相关论文: A parallel-in-time two-sided preconditioning for a…

To address the initial singularity inherent in solutions to fractional partial differential equations (fPDEs), we propose an accelerated Alikhanov discretization formulation implemented on nonuniform time grids. Based on the…

For several classes of mathematical models that yield linear systems, the splitting of the matrix into its Hermitian and skew Hermitian parts is naturally related to properties of the underlying model. This is particularly so for…

Achieving robust control and optimization in high-fidelity physics simulations is extremely challenging, especially for evolutionary systems whose solutions span vast scales across space, time, and physical variables. In conjunction with…

This paper presents a non-intrusive framework for integrating existing unsteady partial differential equation (PDE) solvers into a parallel-in-time simultaneous optimization algorithm. The time-parallelization is provided by the…

This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial…

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…

A simple method for improving cache efficiency of serial and parallel explicit finite procedure with application to casting solidification simulation over three-dimensional complex geometries is presented. The method is based on division of…

This paper applies topology optimisation to the design of structures with periodic microstructural details without length scale separation, i.e. considering the complete macroscopic structure and its response, while resolving all…

This paper addresses boundary prescribed-time stabilization of a one-dimensional heat equation with spatially and temporally varying coefficients. In contrast to asymptotic or exponential stabilization, prescribed-time stabilization ensures…

This paper proposes a novel preconditioned implicit-explicit algorithm enhanced with the extrapolation technique for non-convex optimization problems. The algorithm employs a third-order Adams-Bashforth scheme for the nonlinear and explicit…

Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…

In this paper, we consider partitioned numerical methods for quasi-static multiple-network poroelasticity (MPET) equations, generalizations of the Biot model in poroelasticity for multiple pore networks. Two partitioned numerical methods…

This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such…

Prompt tuning methods have achieved remarkable success in parameter-efficient fine-tuning on large pre-trained models. However, their application to dual-modal fusion-based visual-language pre-trained models (VLPMs), such as GLIP, has…

In this paper, we propose a new finite element approach to simulate the time-dependent Ginzburg-Landau equations under the temporal gauge, and design an efficient preconditioner for the Newton iteration of the resulting discrete system. The…

We present a relative forward error analysis of a mixed-precision preconditioned one-sided Jacobi algorithm, analogous to a two-sided version introduced in [N. J. Higham, F. Tisseur, M. Webb and Z. Zhou, SIAM J. Matrix Anal. Appl. 46…

In this paper, we present a class of nonuniform time-stepping, high-order linear stabilized schemes that can preserve both the discrete energy stability and maximum-bound principle (MBP) for the time-fractional Allen-Cahn equation. To this…

In this paper, we develop the auxiliary space preconditioners for solving the linear system arising from the virtual element methods discretization on polytopal meshes for the second order elliptic equations. The preconditioners are…

In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…

This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…