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This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear systems. This paper introduces a procedure by which the…
A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…
The authors propose a recycling Krylov subspace method for the solution of a sequence of self-adjoint linear systems. Such problems appear, for example, in the Newton process for solving nonlinear equations. Ritz vectors are automatically…
The authors consider the interior Dirichlet problem for Laplace's equation on planar domains with corners. In order to approximate the solution of the corresponding double layer boundary integral equation, they propose a numerical method of…
In this paper, we propose a domain decomposition method for multiscale second order elliptic partial differential equations with highly varying coefficients. The method is based on a discontinuous Galerkin formulation. We present both a…
This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non-overlapping and overlapping groups. Group sparsity regularization refers to a type…
In this paper, a novel augmented Lagrangian preconditioner based on global Arnoldi for accelerating the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure, these systems…
We present a novel preconditioning technique for Krylov subspace algorithms to solve fluid-structure interaction (FSI) linearized systems arising from finite element discretizations. An outer Krylov subspace solver preconditioned with a…
We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…
We present a unified framework to efficiently approximate solutions to fractional diffusion problems of stationary and parabolic type. After discretization, we can take the point of view that the solution is obtained by a matrix-vector…
Linear programming (LP) is an extremely useful tool which 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…
Context. Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary…
We consider using the preconditioned-Krylov subspace method to solve the system of linear equations with a three-by-three block structure. By making use of the three-by-three block structure, eight inexact block factorization…
Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…
The aim of this paper is to develop fast second-order accurate difference schemes for solving one- and two-dimensional time distributed-order and Riesz space fractional diffusion equations. We adopt the same measures for one- and…
This paper investigate on numerical analysis on modified Single-layer approach to exterior Dirichlet problem of Laplace equation. We complete the convergence and error analysis of Petrov-Galerkin and Galerkin-Collocation methods with…
Stationary iterative methods with a symmetric splitting matrix are performed as inner-iteration preconditioning for Krylov subspace methods. We give conditions such that the inner-iteration preconditioning matrix is definite, and show that…
We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the…
A delay Lyapunov matrix corresponding to an exponentially stable system of linear time-invariant delay differential equations can be characterized as the solution of a boundary value problem involving a matrix valued delay differential…
This paper focuses on the design, analysis and implementation of a new preconditioning concept for linear second order partial differential equations, including the convection-diffusion-reaction problems discretized by Galerkin or…