An implicit method for numerical solution of differential equations

The paper presents an implicit method for numerical solution of differential equations, based on the use of the derivatives of the right-hand side jointly with a directed motion in the discrepancy space on passing to the next integration layer. Two examples of solving equations by the proposed method are considered.     

An accurate sampling-based method for approximating geometry

We present a sampling-based method for approximating the boundary of a geometry defined by various geometric operations. Based on a novel adaptive sampling condition, we first construct volumetric grids such that an error-minimizing point can be found in each cell to capture all the geometric objects inside the cell. We then construct a polygonal model from the grid. We guarantee the boundary approximation has the same topology as the exact surfaces, and the maximum approximation error from the exact surfaces is bounded by a user specified tolerance. Our method is robust and easy to implement. We have applied it in various applications such as remeshing of polygonal models, Boolean operations, and offsetting operations. We report experimental results on a variety of CAD models.     

An implicit/explicit spectral method for Burgers' equation

Chebyshev spectral collocation methods for approximating the solution of Burgers' equation are defined and analyzed. Discretization in time by an implicit/explicit single step method is discussed. This method is shown to be stable under a very weak condition on the time step, for the (linear) diffusive part is dealt with implicitly. Besides, fast transform methods can be used to compute the explicit (non linear) convective term. Optimal order error estimates are established in the weighted L²-norm. The research of this author has been partially supported by the U.S. Army through its European Research Office under contract No. DAJA-84-C-0035.     

An implicit off-step point method for the integration of stiff differential equations

Recently England introducedk-step formulas of orderk+2 which use one off-step point for the integration of stiff differential equations. These formulas are slightly modified, theorems on the error constants are given and numerical results are presented.     

Border-tracing algorithm implementation for the femoral geometry reconstruction

In some orthopaedic applications such as the design of custom-made hip prostheses, reconstruction of the bone morphology is a fundamental step. Different methods are available to extract the geometry of the femoral medullary canal from computed tomography (CT) images. In this research, an automatic procedure (border-tracing method) for the extraction of bone contours was implemented and validated. A composite replica of the human femur was scanned and the CT images processed using three different methods, a manual procedure; the border-tracing algorithm; and a threshold-based method. The resulting contours were used to estimate the accuracy of the implemented procedure. The two software techniques were more accurate than the manual procedure. Then, these two procedures were applied to an in vivo CT data set in order to determine to most critical region for repeatability. Only for the images located in this region, the repeatability measurement was carried out for six in vivo CT data sets to evaluate the inter-femur repeatability. The border-tracing method was found to achieve the highest repeatability.     

An implicit relevance feedback method for CBIR with real-time eye tracking

Relevance feedback is an efficient approach to improve the performance of content-based image retrieval systems, and implicit relevance feedback approaches, which gather users’ feedback by biometric devices (e.g. eye tracker), have extensively investigated in recent years. This paper proposes a novel image retrieval system with implicit relevance feedback, named eye tracking based relevance feedback system (ETRFs). ETRFs is composed of three main modules: image retrieval subsystem based on bag-of-word architecture; user relevance assessment that implicitly acquires relevant images with the help of a modern eye tracker; and relevance feedback module that applies a weighted query expansion method to fuse users’ relevance feedback. ETRFs is implemented online and real-time, which makes it remarkably distinguish from other offline systems. Ten subjects participate our experiments on the dataset of Oxford buildings and UKBench. The experimental results demonstrate that ETRFs achieves notable improvement for image retrieval performance.     

An implicit high-order discontinuous Galerkin method for steady and unsteady incompressible flows

This paper presents the latest developments of a discontinuous Galerkin (DG) method for incompressible flows introduced in [Bassi F, Crivellini A, Di Pietro DA, Rebay S. An artificial compressibility flux for the discontinuous Galerkin solution of the incompressible Navier–Stokes equations. J Comput Phys 2006;218(2):794–815] for the steady Navier–Stokes equations and extended in [Bassi F, Crivellini A. A high-order discontinuous Galerkin method for natural convection problems. In: Wesseling P, Oñate E, Periaux J, editors. Electronic proceedings of the ECCOMAS CFD 2006 conference, Egmond aan Zee, The Netherlands, September 5–8; 2006. TU Delft] to the coupled Navier–Stokes and energy equations governing natural convection flows.

