Related papers: An overlapping domain decomposition method for par…
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…
The flux-mortar mixed finite element method was recently developed for a general class of domain decomposition saddle point problems on non-matching grids. In this work we develop the method for Darcy flow using the multipoint flux…
In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…
Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
Using Domain Decomposition (DD) algorithm on non--overlapping domains, we compare couplings of different discretisation models, such as Finite Element (FEM) and Reduced Order (ROM) models for separate subcomponents. In particular, we…
In this paper a discretization based on discontinuous Galerkin (DG) method for an elliptic two-dimensional problem with discontinuous coefficients is considered. The problem is posed on a polygonal region $\Omega$ which is a union of $N$…
In this paper, based on the overlapping domain decomposition method (DDM) proposed in \cite{Leng2015}, an one step preconditioner is proposed to solve 2D high frequency Helmholtz equation. The computation domain is decomposed in both $x$…
We propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to treat more complex parametrized domains in an efficient and straightforward way. The impact of…
Fast and reliable surrogate models are critical for optimization, control and uncertainty analysis in geological carbon-storage projects, yet high-fidelity multiphase simulators remain too expensive. Dynamic Mode Decomposition (DMD) offers…
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…
The FETI-DP algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp.~1235--1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp.~128--149] for solving incompressible Stokes equations, are extended to…
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…
We deal with the numerical solution of the time-dependent partial differential equations using the adaptive space-time discontinuous Galerkin (DG) method. The discretization leads to a nonlinear algebraic system at each time level, the size…
We introduce an embedded-hybridized discontinuous Galerkin (EDG-HDG) method for the coupled Stokes-Darcy system. This EDG-HDG method is a pointwise mass-conserving discretization resulting in a divergence-conforming velocity field on the…
Work presented in this paper describes a general algorithm and its finite element implementation for performing concurrent multiple sub-domain simulations in linear structural dynamics. Using this approach one can solve problems in which…
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…
A priori analysis for a generalized local projection stabilized conforming finite element approximation of Darcy flow and Stokes problems is presented in this paper. A first-order conforming P1 finite element space is used to approximate…
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…