Related papers: Coarse spaces for non-symmetric two-level precondi…
This article investigates the numerical solution of the Diffusive Wave equation posed on domains containing a large number of polygonal perforations, motivated by urban flood modeling. Such geometries induce strong multiscale effects driven…
In this paper, a two-level additive Schwarz preconditioner is proposed for solving the algebraic systems resulting from the finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that 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…
In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the preconditioner is constructed from the corresponding problem with…
In this paper, we consider the balancing domain decomposition by constraints (BDDC) algorithm with adaptive coarse spaces for a class of stochastic elliptic problems. The key ingredient in the construction of the coarse space is the…
BDDC method is the most advanced method from the Balancing family of iterative substructuring methods for the solution of large systems of linear algebraic equations arising from discretization of elliptic boundary value problems. In the…
Fourth-order variational inequalities are encountered in various scientific and engineering disciplines, including elliptic optimal control problems and plate obstacle problems. In this paper, we consider additive Schwarz methods for…
Domain decomposition (DD) methods for solving time-dependent problems can be classified by (i) the method of domain decomposition used, (ii) the choice of decomposition operators (exchange of boundary conditions), and (iii) the splitting…
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…
Reduced basis methods build low-rank approximation spaces for the solution sets of parameterized PDEs by computing solutions of the given PDE for appropriately selected snapshot parameters. Localized reduced basis methods reduce the offline…
The Virtual Element Method (VEM) is used to perform the discretization of the Poisson problem on polygonal and polyhedral meshes. This results in a symmetric positive definite linear system, which is solved iteratively using overlapping…
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…
We examine the use of a two-level deflation preconditioner combined with GMRES to locally solve the subdomain systems arising from applying domain decomposition methods to Helmholtz problems. Our results show that the direct solution method…
The first domain decomposition methods for partial differential equations were already developed in 1870 by H. A. Schwarz. Here we consider a nonlocal Dirichlet problem with variable coefficients, where a nonlocal diffusion operator is…
In this paper we introduce a new Schwarz framework and theory, based on the well-known idea of space decomposition, for nonsymmetric and indefinite linear systems arising from continuous and discontinuous Galerkin approximations of general…
The discretization of surface intrinsic elliptic partial differential equations (PDEs) poses interesting challenges not seen in flat space. The discretization of these PDEs typically proceeds by either parametrizing the surface,…
Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts, including solution of partial differential equations (PDEs). We describe a solver for multiscale fully nonlinear elliptic…
In this paper, we propose an efficient two-level additive Schwarz method for solving large-scale eigenvalue problems arising from the finite element discretization of symmetric elliptic operators, which may compute efficiently more interior…
We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a…
This work proposes a method for solving linear stochastic optimal control (SOC) problems using sum of squares and semidefinite programming. Previous work had used polynomial optimization to approximate the value function, requiring a high…