Related papers: Neumann-Neumann Waveform Relaxation Algorithm in M…
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann and Neumann-Neumann algorithms for the wave equation in space time. Each method is based on a non-overlapping spatial domain decomposition, and the iteration involves…
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann algorithm, formulated specially for multiple subdomains splitting for general parabolic and hyperbolic problems. This method is based on a non-overlapping spatial domain…
We present a waveform relaxation version of the Dirichlet-Neumann and Neumann-Neumann methods for parabolic problems. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain…
We present a waveform relaxation version of the Dirichlet-Neumann method for parabolic problem. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain decomposition, and the iteration…
The Schwarz Waveform Relaxation algorithm (SWR) exchanges the waveform of boundary value between neighbouring sub-domains, which provides a more efficient way than the other Schwarz algorithms to realize distributed computation. However,…
We introduce and compare two domain decomposition based numerical methods, namely the Dirichlet-Neumann and Neumann-Neumann Waveform Relaxation methods (DNWR and NNWR respectively), tailored for solving partial differential equations (PDEs)…
An important challenge when coupling two different time dependent problems is to increase parallelization in time. We suggest a multirate Neumann-Neumann waveform relaxation algorithm to solve two heterogeneous coupled heat equations. In…
We consider Waveform Relaxation (WR) methods for partitioned time-integration of surface-coupled multiphysics problems. WR allows independent time-discretizations on independent and adaptive time-grids, while maintaining high…
We present new Neumann-Neumann algorithms based on a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, the Lagrange multiplier approach provides a coupled…
In this article, we have studied the convergence behavior of the Dirichlet-Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion wave equations in 1D \& 2D for regular domains, where the dimensionless…
In this paper, we apply the Schwarz Waveform Relaxation (SWR) method to the one dimensional Schr{\"o}dinger equation with a general linear or a nonlinear potential. We propose a new algorithm for the Schr{\"o}dinger equation with time…
In this article, we have studied the convergence behavior of the Dirichlet-Neumann and Neumann- Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion-wave equations in 1D & 2D for regular domains, where the…
We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time-adaptive Dirichlet-Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler…
Waveform relaxation (WR) methods are based on partitioning large circuits into sub-circuits which then are solved separately for multiple time steps in so-called time windows, and an iteration is used to converge to the global circuit…
In this study we present a non-overlapping Schwarz waveform relaxation (SWR) method applied to a one dimensional model problem representative of the coupling between the ocean and the atmosphere. This problem includes nonlinear interface…
We present in this paper a proof of well-posedness and convergence for the parallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensional semilinear heat equation. Since the equation we study is an evolution one, each subproblem…
The study of high-dimensional differential equations is challenging and difficult due to the analytical and computational intractability. Here, we improve the speed of waveform relaxation (WR), a method to simulate high-dimensional…
This paper is concerned with global-in-time, nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem. Two approaches are considered: one uses the time-dependent Steklov-Poincar\'e operator and the…
This paper is concerned with the reformulation of Neumann-Neumann Waveform Relaxation (NNWR) methods and Dirichlet-Neumann Waveform Relaxation (DNWR) methods, a family of parallel space-time approaches to solving time-dependent PDEs. By…
We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…