相关论文: Multi-stage waveform Relaxation and Multisplitting…

This paper addresses some numerical and theoretical aspects of dual Schur domain decomposition methods for linear first-order transient partial differential equations. In this work, we consider the trapezoidal family of schemes for…

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…

In this paper, we are concerned with the global pressure formulation of immiscible incompressible two-phase flow between different rock types. We develop for this problem two robust schemes based on domain decomposition (DD) methods and…

Two combined methods for computing solutions of time-varying semilinear differential-algebraic equations (descriptor systems) are obtained. When constructing the methods, time-varying spectral projectors which can be found numerically are…

Current autoencoder-based disentangled representation learning methods achieve disentanglement by penalizing the (aggregate) posterior to encourage statistical independence of the latent factors. This approach introduces a trade-off between…

Differential-algebraic equations (DAEs) with state-dependent events arise in systems whose continuous dynamics are constrained by algebraic equations and interrupted by mode changes, switching logic, impacts, or state reinitializations.…

This work develops a multiscale solution decomposition (MSD) method for nonlocal-in-time problems to separate a series of known terms with multiscale singularity from the original singular solution such that the remaining unknown part…

Infinite-dimensional differential algebraic equations (short DAEs) with input and output are studied. The concepts of operator nodes and system nodes are extended to systems which additionally may include algebraic constraints.…

This paper proposes a dynamical Variable-separation method for solving parameter-dependent dynamical systems. To achieve this, we establish a dynamical low-rank approximation for the solutions of these dynamical systems by successively…

We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…

The simulation of radio frequency (RF) circuits is one of the severest problems in Design Automation: the information signal or envelope is modulated by a carrier signal with a center frequency typically in the GHz range. Due to Nyquist's…

This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for…

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…

Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…

In this paper a new adaptive algorithm for multi-rate circuit simulation encountered in the design of RF circuits based on spline wavelets is presented. The circuit ordinary differential equations are first rewritten by a system of…

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…

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…

In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the $d$-dimensional advection-diffusion equation, our proposal is a two-level algorithm…

In this work, we propose a multi-stage training strategy for the development of deep learning algorithms applied to problems with multiscale features. Each stage of the pro-posed strategy shares an (almost) identical network structure and…

In this paper we present a novel multiscale splitting approach to solve multiscale Schroedinger equation, which have large different time-scales. The energy potential is based on highly oscillating functions, which are magnitudes faster…