Related papers: Two-component domain decomposition scheme with ove…
In this paper we show a simplified optimisation approach for free boundary problems in arbitrary space dimensions. This approach is mainly based on an extended operator splitting which allows a decoupling of the domain deformation and…
A theorem that constructs a path integral solution for general second order partial differential equations is specialized to obtain path integrals that are solutions of elliptic, parabolic, and hyperbolic linear second order partial…
We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub…
This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate…
In a recent paper [{\em F. Bernal, J. Mor\'on-Vidal and J.A. Acebr\'on, Comp.$\&$ Math. App. 146:294-308 (2023)}] an hybrid supercomputing algorithm for elliptic equations has been put forward. The idea is that the interfacial nodal…
A mathematical programming problem with affine equilibrium constraints (AMPEC) is a bilevel programming problem where the lower one is a parametric affine variational inequality. We formulate some classes of bilevel programming in forms of…
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…
We present a domain decomposition approach for the simulation of charge transport in heterojunction semiconductors. The problem is characterized by a large variation of primary variables across an interface region of a size much smaller…
We present a domain decomposition method (DDM) devoted to the iterative solution of time-harmonic electromagnetic scattering problems, involving large and resonant cavities. This DDM uses the electric field integral equation (EFIE) for the…
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
A novel overlapping domain decomposition splitting algorithm based on a Crank-Nisolson method is developed for the stochastic nonlinear Schroedinger equation driven by a multiplicative noise with non-periodic boundary conditions. The…
Operators with fractional perturbations are crucial components for robust preconditioning of interface-coupled multiphysics systems. However, in case the perturbation is strong, standard approaches can fail to provide scalable approximation…
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…
In this work, we study time-splitting strategies for the numerical approximation of evolutionary reaction-diffusion problems. In particular, we formulate a family of domain decomposition splitting methods that overcomes some typical…
In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two…
An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…
In two-phase image segmentation, convex relaxation has allowed global minimisers to be computed for a variety of data fitting terms. Many efficient approaches exist to compute a solution quickly. However, we consider whether the nature of…
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…