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We present a domain decomposition approach for the simulation of charge transport in heterojunction semiconductors. The problem is characterized by a large variation of primary variables across an interface region of a size much smaller…

Computational Physics · Physics 2014-12-30 Timothy Costa , David Foster , Malgorzata Peszynska

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…

Numerical Analysis · Mathematics 2015-01-15 Yingjun Jiang , Xuejun Xu

In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…

Numerical Analysis · Mathematics 2020-08-20 Yalchin Efendiev , Petr N. Vabishchevich

Elliptic diffusion problems with multiscale heterogeneous coefficients lead to poorly conditioned discrete systems and therefore require effective preconditioning strategies. While subspace decomposition preconditioners perform well for…

Numerical Analysis · Mathematics 2026-03-11 Dilini Kolombage , Axel Målqvist , Barbara Verfürth

In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a…

Optimization and Control · Mathematics 2015-08-26 Xiaomao Deng , Xiao-chuan Cai , Jun Zou

We introduce a preconditioner based on a hierarchical low-rank compression scheme of Schur complements. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated,…

Numerical Analysis · Mathematics 2015-09-01 Paolo Gatto , Jan S. Hesthaven

We show that using the multi-splitting algorithm as a preconditioner for the domain wall Dirac linear operator, arising in lattice QCD, effectively reduces the inter-node communication cost, at the expense of performing more on-node…

High Energy Physics - Lattice · Physics 2021-09-09 Jiqun Tu , M. A. Clark , Chulwoo Jung , Robert Mawhinney

This work studies the dependence of the solution with respect to interface geometric perturbations in a multiscaled coupled Darcy flow system in direct variational formulation. A set of admissible perturbation functions and a sense of…

Analysis of PDEs · Mathematics 2020-08-21 Fernando A Morales

In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two…

Numerical Analysis · Mathematics 2024-03-12 Elena Zappon , Andrea Manzoni , Paola Gervasio , Alfio Quarteroni

In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface…

Numerical Analysis · Mathematics 2023-03-07 T. Knoke , S. Kinnewig , S. Beuchler , A. Demircan , U. Morgner , T. Wick

We present a construction of harmonic functions on bounded domains for the spectral fractional Laplacian operator and we classify them in terms of their divergent profile at the boundary. This is used to establish and solve boundary value…

Analysis of PDEs · Mathematics 2015-09-22 Nicola Abatangelo , Louis Dupaigne

We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional…

Numerical Analysis · Mathematics 2025-10-31 Xiaolin Liu , Kuan Xu

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…

Numerical Analysis · Mathematics 2018-02-07 Camille Negrello , Pierre Gosselet , Christian Rey

We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…

Analysis of PDEs · Mathematics 2018-10-22 Alessandro Carbotti , Serena Dipierro , Enrico Valdinoci

We propose and analyze a robust BPX preconditioner for the integral fractional Laplacian on bounded Lipschitz domains. For either quasi-uniform grids or graded bisection grids, we show that the condition numbers of the resulting systems…

Numerical Analysis · Mathematics 2021-06-04 Juan Pablo Borthagaray , Ricardo H. Nochetto , Shuonan Wu , Jinchao Xu

In this paper, we propose closed-form precoding schemes with optimal performance for constructive interference (CI) exploitation in the multiuser multiple-input single-output (MU-MISO) downlink. We first consider an optimization where we…

Information Theory · Computer Science 2017-12-22 Ang Li , Christos Masouros

The flux-mortar mixed finite element method was recently developed for a general class of domain decomposition saddle point problems on non-matching grids. In this work we develop the method for Darcy flow using the multipoint flux…

Numerical Analysis · Mathematics 2023-01-18 Wietse M. Boon , Dennis Gläser , Rainer Helmig , Ivan Yotov

In this article, we present a parallel recursive algorithm based on multi-level domain decomposition that can be used as a precondtioner to a Krylov subspace method to solve sparse linear systems of equations arising from the discretization…

Numerical Analysis · Mathematics 2012-10-24 Rahul S. Sampath , Bobby Philip , Srikanth Allu , Srdjan Simunovic

This paper is concerned with global-in-time, nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem. Two approaches are considered: one uses the time-dependent Steklov-Poincar\'e operator and the…

Numerical Analysis · Mathematics 2013-12-30 Thi Thao Phuong Hoang , Jérôme Jaffré , Caroline Japhet , Michel Kern , Jean Roberts

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…