Related papers: Domain decomposition methods with overlapping subd…
We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the…
We deal with the numerical solution of the time-dependent partial differential equations using the adaptive space-time discontinuous Galerkin (DG) method. The discretization leads to a nonlinear algebraic system at each time level, the size…
We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…
In this paper, we propose two novel Robin-type domain decomposition methods based on the two-grid techniques for the coupled Stokes-Darcy system. Our schemes firstly adopt the existing Robin-type domain decomposition algorithm to obtain the…
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes-Darcy model, in which different time steps can be used in the flow region and in the porous medium. The coupled system is…
A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…
We propose a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the…
We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…
We propose an efficient algorithm that combines overlapping domain decomposition and proper generalized decomposition (PGD) to construct surrogate models of linear elliptic parametric problems. The technique is composed of an offline and an…
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
We propose new domain decomposition methods for systems of partial differential equations in two and three dimensions. The algorithms are derived with the help of the Smith factorization of the operator. This could also be validated by…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…
In this paper, we propose and test a novel diagonal sweeping domain decomposition method (DDM) with source transfer for solving the high-frequency Helmholtz equation in $\mathbb{R}^n$. In the method the computational domain is partitioned…
Unsupervised domain adaptation (UDA) techniques are vital for semantic segmentation in geosciences, effectively utilizing remote sensing imagery across diverse domains. However, most existing UDA methods, which focus on domain alignment at…