Related papers: Dirichlet-Neumann Waveform Relaxation Method with …
In this paper, we propose the invariant subspace approach to find exact solutions of time-fractional partial differential equations (PDEs) with time delay. An algorithmic approach of finding invariant subspaces for the generalized…
We are motivated to solve differential algebraic equations with new multi-stage and multisplitting methods. The multi-stage strategy of the waveform relaxation (WR) methods are given with outer and inner iterations. While the outer…
We consider the Dirichlet-Neumann iteration for partitioned simulation of thermal fluid-structure interaction, also called conjugate heat transfer. We analyze its convergence rate for two coupled fully discretized 1D linear heat equations…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
Many real-world applications require aligning two temporal sequences, including bioinformatics, handwriting recognition, activity recognition, and human-robot coordination. Dynamic Time Warping (DTW) is a popular alignment method, but can…
We study the dynamics of the equation obtained by Schryer and Walker for the motion of domain walls. The reduced equation is a reaction diffusion equation for the angle between the applied field and the magnetization vector. If the hard…
Optimized Schwarz Waveform Relaxation methods have been developed over the last decade for the parallel solution of evolution problems. They are based on a decomposition in space and an iteration, where only subproblems in space-time need…
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…
This work presents a numerical investigation of different approximation techniques for the temporal weights used in the Dual Weighted Residual (DWR) method applied to a time-dependent convection-diffusion equation which is assumed to be…
In this work, a multirate in time approach resolving the different time scales of a convection-dominated transport and coupled fluid flow is developed and studied in view of goal-oriented error control by means of the Dual Weighted Residual…
This paper presents a novel Diffusion-Wavelet (DiWa) approach for Single-Image Super-Resolution (SISR). It leverages the strengths of Denoising Diffusion Probabilistic Models (DDPMs) and Discrete Wavelet Transformation (DWT). By enabling…
This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…
We present new Dirichlet-Neumann and Neumann-Dirichlet algorithms with a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, we use the Lagrange multiplier approach to…
In recent work, Li et al.\ (Comm.\ Math.\ Sci., 7:81-107, 2009) developed a diffuse-domain method (DDM) for solving partial differential equations in complex, dynamic geometries with Dirichlet, Neumann, and Robin boundary conditions. The…
Diffusion-limited reactions (DLR) are usually described within the Smoluchowski theory, which neglects interactions between the diffusing components. We propose a first extension of such frame- work that incorporates excluded-volume…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
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 provide a preliminary comparison of the dispersion properties, specifically the time-amplification factor, the scaled group velocity and the error in the phase speed of four spatiotemporal discretization schemes utilized for solving the…
A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an…
We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which,…