Related papers: Generating Equidistributed Meshes in 2D via Domain…
While solving Partial Differential Equations (PDEs) with finite element methods (FEM), serendipity elements allow us to obtain the same order of accuracy as rectangular tensor-product elements with many fewer degrees of freedom (DOFs). To…
The presented article contains a 2D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes with a prescribed size h of elements. These finite element meshes can serve as standard discrete…
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…
We investigate additive Schwarz methods for semilinear elliptic problems with convex energy functionals, which have wide scientific applications. A key observation is that the convergence rates of both one- and two-level additive Schwarz…
We compare the distribution function and the maximum of solutions of nonlinear elliptic equations defined in general domains with solutions of similar problems defined in a ball using Schwarz symmetrization. As an application, we prove the…
In this paper, we study the defocusing nonlinear Schr\"{o}dinger equation with a locally distributed damping on a smooth bounded domain as well as on the whole space and on an exterior domain. We first construct approximate solutions using…
This paper introduces a novel approach to analyzing overlapping Schwarz methods for N\'{e}d\'{e}lec and Raviart--Thomas vector field problems. The theory is based on new regular stable decompositions for vector fields that are robust to the…
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 develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…
Randomized neural networks (RaNNs), in which hidden layers remain fixed after random initialization, provide an efficient alternative for parameter optimization compared to fully parameterized networks. In this paper, RaNNs are integrated…
In the framework of the rate-independent large-strain Cosserat theory of plasticity we calculate analytically explicit solutions of a two-dimensional shear problem. We discuss two cases where the micro-rotations are stationary solutions of…
Optimization of thin-walled structures like an aircraft wing, aircraft fuselage or submarine hull often involves dividing the shell surface into numerous localized panels, each characterized by its own set of design variables. The process…
We introduce a domain decomposition-based nonlinear preconditioned iteration for solving nonlinear, nonsmooth elliptic optimal control problems, with a nonlinear reaction term, $L^1$ regularization and box constraints on the control…
This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of fixed, arbitrary order and the preconditioner is…
We consider the leapfrog algorithm by Noakes for computing geodesics on Riemannian manifolds. The main idea behind this algorithm is to subdivide the original endpoint geodesic problem into several local problems, for which the endpoint…
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…
In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the $d$-dimensional advection-diffusion equation, our proposal is a two-level algorithm…
The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a…
In this paper, a Schwarz heterogeneous domain decomposition method (DDM) is used to co-simulate an RLC electrical circuit where a part of the domain is modeled with Electro-Magnetic Transients (EMT) modeling and the other part with dynamic…
In the field of Domain Decomposition (DD), Optimized Schwarz Method (OSM) appears to be one of the prominent techniques to solve large scale time-harmonic wave propagation problems. It is based on appropriate transmission conditions using…