Related papers: Time integration of finite element models with non…
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…
Fast-rate models are essential for control design, specifically to address intersample behavior. The aim of this paper is to develop a frequency-domain non-parametric identification technique to estimate fast-rate models of systems that…
Hybrid systems are mostly modelled, simulated, and verified in the time domain by computer scientists. Engineers, however, use both frequency and time domain modelling due to their distinct advantages. For example, frequency domain…
Membrane-type Acoustic Metamaterials (MAMs) have demonstrated unusual capacity in controlling low-frequency sound transmission/reflection. In this paper, an analytical vibroacoustic membrane model is developed to study sound transmission…
We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…
Medical ultrasound imaging is the most widespread real-time non-invasive imaging system and its formulation comprises signal transmission, signal reception, and image formation. Ultrasound signal transmission modelling has been formalized…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…
This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of…
In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…
The paper extends core results of behavioral systems theory from linear to affine time-invariant systems. We characterize the behavior of affine time-invariant systems via kernel, input-output, state-space, and finite-horizon data-driven…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
This work identifies the general approach for linearising any power system component in the harmonic domain, that is with respect to its Fourier series coefficients. This ability enables detailed harmonic analysis, and is key as more power…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the main concerns for the use of nonlocal models in real world…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Stability and convergence analysis for the domain decomposition finite element/finite difference (FE/FD) method is presented. The analysis is designed for semi-discrete finite element scheme for the time-dependent Maxwell's equations. The…
This paper proposes a methodology to estimate stress in the subsurface by a hybrid method combining finite element modeling and neural networks. This methodology exploits the idea of obtaining a multi-frequency solution in the numerical…
In this article, the piecewise-linear finite element method (FEM) is applied to approximate the solution of time-fractional diffusion equations on bounded convex domains. Standard energy arguments do not provide satisfactory results for…