Related papers: Solution of the Dirac equation in lattice QCD usin…
This paper reviews the most popular methods which are used in lattice QCD to compute the determinant of the lattice Dirac operator: Gaussian integral representation and noisy methods. Both of them lead naturally to matrix function problems.…
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…
In this paper, we propose and analyze an additive domain decomposition method (DDM) for solving the high-frequency Helmholtz equation with the Sommerfeld radiation condition. In the proposed method, the computational domain is partitioned…
We present a simple, parallel and distributed algorithm for setting up and partitioning a sparse representation of a regular discretized simulation domain. This method is scalable for a large number of processes even for complex geometries…
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…
This paper deals with balanced domain decomposition by constraints (BDDC) method for solving large-scale linear systems of algebraic equations arising from the space-time finite element discretization of parabolic initial-boundary value…
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…
We review some important ideas in the design and analysis of robust overlapping domain decomposition algorithms for high-contrast multiscale problems and propose a domain decomposition method better performance in terms of the number of…
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…
We show that using the multisplitting algorithm as a preconditioner for conjugate gradient inversion of the domain wall Dirac operator could effectively reduce the inter- node communication cost, at the expense of performing more on-node…
The generalized Dryja--Smith--Widlund (GDSW) preconditioner is a two-level overlapping Schwarz domain decomposition (DD) preconditioner that couples a classical one-level overlapping Schwarz preconditioner with an energy-minimizing coarse…
We propose a primal-dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling…
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 an overlapping Schwarz decomposition algorithm for constrained quadratic programs (QPs). Schwarz algorithms have been traditionally used to solve linear algebra systems arising from partial differential equations, but we have…
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…
Nonlinear Schwarz methods are a type of nonlinear domain decomposition method used as an alternative to Newton's method for solving discretized nonlinear partial differential equations. In this article, the first parallel implementation of…
This paper presents and evaluates a framework for the coupling of subdomain-local projection-based reduced order models (PROMs) using the Schwarz alternating method following a domain decomposition (DD) of the spatial domain on which a…
Accelerating iterative eigenvalue algorithms is often achieved by employing a spectral shifting strategy. Unfortunately, improved shifting typically leads to a smaller eigenvalue for the resulting shifted operator, which in turn results in…
Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic…
A domain decomposition method is proposed based on carefully chosen impedance transmission operators for a hybrid formulation of the eddy current problem. Preliminary analysis and numerical results are provided in the spherical case showing…