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Nonconforming Finite Element Method Applied to the Driven Cavity Problem
Lim, Roktaek,Sheen, Dongwoo Global Science Press 2017 Communications in computational physics Vol.21 No.4
<B>Abstract</B><P>A cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable cheapest nonconforming finite element pair based on <I>P</I>1×<I>P</I>0 on rectangularmeshes [29] is employed with a minimal modification of the discontinuous Dirichlet data on the top boundary, where is the finite element space of piecewise constant pressures with the globally one-dimensional checker-board pattern subspace eliminated. The proposed Stokes elements have the least number of degrees of freedom compared to those of known stable Stokes elements. Three accuracy indications for our elements are analyzed and numerically verified. Also, various numerous computational results obtained by using our proposed element show excellent accuracy.</P>
Damage Identification of Truss Structures Based on Force Method
Kim, Nam-Il,Lee, Seunghye,Ahn, Namshik,Lee, Jaehong Global Science Press 2015 Advances in applied mathematics and mechanics Vol.7 No.2
<B>Abstract</B><P>An computationally efficient damage identification technique for the planar and space truss structures is presented based on the force method and the micro genetic algorithm. For this purpose, the general equilibrium equations and the kinematic relations in which the reaction forces and the displacements at nodes are take into account, respectively, are formulated. The compatibility equations in terms of forces are explicitly presented using the singular value decomposition (SVD) technique. Then governing equations with unknown reaction forces and initial elongations are derived. Next, the micro genetic algorithm (MGA) is used to properly identify the site and extent of multiple damage cases in truss structures. In order to verify the accuracy and the superiority of the proposed damage detection technique, the numerical solutions are presented for the planar and space truss models. The numerical results indicate that the combination of the force method and the MGA can provide a reliable tool to accurately and efficiently identify the multiple damages of the truss structures.</P>
Dynamical Motion Driven by Periodic Forcing on an Open Elastic Tube in Fluid
Lee, Wanho,Lim, Sookkyung,Jung, Eunok Global Science Press 2012 Communications in computational physics Vol.12 No.2
<B>Abstract</B><P>We present a three dimensional model of an open elastic tube immersed in fluid to understand valveless pumping mechanism. A fluid-tube interaction problem is simulated by the volume conserved immersed boundary method which prevents the generation of spurious velocity field near the tube and local cluster of the tube surface. In order to explain pumping phenomena without valves, average net flow is measured by changing parameter values such as pumping frequency, compression duration, and pumping amplitude. Some frequencies that make the system reach maximal or minimal net flow are selected to study case by case. We also study the effectiveness of fluid mixing using the Shannon entropy increase rate.</P>
Parallel Tempering Simulation on Generalized Canonical Ensemble
Xu, Shun,Zhou, Xin,Ou-Yang, Zhong-Can Global Science Press 2012 Communications in computational physics Vol.12 No.5
<B>Abstract</B><P>Parallel tempering simulation is widely used in enhanced sampling of systems with complex energy surfaces. We hereby introduce generalized canonical ensemble (GCE) instead of the usual canonical ensemble into the parallel tempering to further improve abilities of the simulation technique. GCE utilizes an adapted weight function to obtain a unimodal energy distribution even in phase-coexisting region and then the parallel tempering on GCE yields the steady swap acceptance rates (SARs) instead of the fluctuated SARs in that on canonical ensemble. With the steady SARs, we can facilitate assign the parameters of the parallel tempering simulation to more efficiently reach equilibrium among different phases. We illustrate the parallel tempering simulation on GCE in the phase-coexisting region of 2-dimensional Potts model, a benchmark system for new simulation method developing. The result indicates that the new parallel tempering method is more efficient to estimate statistical quantities (i.e., to sample the conformational space) than the normal parallel tempering, specially in phase-coexisting regions of larger systems.</P>
Distributed Feedback Control of the Benjamin-Bona-Mahony-Burgers Equation by a Reduced-Order Model
Piao, Guang-Ri,Lee, Hyung-Chun Global Science Press 2015 East Asian Journal on Applied Mathematics Vol.5 No.1
<B>Abstract</B><P>A reduced-order model for distributed feedback control of the Benjamin-Bona-Mahony-Burgers (BBMB) equation is discussed. To retain more information in our model, we first calculate the functional gain in the full-order case, and then invoke the proper orthogonal decomposition (POD) method to design a low-order controller and thereby reduce the order of the model. Numerical experiments demonstrate that a solution of the reduced-order model performs well in comparison with a solution for the full-order description.</P>
Construction of GPT-Vanishing Structures Using Shape Derivative
Global Science Press 2017 Journal of computational mathematics Vol.35 No.5
<P>The Generalized Polarization Tensors (GPT) is a series of tensors which contain informations on the shape of a domain and its material parameters. The aim of this paper is to provide a method of constructing GPT-vanishing structures using shape derivative for two-dimensional conductivity or anti-plane elasticity problem. We assume a multi-coating geometry as a candidate of GPT-vanishing structure. We define a cost functional to minimize GPT and compute the shape derivative of this functional deriving an asymptotic expansion of the perturbations of the GPTs due to a small deformation of interfaces of the structure. We present some numerical examples of GPT-vanishing structures for several different shaped inclusions.</P>