Related papers: Block Triangular Preconditioning for Stochastic Ga…
The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…
Novel fully discrete schemes are developed to numerically approximate a semilinear stochastic wave equation driven by additive space-time white noise. Spectral Galerkin method is proposed for the spatial discretization, and exponential time…
A class of preconditioners is introduced to enhance geometry optimisation and transition state search of molecular systems. We start from the Hessian of molecular mechanical terms, decompose it and retain only its positive definite part to…
A new high order accurate staggered semi-implicit space-time discontinuous Galerkin (DG) method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions. The staggered DG…
In this paper we propose a new class of preconditioners for the isogeometric discretization of the Stokes system. Their application involves the solution of a Sylvester-like equation, which can be done efficiently thanks to the Fast…
In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new…
Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not…
In this paper, preconditioning the saddle point problem arising from the elliptic boundary optimal control problem with mixed boundary conditions is considered. A block triangular reconditioning method is proposed based on permutations of…
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,…
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…
Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions…
A linearized numerical scheme is proposed to solve the nonlinear time fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson…
Preconditioning of a linear system obtained from spectral discretization of time-dependent PDEs often results in a full matrix which is expensive to compute and store specially when the problem size increases. A matrix-free implementation…
We study preconditioned gradient-based optimization methods where the preconditioning matrix has block-diagonal form. Such a structural constraint comes with the advantage that the update computation is block-separable and can be…
In this paper, we propose and analyze an efficient preconditioning method for the elliptic problem based on the reconstructed discontinuous approximation method. We reconstruct a high-order piecewise polynomial space that arbitrary order…
We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differential equations (PDEs). These systems are typically…
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…
Recently, Garcke et al.[Garcke, Hinze, Kahle, A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow, Applied Numerical Mathematics 99, pp. 151-171, 2016] developed a consistent…
This paper presents a new stochastic preconditioning approach. For symmetric diagonally-dominant M-matrices, we prove that an incomplete LDL factorization can be obtained from random walks, and used as a preconditioner for an iterative…
This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…