Related papers: Comparison of substructured non-overlapping domain…
Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Yet the optimal construction of these methods requires tedious analysis and is often available only in…
The discretization of surface intrinsic PDEs has challenges that one might not face in the flat space. The closest point method (CPM) is an embedding method that represents surfaces using a function that maps points in the flat space to…
We propose a simple domain decomposition method for $d$-dimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse problem. It relies on a space-filling curve to create equally…
Two-level domain decomposition (DD) methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level…
The use of deep learning methods for solving PDEs is a field in full expansion. In particular, Physical Informed Neural Networks, that implement a sampling of the physical domain and use a loss function that penalizes the violation of the…
Sparse direct linear solvers are at the computational core of domain decomposition preconditioners and therefore have a strong impact on their performance. In this paper, we consider the Fast and Robust Overlapping Schwarz (FROSch) solver…
This paper addresses the construction and analysis of a class of domain decomposition methods for the iterative solution of the quasi-static Biot problem in three-field formulation. The considered discrete model arises from time…
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann algorithm, formulated specially for multiple subdomains splitting for general parabolic and hyperbolic problems. This method is based on a non-overlapping spatial domain…
We present and analyze a non-conforming domain decomposition approximation for a hypersingular operator governed by the Helmholtz equation in three dimensions. This operator appears when considering the corresponding Neumann problem in…
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…
We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary…
In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and…
The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…
Solving time-harmonic wave propagation problems in the frequency domain within heterogeneous media poses significant mathematical and computational challenges, particularly in the high-frequency regime. Among the available numerical…
The development of deep neural networks is witnessing fast growth in network size, which requires novel hardware computing platforms with large bandwidth and low energy consumption. Optical computing has been a potential candidate for…
This paper is concerned with the numerical solution of compressible fluid flow in a fractured porous medium. The fracture represents a fast pathway (i.e., with high permeability) and is modeled as a hypersurface embedded in the porous…
Unfitted finite element methods, e.g., extended finite element techniques or the so-called finite cell method, have a great potential for large scale simulations, since they avoid the generation of body-fitted meshes and the use of graph…
In this work, we consider compressible single-phase flow problems in a porous media containing a fracture. In the latter, a non-linear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we…
This paper presents a strategy for a posteriori error estimation for substructured problems solved by non-overlapping domain decomposition methods. We focus on global estimates of the discretization error obtained through the error in…
This paper considers an optimization problem that components of the objective function are available at different nodes of a network and nodes are allowed to only exchange information with their neighbors. The decentralized alternating…