Related papers: Reduced Basis Method for the Elastic Scattering by…
In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…
This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller (\cite{BM71}) boundary integral…
This paper presents a half-analytical elastic solution convenient for parametric studies of 2D cracked pavements. The pavement structure is reduced to three elastic and homogeneous equivalent layers resting on a soil. In a similar way than…
We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…
We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…
We consider model order reduction for a free boundary problem of an osmotic cell that is parameterized by material parameters as well as the initial shape of the cell. Our approach is based on an Arbitrary-Lagrangian-Eulerian description of…
In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the…
The need for accelerating the repeated solving of certain parametrized systems motivates the development of more efficient reduced order methods. The classical reduced basis method is popular due to an offline-online decomposition and a…
In this tutorial paper, we consider the problem of electromagnetic scattering by a bounded two-dimensional dielectric object, and discuss certain interesting properties of the scattered field. Using the electric field integral equation,…
This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…
This work focuses on steady and unsteady Navier-Stokes equations in a reduced order modeling framework. The methodology proposed is based on a Proper Orthogonal Decomposition within a levelset geometry description and the problems of…
We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions…
In this article, a novel analytical approach is presented for the analysis of electromagnetic (EM) scattering from radially inhomogeneous spherical structures (RISSs) based on the duality principle. According to the spherical symmetry,…
This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local…
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…
The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of…
In this work, we present a POD-greedy reduced basis method for parabolic partial differential equations (PDEs), based on the least squares space-time formulation proposed in [Hinze, Kahle, Stahl, A least-squares space-time approach for…
We consider parameter identification problems in parametrized partial differential equations (PDE). This leads to nonlinear ill-posed inverse problems. One way to solve them are iterative regularization methods, which typically require…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…