The method is fully implicit and applies to the governing equations in primitive variable form. Its distinguishing feature is the formulation of the inviscid interface flux, which is based on the solution of local Riemann problems associated with the artificial compressibility perturbation of the Euler equations. The tight coupling between pressure and velocity so introduced stabilizes the method and allows using equal-order approximation spaces for both pressure and velocity. Since, independently of the amount of artificial compressibility added, the interface flux reduces to the physical one for vanishing interface jumps, the resulting method is strongly consistent.

In this paper, we present a review of the method together with two recently developed issues: (i) the high-order DG discretization of the incompressible Euler equations; (ii) the high-order implicit time integration of unsteady flows. The accuracy and versatility of the method are demonstrated by a suite of computations of steady and unsteady, inviscid and viscous incompressible flows.     

An implicit marching method for the two-dimensional reduced Navier-Stokes equations at arbitrary mach number

An implicit marching procedure is developed from a parabolized form of the two-dimensional Navier-Stokes equations with allowance for chemical reaction in an effort to predict the flow in highly viscous chemical laser nozzles. The equations governing the fluid dynamics are linearized and solved as a coupled implicit system in a manner which requires no iteration and in which the pressure gradient for internal flows emerges directly as part of the solution without iteration. Accuracy and stability of the method are tested by computing the flow in the entrance region between parallel flat plates and comparing the results to analytical results as well as experimental data. Upon completion of these tests the procedure is used to predict the highly viscous chemically reacting flow in a laser nozzle and inlet duct.     

隐式B-样条曲线重建的直接Greville纵标法

提出了一种以隐式B-样条曲线为表达形式,基于直接Greville纵标的曲线重建方法。根据点云建立有向距离场,并作为B-样条函数的Greville纵标,然后根据高影响区内的平均代数误差优化Greville纵标;得到一个隐式B-样条函数,该函数的零点集即为重建曲线。该方法具有模型简单,重建速度快,无多余分支,无需手工调节任何参数的优点。实验结果证实了该直接法的效率明显高于点拟合法和普通场拟合法,以几何误差为准则的精度亦优于普通场拟合方法。     

An implicit and incremental formulation for the solution of elastoplastic problems by the finite element method

In this paper, a new approach is developed to solve elastoplastic problems by the finite element method. This approach involves two steps: (1) A mechanical formulation using the principle of virtual work and an implicit incremental form of the constitutive equations. This form is obtained by an approximate integration of the flow rules over the increment and includes the yield criterion itself. (2) A resolution algorithm to solve the nonlinear equations obtained by the mechanical formulation: Two resolution algorithms based on the Newton-Raphson method are proposed and compared. As the mechanical formulation is no more bound to the resolution algorithm, the results obtained by these two algorithms are the same and are path independent. Two numerical examples are presented: A thick cylinder under an internal pressure and a tensile sample. The numerical results obtained by the presented approach are compared with those obtained by the classical I.S.M. The comparison shows that the accuracy of the results does not vary when the load increment size increases as in the I.S.M. For a given accuracy this method requires about 15 times less computer time than the I.S.M. for the same memory space. This approach is easy to implement in a program based on the I.S.M. and has been extended to compressible and viscoplastic materials.     

An introduction to Wu's method for mechanical theorem proving in geometry

Wu's algebraic method for mechanically proving geometry theorems is presented at a level as elementary as possible with sufficient examples for further understanding the complete method.The work reported here was supported by NSF Grant DCR-8503498.     

An auto-tuning method for dominant-pole placement using implicit model reference adaptive control technique

In order to implement dominant-pole placement by means of auto-tuning scheme, an implicit model reference adaptive system (IMRAS) is presented in this paper. Some issues regarding auto-tuning for dominant-pole placement based on the proposed IMRAS are discussed. The proposed auto-tuning scheme is illustrated on four types of linear models. Simulation results show that dominant poles can be placed near the desired ones which are assigned in the dominant-pole-based reference model.     

