Related papers: Domain decomposition methods with overlapping subd…

We present a new methodology for the real-time reduced-order modeling of stochastic partial differential equations called the dynamically/bi-orthonormal (DBO) decomposition. In this method, the stochastic fields are approximated by a…

Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of delay-coordinates embedding and DMD, i.e., delay-coordinates…

Decomposing the domain of a function into parts has many uses in mathematics. A domain may naturally be a union of pieces, a function may be defined by cases, or different boundary conditions may hold on different regions. For any…

Compactly expressing large-scale datasets through Multivariate Functional Approximations (MFA) can be critically important for analysis and visualization to drive scientific discovery. Tackling such problems requires scalable data…

Parabolic equations on evolving domains model a multitude of applications including various industrial processes such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations…

We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multi-resolution analysis allows for a decomposition method capable of robustly separating complex systems into a hierarchy of…

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory…

Modal decomposition techniques are showing a fast growth in popularity for their good properties as data-driven tools. There are several modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode…

This paper presents a strategy for the computation of structures with repeated patterns based on domain decomposition and block Krylov solvers. It can be seen as a special variant of the FETI method. We propose using the presence of…

We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it…

In many modern computer application problems, the classification of image data plays an important role. Among many different supervised machine learning models, convolutional neural networks (CNNs) and linear discriminant analysis (LDA) as…

Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and…

The discretization of certain integral equations, e.g., the first-kind Fredholm equation of Laplace's equation, leads to symmetric positive-definite linear systems, where the coefficient matrix is dense and often ill-conditioned. We…

Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in…

In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element…

This work considers numerical methods for the time-dependent Schr\"{o}dinger equation of incommensurate systems. By using a plane wave method for spatial discretization, the incommensurate problem is lifted to a higher dimension that…

Dual decomposition is widely utilized in distributed optimization of multi-agent systems. In practice, the dual decomposition algorithm is desired to admit an asynchronous implementation due to imperfect communication, such as time delay…

Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…

In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…

Hybrid algorithms, which combine black-box machine learning methods with experience from traditional numerical methods and domain expertise from diverse application areas, are progressively gaining importance in scientific machine learning…