相关论文: Accurate Coarse Residual for Two-Level Asynchronou…

We investigate the parallel one-level overlapping Schwarz method for solving finite element discretization of high-frequency Helmholtz equations. The resulting linear systems are large, indefinite, ill-conditioned, and complex-valued. We…

With the advent of convolutional neural networks, stereo matching algorithms have recently gained tremendous progress. However, it remains a great challenge to accurately extract disparities from real-world image pairs taken by…

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…

We present sharp estimates for the extremal eigenvalues of the Schur complements arising in saddle point problems. These estimates are derived using the auxiliary space theory, in which a given iterative method is interpreted as an…

The Schur decomposition of a square matrix $A$ is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following…

For subspace recovery, most existing low-rank representation (LRR) models performs in the original space in single-layer mode. As such, the deep hierarchical information cannot be learned, which may result in inaccurate recoveries for…

The Parareal parallel-in-time integration method often performs poorly when applied to hyperbolic partial differential equations. This effect is even more pronounced when the coarse propagator uses a reduced spatial resolution. However,…

Numerical evolution of the spherically symmetric, massive Klein-Gordon field is presented using a new adaptive mesh refinement (AMR) code with fourth order discretization in space and time, along with compactification in space. The system…

Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an inherently sequential predictor-corrector method in which…

Solving time-harmonic wave propagation problems in the frequency domain within heterogeneous media poses significant mathematical and computational challenges, particularly in the high-frequency regime. Among the available numerical…

We study the effect of adaptive mesh refinement on a parallel domain decomposition solver of a linear system of algebraic equations. These concepts need to be combined within a parallel adaptive finite element software. A prototype…

We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…

Data synchronization is a fundamental problem with applications in diverse fields such as cloud storage, genomics, and distributed systems. This paper addresses the challenge of synchronizing two files, one of which is a subsequence of the…

A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…

With the emergence of new storage and communication methods, the insertion, deletion, and substitution (IDS) channel has attracted considerable attention. However, many topics on the IDS channel and the associated Levenshtein distance…

Incompressible fluid flow problems appear frequently in different applications. The discretization of such problems may result in large and ill-conditioned systems of linear equations. We consider the case of the Stokes equations…

In Lattice QCD computations a substantial amount of work is spent in solving the Dirac equation. In the recent past it has been observed that conventional Krylov solvers tend to critically slow down for large lattices and small quark…

We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and…

Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of…

Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…