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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 present convergence results in expectation for stochastic subspace correction schemes and their accelerated versions to solve symmetric positive-definite variational problems, and discuss their potential for achieving fault tolerance in…
Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
In this article, we analyse the domain mapping method approach to approximate statistical moments of solutions to linear elliptic partial differential equations posed over random geometries including smooth surfaces and bulk-surface…
This paper introduces a novel approach to approximating continuous functions over high-dimensional hypercubes by integrating matrix CUR decomposition with hyperinterpolation techniques. Traditional Fourier-based hyperinterpolation methods…
This paper presents a numerical study on multigrid algorithms of $V$-cycle type for problems posed in the Hilbert space $H(\mathbf{curl})$ in three dimensions. The multigrid methods are designed for discrete problems originated from the…
The transferable neural network (TransNet) is a two-layer shallow neural network with pre-determined and uniformly distributed neurons in the hidden layer, and the least-squares solvers can be particularly used to compute the parameters of…
In ptychography experiments, redundant scanning is usually required to guarantee the stable recovery, such that a huge amount of frames are generated, and thus it poses a great demand of parallel computing in order to solve this large-scale…
In this study, we develop a new parallel algorithm for solving systems of linear algebraic equations with the same block-tridiagonal matrix but with different right-hand sides. The method is a generalization of the parallel dichotomy…
In this article, we analyse the convergence behaviour and scalability properties of the one-level Parallel Schwarz method (PSM) for domain decomposition problems in which the boundaries of many subdomains lie in the interior of the global…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
Linear algebraic operations are ubiquitous in engineering applications, and arise often in a variety of fields including statistical signal processing and machine learning. With contemporary large datasets, to perform linear algebraic…
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…