Related papers: Overlapping Domain Decomposition Methods for Linea…
This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…
The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
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 review some important ideas in the design and analysis of robust overlapping domain decomposition algorithms for high-contrast multiscale problems and propose a domain decomposition method better performance in terms of the number of…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…
We propose a primal-dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling…
We introduce a new overlapping Domain Decomposition Method (DDM) to solve the fully nonlinear Monge-Amp\`ere equation. While DDMs have been extensively studied for linear problems, their application to fully nonlinear partial differential…
A local approach to the time integration of PDEs by exponential methods is proposed, motivated by theoretical estimates by A.Iserles on the decay of off-diagonal terms in the exponentials of sparse matrices. An overlapping domain…
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…
In this paper, we aim to solve the system of equations governing linear elasticity in parallel using domain decomposition. Through a non-overlapping decomposition of the domain, our approach aims to target the resulting interface problem,…
We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms 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…
A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and…
With recent advancements in computer hardware and software platforms, there has been a surge of interest in solving partial differential equations with deep learning-based methods, and the integration with domain decomposition strategies…
A parallelizable iterative procedure based on domain decomposition is presented and analyzed for weak Galerkin finite element methods for second order elliptic equations. The convergence analysis is established for the decomposition of the…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
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…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…
In this paper, we propose and analyze an additive domain decomposition method (DDM) for solving the high-frequency Helmholtz equation with the Sommerfeld radiation condition. In the proposed method, the computational domain is partitioned…
Parabolic equations on evolving domains model a multitude of applications including various industrial processes such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations…