Related papers: A block $\alpha$-circulant based preconditioned MI…
In this paper, we develop a fast numerical method for solving the time-dependent Riesz space fractional diffusion equations with a nonlinear source term in the convex domain. An implicit finite difference method is employed to discretize…
A fluid-structure interaction (FSI) problem is solved via a monolithic coupling of the fluid, structure, and geometry subproblems. The iterative GMRES solver is accelerated with the FaCSI block preconditioner. In the FaCSI factorization,…
Fast Fourier Transform (FFT)-based solvers for the Poisson equation are highly efficient, exhibiting $O(N\log N)$ computational complexity and excellent parallelism. However, their application is typically restricted to simple, regular…
The phase separation processes are typically modeled by Cahn-Hilliard equations. This equation was originally introduced to model phase separation in binary alloys, where phase stands for concentration of different components in alloy. When…
We study the solution of large symmetric positive-definite linear systems in a matrix-free setting with a limited iteration budget. We focus on the preconditioned conjugate gradient (PCG) method with spectral preconditioning. Spectral…
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…
This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation, that is based on a proposed modified version of the mortar method. The…
We propose a preconditioner that can accelerate the rate of convergence of the Multiple Shooting Shadowing (MSS) method. This recently proposed method can be used to compute derivatives of time-averaged objectives (also known as…
A min-max formula is proved for the minimum of an integer-valued separable discrete convex function where the minimum is taken over the set of integral elements of a box total dual integral (box-TDI) polyhedron. One variant of the theorem…
In this paper we are concerned with fast algorithms for the systems arising from the plane wave discretizations for two-dimensional Helmholtz equations with large wave numbers. We consider the plane wave weighted least squares (PWLS) method…
Use of the stochastic Galerkin finite element methods leads to large systems of linear equations obtained by the discretization of tensor product solution spaces along their spatial and stochastic dimensions. These systems are typically…
This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…
We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence…
We consider the solution of full column-rank least squares problems by means of normal equations that are preconditioned, symmetrically or non-symmetrically, with a randomized preconditioner. With an effective preconditioner, the solutions…
We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many…
This paper describes the recently developed mixed mimetic spectral element method for the Stokes problem in the vorticity-velocity-pressure formulation. This compatible discretization method relies on the construction of a conforming…
In this article, a two-level overlapping domain decomposition preconditioner is developed for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element…
In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary…
The Potts model has many applications. It is equivalent to some min-cut and max-flow models. Primal-dual algorithms have been used to solve these problems. Due to the special structure of the models, convergence proof is still a difficult…
We describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block…