Related papers: A Parallel Augmented Subspace Method for Eigenvalu…
Recently, lower-level constrained bilevel optimization has attracted increasing attention. However, existing methods mostly focus on either deterministic cases or problems with linear constraints. The main challenge in stochastic cases with…
Motivated by recent work on coarse spaces for Helmholtz problems, we provide in this paper a comparative study on the use of spectral coarse spaces of GenEO type for heterogeneous indefinite elliptic problems within an additive overlapping…
Multi-level numerical methods that obtain the exact solution of a linear system are presented. The methods are devised by combining ideas from the full multi-grid algorithm and perfect reconstruction filters. The problem is stated as…
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
We propose a non grid-based interpolation scheme based on the information from the data collected from the vicinity of the query point. As a non-grid-based interpolation, the data points can be distributed randomly in a small region, and…
We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations…
The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to…
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…
Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…
The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
Learning fine-grained embeddings from coarse labels is a challenging task due to limited label granularity supervision, i.e., lacking the detailed distinctions required for fine-grained tasks. The task becomes even more demanding when…
This paper mainly investigates the classic resonant cavity problem with anisotropic and nonconductive media, which is a linear vector Maxwell's eigenvalue problem. The finite element method based on edge element of the lowest-order and…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad--Shafranov equation. The presence of uncertainty in the model parameters…
The full approximation storage (FAS) scheme is a widely used multigrid method for nonlinear problems. In this paper, a new framework to design and analyze FAS-like schemes for convex optimization problems is developed. The new method, the…
We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…