Related papers: Hardware-Oriented Krylov Methods for High-Performa…
This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature,…
It is well known that the block Krylov subspace solvers work efficiently for some cases of the solution of differential equations with multiple right-hand sides. In lattice QCD calculation of physical quantities on a given configuration…
Meshless collocation with multiquadric radial basis functions (MQ-RBFs) delivers high accuracy for the three-dimensional Helmholtz equation but produces dense, severely ill-conditioned linear systems. We develop and evaluate three…
We propose a novel algorithm based on inexact GMRES methods for linear response calculations in density functional theory. Such calculations require iteratively solving a nested linear problem $\mathcal{E} \delta\rho = b$ to obtain the…
In this paper we present a novel extended Krylov subspace reduced-order modeling technique to efficiently simulate time- and frequency-domain wavefields in open complex structures. To simulate the extension to infinity, we use an optimal…
Randomized-subspace methods reduce the cost of first-order optimization by using only low-dimensional projected-gradient information, a feature that is attractive in forward-mode automatic differentiation and communication-limited settings.…
We have developed an application and implemented parallel algorithms in order to provide a computational framework suitable for massively parallel supercomputers to study the unitary dynamics of quantum systems. We use renowned parallel…
In this paper, we introduce a unified framework for nonlinear Krylov subspace methods (nlKrylov) to solve systems of nonlinear equations. Building on classical GCR-like/type linear Krylov solvers such as GMRESR, we generalize these…
Distributed optimization methods are actively researched by optimization community. Due to applications in distributed machine learning, modern research directions include stochastic objectives, reducing communication frequency, and…
Block iterative methods are extremely important as smoothers for multigrid methods, as preconditioners for Krylov methods, and as solvers for diagonally dominant linear systems. Developing robust and efficient algorithms suitable for…
During the past decade, Model Order Reduction (MOR) has become key enabler for the efficient simulation of large circuit models. MOR techniques based on moment-matching are well established due to their simplicity and computational…
In this thesis, we propose new theoretical frameworks for the analysis of stochastic and distributed methods with error compensation and local updates. Using these frameworks, we develop more than 20 new optimization methods, including the…
This research introduce our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for single GPU and multiple GPUs are implemented. A HEC matrix format and…
Quantum subspace diagonalization and quantum Krylov algorithms offer a feasible, pre- or early-fault tolerant alternative to quantum phase estimation for using quantum computers to estimate the low-lying spectra of quantum systems. However,…
With the steady advance of high performance computing systems featuring smaller and smaller hardware components, the systems and algorithms used for numerical simulations increasingly contend with disruptions caused by hardware failures and…
This paper presents a novel space-time topology optimisation framework for time-dependent thermal conduction problems, aiming to significantly reduce the time-to-solution. By treating time as an additional spatial dimension, we discretise…
We propose an acceleration scheme for first-order methods (FOMs) for convex quadratic programs (QPs) that is analogous to Anderson acceleration and the Generalized Minimal Residual algorithm for linear systems. We motivate our proposed…
We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a…
Stochastic bilevel optimization tackles challenges involving nested optimization structures. Its fast-growing scale nowadays necessitates efficient distributed algorithms. In conventional distributed bilevel methods, each worker must…
In this paper we propose an adaptive approach for clustering and visualization of data by an orthogonalization process. Starting with the data points being represented by a Markov process using the diffusion map framework, the method…