Related papers: A posteriori error analysis for Schwarz overlappin…
To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network…
We propose two variants of the overlapping additive Schwarz method for the finite element discretiza- tion of the elliptic problem in 3D with highly heterogeneous coefficients. The methods are efficient and simple to construct using the…
In this paper, we propose an overlapping additive Schwarz method for total variation minimization based on a dual formulation. The $O(1/n)$-energy convergence of the proposed method is proven, where $n$ is the number of iterations. In…
This paper presents and evaluates a framework for the coupling of subdomain-local projection-based reduced order models (PROMs) using the Schwarz alternating method following a domain decomposition (DD) of the spatial domain on which a…
We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…
Domain decomposition (DD) methods are a natural way to take advantage of parallel computers when solving large scale linear systems. Their scalability depends on the design of the coarse space used in the two-level method. The analysis of…
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 consider a variational method to solve the optical flow problem with varying illumination. We apply an adaptive control of the regularization parameter which allows us to preserve the edges and fine features of the computed flow. To…
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 develop a domain decomposition method for the nonlinear Poisson-Boltzmann equation based on a solvent-excluded surface widely used in computational chemistry. The model relies on a nonlinear equation defined in…
We propose a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
A two-level overlapping Schwarz method is developed for second order elliptic problems with highly oscillatory and high contrast coefficients, for which it is known that the standard coarse problem fails to give a robust preconditioner. In…
We propose an efficient algorithm that combines overlapping domain decomposition and proper generalized decomposition (PGD) to construct surrogate models of linear elliptic parametric problems. The technique is composed of an offline and an…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
Adjoint variable method in combination with gradient descent optimization has been widely used for the inverse design of nanophotonic devices. In many of such optimizations, the design region is only a small fraction of the total…
We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…
Nonlinear Schwarz methods are a type of nonlinear domain decomposition method used as an alternative to Newton's method for solving discretized nonlinear partial differential equations. In this article, the first parallel implementation of…
This paper presents and evaluates an approach for coupling together subdomain-local reduced order models (ROMs) constructed via non-intrusive operator inference (OpInf) with each other and with subdomain-local full order models (FOMs),…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…