Related papers: Linear and Nonlinear Parareal Methods for the Cahn…

Numerical solutions of time-fractional differential equations encounter significant challenges arising from solution singularities at the initial time. To address this issue, the construction of nonuniform temporal meshes satisfying…

The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather…

This paper introduces a parallel-in-time algorithm for efficient steady-state solution of the eddy current problem. Its main idea is based on the application of the well-known multi-harmonic (or harmonic balance) approach as the coarse…

The Cahn-Hilliard equation is a fundamental model that describes the phase separation process in multi-component mixtures. It has been successfully extended to many different contexts in several scientific fields. In this survey article, we…

Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit…

This paper is concerned with the designing, analyzing and implementing linear and nonlinear discretization scheme for the distributed optimal control problem (OCP) with the Cahn-Hilliard (CH) equation as constrained. We propose three…

We present the design of a multiscale parareal method for kinetic equations in the fluid dynamic regime. The goal is to reduce the cost of a fully kinetic simulation using a parallel in time procedure. Using the multiscale property of…

We prove a weak rate of convergence of a fully discrete scheme for stochastic Cahn--Hilliard equation with additive noise, where the spectral Galerkin method is used in space and the backward Euler method is used in time. Compared with the…

This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…

The numerical simulation of the time-dependent Schr\"odinger equation for quantum systems is a very active research topic. Yet, resolving the solution sufficiently in space and time is challenging and mandates the use of modern…

This paper focuses on efficient steady-state computations of induction machines. In particular, the periodic Parareal algorithm with initial-value coarse problem (PP-IC) is considered for acceleration of classical time-stepping simulations…

This paper presents a concurrent global-local numerical method for solving multiscale parabolic equations in divergence form. The proposed method employs hybrid coefficient to provide accurate macroscopic information while preserving…

Phase-field models are a popular choice in computational physics to describe complex dynamics of substances with multiple phases and are widely used in various applications. We present nonlocal non-isothermal phase-field models of…

In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

Parametric linear programming is central in polyhedral computations and in certain control applications.We propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.

Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type…

This paper is devoted to the problem of time parallelization of assimilation methods applying on unbounded time domain. In this way, we present a general procedure to couple the Luenberger observer with time parallelization algorithm. Our…

Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard type equations, have been widely used to investigate interfacial dynamic problems. Designing accurate, efficient, and stable numerical algorithms for solving the phase…

We propose and analyse new stabilized time marching schemes for Phase Fields model such as Allen-Cahn and Cahn-Hillard equations, when discretized in space with high order finite differences compact schemes. The stabilization applies to…

We present the application of a micro/macro parareal algorithm for a 1-D energy balance climate model with discontinuous and non-monotone coefficients and forcing terms. The micro/macro parareal method uses a coarse propagator, based on a…