Related papers: Multiprecision computations with Schwarz methods
We propose a multi-precision extension of the Quadratic Regularization (R2) algorithm that enables it to take advantage of low-precision computations, and by extension to decrease energy consumption during the solve. The lower the precision…
Parallel algorithms and simulators with good scalabilities are particularly important for large-scale reservoir simulations on modern supercomputers with a large number of processors. In this paper, we introduce and study a family of highly…
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…
This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…
A new approach of implementing initial and boundary conditions for the lattice Boltzmann method is presented. The new approach is based on an extended collision operator that uses the gradients of the fluid velocity. The numerical…
Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation - precisely the case where rational functions outperform polynomials by a landslide. We show that far…
We show that applying a classical Schwarz method to the time harmonic Navier equations, which are an important model for linear elasticity, leads in general to a divergent method for low to intermediate frequencies. This is even worse than…
The Schwarz domain decomposition method can be used for approximately solving a Laplace equation on a domain formed by the union of two overlapping discs. We consider an inexact variant of this method in which the subproblems on the discs…
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…
A symmetric and a nonsymmetric variant of the additive Schwarz preconditioner are proposed for the solution of a nonsymmetric system of algebraic equations arising from a general finite volume element discretization of symmetric elliptic…
In the early days of computing, severe memory constraints made it necessary to use lower floating-point precision. As hardware capabilities have advanced, modern systems, particularly in computational statistics and scientific computing,…
In this paper, we apply the optimized Schwarz method to the two dimensional nonlinear Schr{\"o}dinger equation and extend this method to the simulation of Bose-Einstein condensates (Gross-Pitaevskii equation). We propose an extended version…
The multilevel Schwarz preconditioner is one of the most popular parallel preconditioners for enhancing convergence and improving parallel efficiency. However, its parallel implementation on arbitrary unstructured triangular/tetrahedral…
We consider additive Schwarz methods for boundary value problems involving the $p$-Laplacian. While existing theoretical estimates suggest a sublinear convergence rate for these methods, empirical evidence from numerical experiments…
We define and analyze (local) multilevel diagonal preconditioners for isogeometric boundary elements on locally refined meshes in two dimensions. Hypersingular and weakly-singular integral equations are considered. We prove that the…
Recently, asynchronous coarse-space correction has been achieved within both the overlapping Schwarz and the primal Schur frameworks. Both additive and multiplicative corrections have been discussed. In this paper, we address some…
Some improvements of the celebrated Schwarz inequality in complex inner product spaces are given. Applications for n-tuples of complex numbers are provided.
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…
In this paper, we consider two variants of the concept of sharp minimum for mathematical programming problems with quasiconvex objective function and inequality constraints. It investigated the problem of describing a variant of a simple…