Related papers: A parallel-in-time solver for nonlinear degenerate…
In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a…
The focus of my PhD thesis is on exploring parallel approaches to efficiently solve problems modeled by constraints and presenting a new proposal. Current solvers are very advanced; they are carefully designed to effectively manage the…
Parallel-in-time methods are developed to accelerate the direct-adjoint looping procedure. Particularly, we utilize the Paraexp algorithm, previously developed to integrate equations forward in time, to accelerate the direct-adjoint looping…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
We consider a periodic evolution inclusion defined on an evolution triple of spaces. The inclusion involves also a subdifferential term. We prove existence theorems for both the convex and the nonconvex problem, and we also produce extremal…
We consider time discretization methods for abstract parabolic problems with inhomogeneous linear constraints. Prototype examples that fit into the general framework are the heat equation with inhomogeneous (time dependent) Dirichlet…
In this paper, we propose a parallel-in-time algorithm for approximately solving parabolic equations. In particular, we apply the $k$-step backward differentiation formula, and then develop an iterative solver by using the waveform…
This article deals with a simultaneous abstract evolution equation. This includes a parabolic-hyperbolic phase-field system as an example which consists of a parabolic equation for the relative temperature coupled with a semilinear damped…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…
We consider a non-linear extension of Biot's model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. We perform an implicit discretization in time (backward Euler) and propose two…
In this paper, we propose a space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space-time domain. We focus on the linear solver and its computational…
Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…
Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a…
We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds and exponential stability of discrete approximations…
Within this paper, we introduce partially and fully decoupled time stepping schemes for linear thermo-poroelasticity. This means that the mechanics, heat, and flow equations can be solved sequentially. We provide sufficient conditions on…
Harnessing parallelism in seemingly sequential models is a central challenge for modern machine learning. Several approaches have been proposed for evaluating sequential processes in parallel using iterative fixed-point methods, like…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…