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We propose an alternative implementation of preconditioning techniques for the solution of non-linear problems. Within the framework of Newton-Krylov methods, preconditioning techniques are needed to improve the performance of the solvers.…
We present robust and highly parallel multilevel non-overlapping Schwarz preconditioners, to solve an interior penalty discontinuous Galerkin finite element discretization of a system of steady state, singularly perturbed reaction-diffusion…
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…
A nested Schur complement solver is proposed for iterative solution of linear systems arising in exponential and implicit time integration of the Maxwell equations with perfectly matched layer (PML) nonreflecting boundary conditions. These…
We present a hybridization technique for summation-by-parts finite difference methods with weak enforcement of interface and boundary conditions for second order, linear elliptic partial differential equations. The method is based on…
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…
LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…
We present an algorithm which allows to solve analytically linear systems of differential equations which factorize to first order. The solution is given in terms of iterated integrals over an alphabet where its structure is implied by the…
Ill-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system…
Solving time-harmonic wave propagation problems by iterative methods is a difficult task, and over the last two decades, an important research effort has gone into developing preconditioners for the simplest representative of such wave…
We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…
In this paper, two efficient iterative algorithms based on the simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting…
While preconditioning is a long-standing concept to accelerate iterative methods for linear systems, generalizations to matrix functions are still in their infancy. We go a further step in this direction, introducing polynomial…
This paper presents a scalable physics-based block preconditioner for mixed-dimensional models in beam-solid interaction and their application in engineering. In particular, it studies the linear systems arising from a regularized…
Several preconditioned AOR methods have been proposed to solve system of linear equations $Ax=b$, where $A \in \mathbb{R}^{n \times n}$ is a unit Z-matrix. The aim of this paper is to give a comparison result for a class of preconditioners…
We present a robust and scalable solver for direct-forcing immersed boundary simulations, based on a preconditioned SIMPLE algorithm. The method applies block elimination to the pressure-force coupled system, and utilizes the discrete…
Recently Ahmadi et al. (2021) and Tagliaferro (2022) proposed some iterative methods for the numerical solution of linear systems which, under the classical hypothesis of strict diagonal dominance, typically converge faster than the Jacobi…
Stochastic Galerkin finite element discretizations of partial differential equations with coefficients characterized by arbitrary distributions lead, in general, to fully block dense linear systems. We propose two novel strategies for…
We deal with the numerical solution of linear elliptic problems with varying diffusion coefficient by the $hp$-discontinuous Galerkin method. We develop a two-level hybrid Schwarz preconditioner for the arising linear algebraic systems. The…
By applying the linearly implicit conservative difference scheme proposed in [D.-L. Wang, A.-G. Xiao, W. Yang. J. Comput. Phys. 2014;272:670-681], the system of repulsive space fractional coupled nonlinear Schr\"odinger equations leads to a…