Related papers: Fast and flexible preconditioners for solving mult…
The Newton's method for solving stationary Navier-Stokes equations (NSE) is known to convergent fast, however, may fail due to a bad initial guess. This work presents a simple-to-implement nonlinear preconditioning of Newton's iteration,…
We show that preconditioners constructed by random sampling can perform well without meeting the standard requirements of iterative methods. When applied to graph Laplacians, this leads to ultra-sparsifiers that in expectation behave as the…
I will present a method for providing initial guesses to a linear solver for systems with multiple shifts. This can also be extended to the case of multiple sources each with a different shift.
In this paper, we consider flow simulation in highly heterogeneous media that has many practical applications in industry. To enhance mass conservation, we write the elliptic problem in a mixed formulation and introduce a robust two-grid…
This paper deals with solving a class of three-by-three block saddle point problems. The systems are solved by preconditioning techniques. Based on an iterative method, we construct a block upper triangular preconditioner. The convergence…
The paper studies the convergence of some parallel multisplitting block iterative methods for the solution of linear systems arising in the numerical solution of Euler equations. Some sufficient conditions for convergence are proposed. As…
Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability; but, need to be used with an appropriate preconditioner (e.g.,…
In this paper we study fast iterative solvers for the large sparse linear systems resulting from the stochastic Galerkin discretization of stochastic partial differential equations. A block triangular preconditioner is introduced and…
It is well known that the choice of the iterative method is crucial in determining the speed of the converged solution. This article presents a detailed comparison between several iterative techniques for solving incmopressible…
Solving the indefinite Helmholtz equation is not only crucial for the understanding of many physical phenomena but also represents an outstandingly-difficult benchmark problem for the successful application of numerical methods. Here we…
This paper studies the solution of nonsymmetric linear systems by preconditioned Krylov methods based on the normal equations, LSQR in particular. On some examples, preconditioned LSQR is seen to produce errors many orders of magnitude…
We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant advantages over more standard finite element or finite…
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Gr\"unwald difference in space leads to dense…
We consider large linear systems arising from the isogeometric discretization of the Poisson problem on a single-patch domain. The numerical solution of such systems is considered a challenging task, particularly when the degree of the…
The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this…
We consider the iterative solution of symmetric saddle-point matrices with a singular leading block. We develop a new ideal positive definite block diagonal preconditioner that yields a preconditioned operator with four distinct…
The Onsager-Stefan-Maxwell (OSM) equations are an important model of mass transport in multicomponent flows with multiple chemical species. They describe the coupling of diffusive fluxes between species, accounting for their interactions…
We develop a robust and efficient method for soliton calculations for nonlinear Schr\"odinger equations. The method is based on the recently developed sparsifying preconditioner combined with Newton's iterative method. The performance of…
In this paper we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the proposed preconditioner, we use the simplest coarse solver…
We consider the use of multipreconditioning, which allows for multiple preconditioners to be applied in parallel, on high-frequency Helmholtz problems. Typical applications present challenging sparse linear systems which are complex…