相关论文: A power Schur complement Low-Rank correction preco…
We investigate the SPAI and PSAI preconditioning procedures and shed light on two important features of them: (i) For the large linear system $Ax=b$ with $A$ irregular sparse, i.e., with $A$ having $s$ relatively dense columns, SPAI may be…
The numerical modeling of fracture contact thermo-poromechanics is crucial for advancing subsurface engineering applications, including CO2 sequestration, production of geo-energy resources, energy storage and wastewater disposal…
Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…
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…
A new hybrid algorithm for LDU-factorization for large sparse matrix combining iterative solver, which can keep the same accuracy as the classical factorization, is proposed. The last Schur complement will be generated by iterative solver…
The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a…
In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…
In this paper, we consider using Schur complements to design preconditioners for twofold and block tridiagonal saddle point problems. One type of the preconditioners are based on the nested (or recursive) Schur complement, the other is…
Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extensions that can be applied when the system has a block…
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…
A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…
Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification,…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…
The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume…
Our interest lies in the robust and efficient solution of large sparse linear least-squares problems. In recent years, hardware developments have led to a surge in interest in exploiting mixed precision arithmetic within numerical linear…
Hierarchical matrices (usually abbreviated ${\mathcal H}$-matrices) are frequently used to construct preconditioners for systems of linear equations. Since it is possible to compute approximate inverses or $LU$ factorizations in ${\mathcal…
The importance of Schur complement based preconditioners are well-established for classical saddle point problems in $\mathbb{R}^N \times \mathbb{R}^M$. In this paper we extend these results to multiple saddle point problems in Hilbert…
In this paper, a class of new preconditioners based on matrix splitting are presented for generalized saddle-point linear systems, which can be viewed as further modified improvements of some recently published preconditioners. Moreover, we…