Related papers: Aitken-Schwarz heterogeneous Domain Decomposition …
We present non-overlapping Domain Decomposition Methods (DDM) based on quasi-optimal transmission operators for the solution of Helmholtz transmission problems with piece-wise constant material properties. The quasi-optimal transmission…
By utilizing the perfectly matched layer (PML) and source transfer techniques, the diagonal sweeping domain decomposition method (DDM) was recently developed for solving the high-frequency Helmholtz equation in $\mathbb{R}^n$, which uses…
The paper is concerned with the derivation and analysis of nonoverlapping domain decomposition for heterogeneous, anisotropic diffusion problems discretized by the finite element cell-centered (FECC) scheme. Differently from the standard…
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…
Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack…
We propose a novel hybrid domain decomposition method that couples sub-domain-local high-fidelity finite element (FE) models with reduced order models (ROMs) using the Schwarz alternating method. By integrating the noninstrusive Operator…
Domain decomposition methods are widely used to solve sparse linear systems from scientific problems, but they are not suited to solve sparse linear systems extracted from integrated circuits. The reason is that the sparse linear system of…
This paper proposes a new non-iterative time-domain simulation approach using Differential Transform Method (DTM) to solve the set of non-linear Differential-Algebraic Equations (DAEs) involved in a DFIG-based wind power system. The DTM is…
Schwarz methods use a decomposition of the computational domain into subdomains and need to put boundary conditions on the subdomain boundaries. In domain truncation one restricts the unbounded domain to a bounded computational domain and…
We study for the first time Schwarz domain decomposition methods for the solution of the Navier equations modeling the propagation of elastic waves. These equations in the time harmonic regime are difficult to solve by iterative methods,…
We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…
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…
The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require considerable computational and memory resources. The Random Batch…
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…
Nonequilibrium dynamics governed by electron-phonon (e-ph) interactions plays a key role in electronic devices and spectroscopies and is central to understanding electronic excitations in materials. The real-time Boltzmann transport…
A domain decomposition method is proposed based on carefully chosen impedance transmission operators for a hybrid formulation of the eddy current problem. Preliminary analysis and numerical results are provided in the spherical case showing…
This paper deals with the parallel simulation of delamination problems at the meso-scale by means of multi-scale methods, the aim being the Virtual Delamination Testing of Composite parts. In the non-linear context, Domain Decomposition…
Digital Twins (DTs) represent digital counterparts of physical systems, assets, or processes, referred to as the actual twin (AT). DTs integrate heterogeneous data, models, and semantic technologies to support monitoring, simulation,…
This paper is concerned with the optimized Schwarz waveform relaxation method and Ventcel transmission conditions for the linear advection-diffusion equation. A mixed formulation is considered in which the flux variable represents both…
Generative dynamic texture models (GDTMs) are widely used for dynamic texture (DT) segmentation in the video sequences. GDTMs represent DTs as a set of linear dynamical systems (LDSs). A major limitation of these models concerns the…