Related papers: High Performance Parallel Solvers for the time-har…
We develop a fast solver for the spectral element method (SEM) applied to the two-sided fractional diffusion equation on uniform, geometric and graded meshes. By approximating the singular kernel with a degenerate kernel, we construct a…
Despite hundreds of papers on preconditioned linear systems of equations, there remains a significant lack of comprehensive performance benchmarks comparing various preconditioners for solving symmetric positive definite (SPD) systems. In…
We present a matrix-free parallel scalable multilevel deflation preconditioned method for heterogeneous time-harmonic wave problems. Building on the higher-order deflation preconditioning proposed by Dwarka and Vuik (SIAM J. Sci. Comput.…
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…
A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with $O(N \log^2 N)$…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We consider a mixed hybrid finite element formulation for coupled poromechanics. A stabilization strategy based on a macro-element approach is advanced to eliminate the spurious pressure modes appearing in undrained/incompressible…
This paper presents different methods for solving parallel machine scheduling problems with precedence constraints and setup times between the jobs. Limited discrepancy search methods mixed with local search principles, dominance conditions…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
Topology optimization problems generally support multiple local minima, and real-world applications are typically three-dimensional. In previous work [I. P. A. Papadopoulos, P. E. Farrell, and T. M. Surowiec, Computing multiple solutions of…
We derive a new parallel-in-time approach for solving large-scale optimization problems constrained by time-dependent partial differential equations arising from fluid dynamics. The solver involves the use of a block circulant approximation…
We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of…
We present both, theory and an algorithm for solving time-harmonic wave problems in a general setting. The time-harmonic solutions will be achieved by computing time-periodic solutions of the original wave equations. Thus, an exact…
Neural preconditioners for real-time physics simulation offer promising data-driven priors, but they often fail to capture long-range couplings efficiently because they inherit local message passing or sparse-operator access patterns. We…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
Randomized methods are becoming increasingly popular in numerical linear algebra. However, few attempts have been made to use them in developing preconditioners. Our interest lies in solving large-scale sparse symmetric positive definite…
As integrated circuits become increasingly complex, the demand for efficient and accurate simulation solvers continues to rise. Traditional solvers often struggle with large-scale sparse systems, leading to prolonged simulation times and…
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially…
We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…
The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale…