Related papers: A parallel-in-time solver for nonlinear degenerate…
In this paper, for solving a class of linear parabolic equations in rectangular domains, we have proposed an efficient Parareal exponential integrator finite element method. The proposed method first uses the finite element approximation…
The high cost of sequential time integration is one major constraint that limits the speedup of a time-parallel algorithm like the Parareal algorithm due to the difficulty of coarsening time steps in a stiff numerical problem. To address…
In this paper we proposed two new quasi-boundary value methods for regularizing the ill-posed backward heat conduction problems. With a standard finite difference discretization in space and time, the obtained all-at-once nonsymmetric…
Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that…
Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial…
Time-parallel algorithms seek greater concurrency by decomposing the temporal domain of a Partial Differential Equation (PDE), providing possibilities for accelerating the computation of its solution. While parallelisation in time has…
We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having…
We present the conditions under which the time-optimal control problem for a nonlinear non-autonomous linearizable system can be solved by the method of successive approximations, at each step of which a power Markov moment min-problem is…
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the…
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
Recently, ParaExp was proposed for the time integration of hyperbolic problems. It splits the time interval of interest into sub-intervals and computes the solution on each sub-interval in parallel. The overall solution is decomposed into a…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
Parabolic optimal control problems arise in numerous scientific and engineering applications. They typically lead to large-scale coupled forward-backward systems that cannot be treated with classical time-stepping schemes and are…
The aim of the paper is to introduce general techniques in order to optimize the parallel execution time of sorting on a distributed architectures with processors of various speeds. Such an application requires a partitioning step. For…
Recently, inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications. After the discretization, many of inverse problems are reduced to linear systems.…
Different possible sources are discussed for enhancement of the calculation time when solving ordinary differential equations systems to forecast space objects' motion. This paper presents an approach for building an integrator of ordinary…
In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…
We present a unified framework for the analysis of space-time methods based on Galerkin-type time discretizations for parabolic and hyperbolic problems. Crucially, the stability analysis relies on a suitable choice of test functions to…
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…