Related papers: Hybrid preconditioning for iterative diagonalizati…

Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…

This paper introduces a hierarchical interpolative decomposition butterfly-LU factorization (H-IDBF-LU) preconditioner for solving two-dimensional electric-field integral equations (EFIEs) in electromagnetic scattering problems of perfect…

Variational quantum algorithms provide a direct, physics-based approach to protein structure prediction, but their accuracy is limited by the coarse resolution of the energy landscapes generated on current noisy devices. We propose a hybrid…

The generalized stacking-fault energy (GSFE) is the fundamental but key parameter for the plastic deformation of materials. We perform first-principles calculations by full-potential linearized augmented planewave (FLAPW) method to evaluate…

In this work we propose a novel block preconditioner, labelled Explicit Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov subspace solvers used to address the sequence of non-symmetric systems of linear…

This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…

We introduce a novel hybrid quantum-classical algorithm for the near-term computation of expectation values in quantum systems at finite temperatures. This is based on two stages: on the first one, a mixed state approximating a fiducial…

A longstanding computational challenge is the accurate simulation of many-body particle systems. Especially for deriving key characteristics of high-impact but complex systems such as battery materials and high entropy alloys (HEA). While…

An algebraic multilevel iteration method for solving system of linear algebraic equations arising in $H(\mathrm{curl})$ and $H(\mathrm{div})$ spaces are presented. The algorithm is developed for the discrete problem obtained by using the…

Barren plateaus present a major challenge in the training of variational quantum algorithms (VQAs), particularly for large-scale discretizations of nonlinear partial differential equations. In this work, we introduce a domain decomposition…

The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…

Large symmetric eigenvalue problems are commonly observed in many disciplines such as Chemistry and Physics, and several libraries including cuSOLVERMp, MAGMA and ELPA support computing large eigenvalue decomposition on multi-GPU or…

We present a new hybrid quantum-classical algorithm for optimizing unitary coupled-cluster (UCC) wave functions deemed the projective quantum eigensolver (PQE), amenable to near-term noisy quantum hardware. Contrary to variational quantum…

We present the hybridization of flux reconstruction methods for advection-diffusion problems. Hybridization introduces a new variable into the problem so that it can be reduced via static condensation. This allows the solution of implicit…

Fully homomorphic encryption (FHE) allows an untrusted party to evaluate arithmetic cir- cuits, i.e., perform additions and multiplications on encrypted data, without having the decryp- tion key. One of the most efficient class of FHE…

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…

We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods…

This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…

GenEO (`Generalised Eigenvalue problems on the Overlap') is a method from the family of spectral coarse spaces that can efficiently rely on local eigensolves in order to build a robust parallel domain decomposition preconditioner for…

We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations. Typical of hybridized discontinuous Galerkin methods, the method has degrees-of-freedom…