Identifying the wavenumber for the inverse Helmholtz problem using an enriched finite element formulation

Abstract

, (2018) 'Identifying the wavenumber for the inverse Helmholtz problem using an enriched nite element formulation.', Computer methods in applied mechanics and engineering., 340. pp. 615-629.

Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition

“…Our second test example consists of a plane wave scattering by a circular cylinder studied for example in [78,22]. If the incident wave propagates in the negative x-axis direction then the scattered wave field can be evaluated analytically using the expression…”

Adaptive Boundary Control of Flexible Manipulators with Parameter Uncertainty Based on RBF Neural Network

“…From (77), we can derive that u (4) i (L i , t) � 0. Based on the variable separation method, let the solution be u i (x i , t) � U i (x i ) • T(t); then, the transversal deformations of the two flexible links can be written as…”

“…i.e., U (4) i (x i ) − μ € X � 0. Substituting the boundary conditions (11), (15), and (17), we can get the solution of equation (78) that U i (x i ) � 0, which means q � 0. us, the system performance can be asymptotically stabilized with properly choosing the control parameters, leading to the tracking error e i ⟶ 0, u i (x i ) ⟶ 0, and _ u i (x i ) ⟶ 0 as t ⟶ ∞.…”

“…e dynamics of such class of systems is usually governed by a combination of ODEs, PDEs, and a set of boundary conditions. Conventional control algorithms for parameter uncertainty are generally constructed on dynamic models derived from the assumed mode method or finite element method [2][3][4], both using mode truncations. In spite of the convenience, some defects still exist in these methods, such as spillover instability caused by neglected higher modes, error of mode truncations, and higher order of the controller.…”

Explicit time integration with lumped mass matrix for enriched finite elements solution of time domain wave problems

“…The partition of unity enrichment technique led to a vast amount of literature comprising different approaches such as the generalized finite element method [20,21], the ultra-weak variational formulation [22,23], as well as the discontinuous enrichment method [24][25][26][27][28]. The PUFEM is also adapted for solving forward problems for heterogeneous materials [29], elastic waves [30,31] and more recently for inverse problem [32]. In [33][34][35] the authors adopt the PUFEM with implicit integration in time for solving various transient diffusion problems.…”