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We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
Modern inference and learning often hinge on identifying low-dimensional structures that approximate large scale data. Subspace clustering achieves this through a union of linear subspaces. However, in contemporary applications data is…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random…
Shifted Laplacian multigrid preconditioner has become a tool du jour for solving highly indefinite Helmholtz equations. The idea is to add a complex damping to the original Helmholtz operator and then apply a multigrid processing to the…
Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear…
We consider using the preconditioned-Krylov subspace method to solve the system of linear equations with a three-by-three block structure. By making use of the three-by-three block structure, eight inexact block factorization…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
Structured dense matrices result from boundary integral problems in electrostatics and geostatistics, and also Schur complements in sparse preconditioners such as multi-frontal methods. Exploiting the structure of such matrices can reduce…
Scientific workflows have been predominantly used for complex and large scale data analysis and scientific computation/automation and the need for robust workflow scheduling techniques has grown considerably. But, most of the existing…
It has long been a recognized problem that many datasets contain significant levels of missing numerical data. A potentially critical predicate for application of machine learning methods to datasets involves addressing this problem.…
Semi-Lagrangian schemes with various splitting methods, and with different reconstruction/interpolation strategies have been applied to kinetic simulations. For example, the order of spatial accuracy of the algorithms proposed in {[Qiu and…
We revisit the Hierarchical Poincar\'e-Steklov (HPS) method in a preconditioned iterative setting for variable-coefficient Helmholtz problems with impedance boundary conditions. HPS is commonly presented as a direct solver based on nested…
The solution of sparse linear systems constitutes the dominant computational bottleneck in interior point methods (IPMs), frequently consuming over 70% of the total solution time. As optimization problems scale to millions of variables,…
LU factorization for sparse matrices is the most important computing step for many engineering and scientific computing problems such as circuit simulation. But parallelizing LU factorization with the Graphic Processing Units (GPU) still…
To optimize large Transformer model training, both efficient parallel computing and advanced data management are indispensable. However, current methods often assume a stable and uniform training workload, neglecting data-induced…
Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, and supervised learning tasks, depend crucially on the choice…
Problem statement: Clustering has a number of techniques that have been developed in statistics, pattern recognition, data mining, and other fields. Subspace clustering enumerates clusters of objects in all subspaces of a dataset. It tends…
Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) $V$-cycle for reducing high-frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has…
This work presents a matrix-free finite element solver for finite-strain elasticity adopting an $hp$-multigrid preconditioner. Compared to classical algorithms relying on a global sparse matrix, matrix-free solution strategies significantly…