Related papers: Tridiagonal and Block Tridiagonal computed Sparse …
In this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with $\mathcal{H}^2$-matrices. We propose several new preconditioners…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
We discuss techniques for accelerating the self consistent field (SCF) iteration for solving the Kohn-Sham equations. These techniques are all based on constructing approximations to the inverse of the Jacobian associated with a fixed point…
The solution of a sparse system of linear equations is ubiquitous in scientific applications. Iterative methods, such as the Preconditioned Conjugate Gradient method (PCG), are normally chosen over direct methods due to memory and…
In the context of training neural network-based approximations of solutions of parameter-dependent PDEs, we investigate the effect of preconditioning via well-conditioned frame representations of operators and demonstrate a significant…
We explore a scaled spectral preconditioner for the efficient solution of sequences of symmetric and positive-definite linear systems. We design the scaled preconditioner not only as an approximation of the inverse of the linear system but…
When solving linear systems with nonsymmetric Toeplitz or multilevel Toeplitz matrices using Krylov subspace methods, the coefficient matrix may be symmetrized. The preconditioned MINRES method can then be applied to this symmetrized…
This work presents a fast direct solver strategy for electromagnetic integral equations in the high-frequency regime. The new scheme relies on a suitably preconditioned combined field formulation and results in a single skeleton form plus…
Numerical simulation of fracture contact poromechanics is essential for various applications, including CO2 sequestration, geothermal energy production and underground gas storage. Modeling this problem accurately presents significant…
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…
We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…
The Extracellular-Membrane-Intracellular (EMI) model is a novel mathematical framework for cardiac electrophysiology simulations. The EMI model provides a more detailed description of the heart's electrical activity compared to traditional…
A hybrid surface integral equation partial differential equation (SIE-PDE) formulation without the boundary condition requirement is proposed to solve the transverse magnetic (TM) electromagnetic problems. In the proposed formulation, the…
Modification of coupled integral equations method (CIEM) for calculating the characteristics of the accelerating structures is presented in this paper. In earlier developed CIEM schemes the coupled integral equations are derived for the…
Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing…
While doing electromagnetic analysis using FEM (Finite element method), if we can implement the underlying symmetric nature of the problem, there will be significant reduction in the computational cost. Symmetric nature of the problem can…
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…
Unless special conditions apply, the attempt to solve ill-conditioned systems of linear equations with standard numerical methods leads to uncontrollably high numerical error. Often, such systems arise from the discretization of operator…
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 apply preconditioning, which is widely used in classical solvers for linear systems $A\textbf{x}=\textbf{b}$, to the variational quantum linear solver. By utilizing incomplete LU factorization as a preconditioner for linear equations…