相关论文: Non-overlapping block smoothers for the Stokes equ…

We develop a novel iterative solution method for the incompressible Navier-Stokes equations with boundary conditions coupled with reduced models. The iterative algorithm is designed based on the variational multiscale formulation and the…

The demand for inverse design is increasing as the ability to fabricate sub-10 nm features expands the design space by orders of magnitude. Efficient inverse design benefits from differentiable models of light-structure interaction. While…

In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at…

Constructing discrete models of stochastic partial differential equations is very delicate. Stochastic centre manifold theory provides novel support for coarse grained, macroscale, spatial discretisations of nonlinear stochastic partial…

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…

The goal of co-clustering is to simultaneously identify a clustering of rows as well as columns of a two dimensional data matrix. A number of co-clustering techniques have been proposed including information-theoretic co-clustering and the…

We propose the first optimal geometric multigrid solver for hybrid high-order discretizations that can handle arbitrary polytopal agglomeration hierarchies in both two and three dimensions. The key ingredient is the use of modified skeleton…

This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…

In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in [50] is a…

Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…

Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method…

In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper invstigates the more general problem of putting a set of matrices into block triangular or block-diagonal form…

The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…

The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and divergence-free. When…

We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…

We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…

We present iterative solvers to approximate the solution of numerical schemes for stochastic Stefan problems. After briefly talking about the convergence results, we tackle the question of efficient strategies for solving the nonlinear…

Block coordinate descent is an optimization paradigm that iteratively updates one block of variables at a time, making it quite amenable to big data applications due to its scalability and performance. Its convergence behavior has been…

Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…