Related papers: Weak Scalability of time parallel Schwarz methods …
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…
Optimization with time-dependent partial differential equations (PDEs) as constraints {appears} in many science and engineering applications. The associated first-order necessary optimality system consists of one forward and one backward…
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…
In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a…
Time-harmonic wave propagation problems, especially those governed by Maxwell's equations, pose significant computational challenges due to the non-self-adjoint nature of the operators and the large, non-Hermitian linear systems resulting…
In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization,…
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 this work we study the convergence properties of the one-level parallel Schwarz method with Robin transmission conditions applied to the one-dimensional and two-dimensional Helmholtz and Maxwell's equations. One-level methods are not…
We present new Neumann-Neumann algorithms based on a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, the Lagrange multiplier approach provides a coupled…
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…
This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular.…
The Helmholtz equation is notoriously difficult to solve with standard numerical methods, increasingly so, in fact, at higher frequencies. Controllability methods instead transform the problem back to the time-domain, where they seek 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…
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 article, we analyse the convergence behaviour and scalability properties of the one-level Parallel Schwarz method (PSM) for domain decomposition problems in which the boundaries of many subdomains lie in the interior of the global…
In this paper we analyze the Schwarz alternating method for unconstrained elliptic optimal control problems. We discuss the convergence properties of the method in the continuous case first and then apply the arguments to the finite…
This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…
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…