Boundary element method for convex boundary control problems

summary:In this paper, we discuss the numerical methods for a class of convex boundary control problems. The boundary element method is applied for the approximations of the problems. The a posteriori error estimators for the boundary element approximations are presented, which can be applied as the indicators of the adaptive mesh refinement of the related boundary element methods

On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations

AbstractIt is well known that, in contrast to Fredholm integral equations, iterated collocation solutions (based on collocation at the Gauss points) to Volterra integral equations of the second kind exhibit optimal discrete superconvergence only at the mesh points. Here, we show that some degree of global superconvergence is possible on the entire interval

Multiscale reconstruction of porous media based on multiple dictionaries learning

Digital modeling of the microstructure is important for studying the physical and transport properties of porous media. Multiscale modeling for porous media can accurately characterize macro-pores and micro-pores in a large-FoV (field of view) high-resolution three-dimensional pore structure model. This paper proposes a multiscale reconstruction algorithm based on multiple dictionaries learning, in which edge patterns and micro-pore patterns from homology high-resolution pore structure are introduced into low-resolution pore structure to build a fine multiscale pore structure model. The qualitative and quantitative comparisons of the experimental results show that the results of multiscale reconstruction are similar to the real high-resolution pore structure in terms of complex pore geometry and pore surface morphology. The geometric, topological and permeability properties of multiscale reconstruction results are almost identical to those of the real high-resolution pore structures. The experiments also demonstrate the proposal algorithm is capable of multiscale reconstruction without regard to the size of the input. This work provides an effective method for fine multiscale modeling of porous media

Optimization of sub-grid scale model for abrasive flow machining curved tube based on large eddy simulation

Abrasive flow machining technology is a new type of precision machining technology. Due to its unique rheological properties, it can process any complex structure and size parts to meet the requirements that conventional machining cannot meet. Combined with the turbulent flow characteristics of the abrasive flow, the large eddy simulation numerical method is used to simulate the machining process of the abrasive flow. The influence of different sub-grid scale models on the simulation results is discussed. Taking curved tube as the research object, the static pressure, dynamic pressure and velocity of different sub-grid models are analyzed to find the best sub-grid scale model. Large eddy simulation method is used to simulate the complex flow channel parts, and the best sub-grid scale model suitable for complex flow channels is determined, which reveals the grinding and polishing rule of abrasive flow and provides academic support for future research. Therefore, it has frontier and important research value

A convergent adaptive finite element method for elliptic Dirichlet boundary control problems

This paper concerns the adaptive finite element method for elliptic Dirichlet boundary control problems in the energy space. The contribution of this paper is twofold. First, we rigorously derive efficient and reliable a posteriori error estimates for finite element approximations of Dirichlet boundary control problems. As a by-product, a priori error estimates are derived in a simple way by introducing appropriate auxiliary problems and establishing certain norm equivalence. Secondly, for the coupled elliptic partial differential system that resulted from the first-order optimality system, we prove that the sequence of adaptively generated discrete solutions including the control, the state and the adjoint state, guided by our newly derived a posteriori error indicators, converges to the true solution along with the convergence of the error estimators. We give some numerical results to confirm our theoretical findings

Blood Flow Velocity Changes in the Middle Cerebral Artery Induced by Driving Fatigue

Abstract. The cerebral blood flow velocity (CBFV) of middle cerebral artery (MCA) was detected during the fatigue driving using Transcranial Doppler. The CBFV was also analyzed after the fatigue driving by different means of relaxation to alleviate brain fatigue. The results show that the CBFV in MCA is reduced by driving fatigue

Largely tunable band structures of few-layer InSe by uniaxial strain

Due to the strong quantum confinement effect, few-layer {\gamma}-InSe exhibits a layer-dependent bandgap, spanning the visible and near infrared regions, and thus recently draws tremendous attention. As a two-dimensional material, the mechanical flexibility provides an additional tuning knob for the electronic structure. Here, for the first time, we engineer the band structures of few-layer and bulk-like InSe by uniaxial tensile strain, and observe salient shift of photoluminescence (PL) peaks. The shift rate of the optical gap is approximately 90-100 meV per 1% strain for 4- to 8-layer samples, which is much larger than that for the widely studied MoS2 monolayer. Density functional calculations well reproduce the observed layer-dependent bandgaps and the strain effect, and reveal that the shift rate decreases with increasing layer number for few-layer InSe. Our study demonstrates that InSe is a very versatile 2D electronic and optoelectronic material, which is suitable for tunable light emitters, photo-detectors and other optoelectronic devices.Comment: submitte