…
Domain decomposition (DD) methods for solving time-dependent problems can be classified by (i) the method of domain decomposition used, (ii) the choice of decomposition operators (exchange of boundary conditions), and (iii) the splitting…
We present an overlapping Schwarz decomposition algorithm for constrained quadratic programs (QPs). Schwarz algorithms have been traditionally used to solve linear algebra systems arising from partial differential equations, but we have…
We propose a time domain decomposition approach to optimal control of partial differential equations (PDEs) based on semigroup theoretic methods. We formulate the optimality system consisting of two coupled forward-backward PDEs, the state…
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer…
Schwarz methods are attractive parallel solution techniques for solving large-scale linear systems obtained from discretizations of partial differential equations (PDEs). Due to the iterative nature of Schwarz methods, convergence rates are…
The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cell-centered finite differences. Two localized exponential time differencing methods are…
Schwarz methods use a decomposition of the computational domain into subdomains and need to put boundary conditions on the subdomain boundaries. In domain truncation one restricts the unbounded domain to a bounded computational domain and…
In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could…
We introduce a new domain decomposition strategy for time harmonic Maxwell's equations that is valid in the case of automatically generated subdomain partitions with possible presence of cross-points. The convergence of the algorithm is…
The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…
We present an optimize-then-discretize framework for solving linear-quadratic optimal control problems (OCP) governed by time-inhomogeneous ordinary differential equations (ODEs). Our method employs a modified overlapping Schwarz…
Convergence is proven for Schwarz-like methods applied to degenerate elliptic-parabolic equations with a $p$-structure. This family of PDEs, e.g., arises when modelling nonlinear diffusion processes. The Schwarz-like approximation methods…
In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…
We present new Dirichlet-Neumann and Neumann-Dirichlet algorithms with a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, we use the Lagrange multiplier approach to…