Related papers: Fully algebraic domain decomposition preconditione…
This paper introduces a bi-discriminator GAN for synthesizing tabular datasets containing continuous, binary, and discrete columns. Our proposed approach employs an adapted preprocessing scheme and a novel conditional term for the generator…
A new preconditioner is developed for high order finite element approximation of linear elastic problems on triangular meshes in two dimensions. The new preconditioner results in a condition number that is bounded independently of the…
Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already…
We present a modified version of the PRESB preconditioner for two-by-two block system of linear equations with the coefficient matrix $$\textbf{A}=\left(\begin{array}{cc} F & -G^* G & F \end{array}\right),$$ where $F\in\mathbb{C}^{n\times…
Two-level domain decomposition (DD) methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level…
Wave propagation problems governed by the Helmholtz equation remain among the most challenging in scientific computing, due to their indefinite nature. Domain decomposition methods with spectral coarse spaces have emerged as some of the…
We introduce a novel strategy for constructing symmetric positive definite (SPD) preconditioners for linear systems with symmetric indefinite matrices. The strategy, called absolute value preconditioning, is motivated by the observation…
We construct an algebraic multigrid (AMG) based preconditioner for the reduced Hessian of a linear-quadratic optimization problem constrained by an elliptic partial differential equation. While the preconditioner generalizes a geometric…
In the past decade, there are many works on the finite element methods for the fully nonlinear Hamilton--Jacobi--Bellman (HJB) equations with Cordes condition. The linearised systems have large condition numbers, which depend not only on…
We introduce a new preconditioner for a recently developed pressure-robust hybridized discontinuous Galerkin (HDG) finite element discretization of the Stokes equations. A feature of HDG methods is the straightforward elimination of…
The efficient solution of discretisations of coupled systems of partial differential equations (PDEs) is at the core of much of numerical simulation. Significant effort has been expended on scalable algorithms to precondition Krylov…
This paper introduces a fully algebraic two-level additive Schwarz preconditioner for general sparse large-scale matrices. The preconditioner is analyzed for symmetric positive definite (SPD) matrices. For those matrices, the coarse space…
A new iteration bound for the preconditioned conjugate gradient (PCG) method is presented that more accurately captures convergence for systems with clustered eigenspectra, where the classical condition number-based bound is too…
We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…
In [McDonald, Pestana and Wathen, \textit{SIAM J. Sci. Comput.}, 40 (2018), pp. A1012--A1033], a block circulant preconditioner is proposed for all-at-once linear systems arising from evolutionary partial differential equations, in which…
Polynomial preconditioning is an important tool in solving large linear systems and eigenvalue problems. A polynomial from GMRES can be used to precondition restarted GMRES and restarted Arnoldi. Here we give methods for indefinite matrices…
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…
Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential…
Unfitted finite element methods, e.g., extended finite element techniques or the so-called finite cell method, have a great potential for large scale simulations, since they avoid the generation of body-fitted meshes and the use of graph…
The discretization of certain integral equations, e.g., the first-kind Fredholm equation of Laplace's equation, leads to symmetric positive-definite linear systems, where the coefficient matrix is dense and often ill-conditioned. We…