Related papers: Improved non-overlapping domain decomposition algo…
Convergence is proven for Schwarz-like methods applied to degenerate elliptic-parabolic equations with a $p$-structure. This family of PDEs, e.g., arises when modelling nonlinear diffusion processes. The Schwarz-like approximation methods…
We present new Dirichlet-Neumann and Neumann-Dirichlet algorithms with a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, we use the Lagrange multiplier approach to…
A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as…
Computing the electric eddy currents in non-linear materials, such as superconductors, is \E{not straightforward}. The design of superconducting magnets and power applications needs electromagnetic computer modeling, being in many cases a…
The classical EMD algorithm has been used extensively in the literature to decompose signals that contain nonlinear waves. However when a signal contain two or more frequencies that are close to one another the decomposition might fail. In…
This paper proposes a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the…
The EMD algorithm, first proposed in [11], made more robust as well as more versatile in [12], is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of…
This paper explores a family of generalized sweeping preconditionners for Helmholtz problems with non-overlapping checkerboard partition of the computational domain. The domain decomposition procedure relies on high-order transmission…
Hybrid algorithms, which combine black-box machine learning methods with experience from traditional numerical methods and domain expertise from diverse application areas, are progressively gaining importance in scientific machine learning…
This paper presents four novel domain decomposition algorithms integrated with nonlinear mapping techniques to address collocation-based solutions of eigenvalue problems involving sharp interfaces or steep gradients. The proposed methods…
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…
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…
We present the mathematical theory and its numerical validation of a method tailored to include eddy-current effects only in a part of the domain. This results in a heterogeneous problem combining an eddy-current model in a subset of the…
We present new Neumann-Neumann algorithms based on a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, the Lagrange multiplier approach provides a coupled…
The goal of this work is to improve images of traffic scenes that are degraded by natural causes such as fog, rain and limited visibility during the night. For these applications, it is next to impossible to get pixel perfect pairs of the…
In this paper, we partially answer open questions about the convergence of overlapping Schwarz methods. We prove that overlapping Schwarz methods with Dirichlet transmission conditions for semilinear elliptic and parabolic equations always…
We propose V--cycle multigrid methods for vector field problems arising from the lowest order hexahedral N\'{e}d\'{e}lec finite element. Since the conventional scalar smoothing techniques do not work well for the problems, a new type of…
In this paper, we present a new multiscale domain decomposition algorithm for computing solutions of static Eikonal equations. The new method is an iterative two-scale method that uses a parareal-like update scheme in combination with…
In this paper we propose on continuous level a class of domain decomposition methods of Robin-Robin type to solve the problems of unilateral contact between elastic bodies with nonlinear Winkler covers. These methods are based on abstract…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…