Related papers: Hessian-Enhanced Alternating Frequency/Time method…
The design of numerical boundary conditions is a challenging problem that has been tackled in different ways depending on the nature of the problem and the numerical scheme used to solve it. In this paper we present a new weighted…
This paper aims to combine the advantages of the Jordan-Moore-Gibson-Thompson JMGT equation as an advanced model in nonlinear acoustics with a frequency domain formulation of the forward and inverse problem of acoustic nonlinearity…
The transmission of acoustic phonons is an important element in the design and performance of nano-mechanical devices operating in the mesoscopic limit. Analytic expressions for the power transmission coefficient, T, exist only in the…
A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix splittings for $\mathsf H$-matrices. The…
In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a…
We show that the use of the electromagnetic inverse source framework offers great flexibility in the design of metasurfaces. In particular, this approach is advantageous for antenna design applications where the goal is often to satisfy a…
This study presents a meshfree two-dimensional fractional-order Element-Free Galerkin (2D f-EFG) method as a viable alternative to conventional mesh-based FEM for a numerical solution of (spatial) fractional-order differential equations…
This paper presents an efficient method for extracting the second-order sensitivities from a system of implicit nonlinear equations on upcoming graphical processing units (GPU) dominated computer systems. We design a custom automatic…
Marine controlled-source electromagnetic (CSEM) method has proved its potential in detecting highly resistive hydrocarbon bearing formations. A novel frequency domain CSEM inversion approach using fictitious wave domain time stepping…
In this paper, we focus on the finite difference approximation of nonlinear degenerate parabolic equations, a special class of parabolic equations where the viscous term vanishes in certain regions. This vanishing gives rise to additional…
This article proposes a new numerical algorithm for second order elliptic equations in non-divergence form. The new method is based on a discrete weak Hessian operator locally constructed by following the weak Galerkin strategy. The…
Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model analysis and regression diagnostics. When nonlinear models…
The ability to perform mathematical computations using metastructures is an emergent paradigm that carries the potential of wave-based analog computing to the realm of near-speed-of-light, low-loss, compact devices. We theoretically…
The structural properties of mechanical metamaterials are typically studied with two-scale methods based on computational homogenization. Because such materials have a complex microstructure, enriched schemes such as second-order…
We leverage second-order information for tuning of inverse optimal controllers for a class of discrete-time nonlinear input-affine systems. For this, we select the input penalty matrix, representing a tuning knob, to yield the Hessian of…
This paper presents an innovative approach to computational acoustic imaging of biperiodic surfaces, exploiting the capabilities of an acoustic superlens to overcome the diffraction limit. We address the challenge of imaging physical…
In this paper, we present a novel second-order accurate Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming polygonal grids, in order to avoid the typical mesh distortion caused by shear flows in Lagrangian-type…
Environmental Sound Classification (ESC) is a rapidly evolving field that recently demonstrated the advantages of application of visual domain techniques to the audio-related tasks. Previous studies indicate that the domain-specific…
We investigate the computation of Hessian matrices via Automatic Differentiation, using a graph model and an algebraic model. The graph model reveals the inherent symmetries involved in calculating the Hessian. The algebraic model, based on…
This article is concerned with tensor field tomography in a fairly general setting, that takes refraction, attenuation and time-dependence of tensor fields into account. The mathematical model is given by attenuated ray transforms of the…