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Incomplete LU factorizations of sparse matrices are widely used as preconditioners in Krylov subspace methods to speed up solving linear systems. Unfortunately, computing the preconditioner itself can be time-consuming and sensitive to…
State of the art domain decomposition algorithms for large-scale boundary value problems (with $M\gg 1$ degrees of freedom) suffer from bounded strong scalability because they involve the synchronisation and communication of workers…
Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…
We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…
The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite and become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…
Although the matrix multiplication plays a vital role in computational linear algebra, there are few efficient solutions for matrix multiplication of the near-sparse matrices. The Sparse Approximate Matrix Multiply (SpAMM) is one of the…
Linear systems with large differences between coefficients ("discontinuous coefficients") arise in many cases in which partial differential equations(PDEs) model physical phenomena involving heterogeneous media. The standard approach to…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…
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…
In real-time Visual SLAM systems, local mapping must operate under strict latency constraints, as delays degrade map quality and increase the risk of tracking failure. GPU parallelization offers a promising way to reduce latency. However,…
There are variety of computational algorithms need sequential sweeping; sweeping based on specific order; on a structured grid, e.g., preconditioning (smoothing) by SOR or ILU methods and solution of eikonal equation by fast sweeping…
Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This…
Sparse Matrix-matrix Multiplication (SpMM) and Sampled Dense-dense Matrix Multiplication (SDDMM) are important sparse operators in scientific computing and deep learning. Tensor Core Units (TCUs) enhance modern accelerators with superior…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…
Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual…
A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the…
The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…