An implicit, exact dual adjoint solution method for turbulent flows on unstructured grids

An implicit algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The current implementation allows for multiple right-hand side vectors, enabling simultaneous adjoint solutions for several cost functions or constraints with minimal additional storage requirements, while reducing the solution time compared to serial applications of the adjoint solver. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.     

An iterative matrix-free method in implicit immersed boundary/continuum methods

The objective of this paper is to present an iterative solution strategy for implicit immersed boundary/continuum methods. An overview of the newly proposed immersed continuum method in conjunction with the traditional immersed boundary method will also be presented. As a key ingredient of the fully implicit time integration, a matrix-free combination of Newton–Raphson iteration and GMRES iterative linear solver is proposed.     

用于超分辨率重建的同构过完备字典学习方法

构造合适的过完备字典是基于稀疏表示的超分辨率重建中的关键问题之一。在最大似然估计准则下,建立基于混合高斯的同构过完备字典学习模型。模型采用加权的l2范数来刻画分解残差,由分解残差设计权值矩阵,并且将同构的双字典学习问题转化为单字典的学习。采用稀疏编码和字典更新的交替迭代策略完成目标函数的求解,由内点法进行稀疏编码,采用拉格朗日对偶法完成字典更新。最后将学习得到的字典用于超分辨率重建实验,并与其他方法进行比较。实验结果验证了该模型和算法的有效性。     

An efficient iterative method for nearly perfect reconstruction non-uniform filter bank

In this paper, a computationally efficient iterative algorithm is presented for the design of multi-channel nearly perfect reconstruction nonuniform filter bank using the modified window functions such as Kaiser, Cosh and Exponential windows with exploiting a new perfect reconstruction condition of nonuniform filter banks instead of using complex objective functions. The cutoff frequency is optimized using linear optimization technique such that the magnitude response of a prototype filter at quadrature frequency is approximately equal to 0.707. The simulation results illustrate significant reduction in amplitude distortion, number of iteration and computation time as compared to earlier existing techniques. The proposed algorithm is simple, easy to implement, and linear in nature. When exploited for subband coding of electrocardiogram (ECG) signals, the proposed method yields good fidelity performance measuring parameters.     

An implicit method for three dimensional viscous flow with application to cones at angle of attack

An iteration method for solving the implicit difference equations associated with three nonlinear parabolic differential equations is derived and analyzed. The method is applied to the high Reynolds number viscous flow around a cone at high angle of attack. The requirements which must be met to ensure convergence of the iterations are obtained. In addition, an analysis of the stability of the difference equations is presented and discussed. The numerical results are compared with experimental data for a 10° cone at 12° angle of attack, and a 5·6° cone at 8° angle of attack. The agreement is very good.     

一种跟踪隐式曲面交线的算法*

传统的跟踪方法在求下一个跟踪点时一般是采用迭代法,而迭代法会出现初始值的选取和迭代收敛的问题。为此提出一种跟踪隐式曲面交线的算法。该方法最主要的优点是：在跟踪隐式曲面的交线时,在前一个跟踪交点已经求得的情况下,利用正方形与两个隐式曲面的交点,即可快速有效地求出下一个跟踪点,而不用涉及迭代收敛的判断。     

Wearable artificial skin layer for the reconstruction of touched geometry by morphological computation

ABSTRACT

This paper proposes a wearable haptic sensor for the reconstruction of the surface geometry of an object to be touched. The proposed haptic sensor is a thin rubber artificial skin layer that is formed around the user's finger or other body part and contains a small embedded strain gauge for measuring large deformations. The sensor can be easily fabricated by rubber dipping. First, it was demonstrated that the proposed sensor is not only able to statically detect the curvature of the touched surface but can also measure deformations due to rapid light tapping with robustness against motion noise. As an illustrative demonstration of morphological computation in haptics, it was then demonstrated that it is possible to reconstruct the geometry of tiny undulations in the surface of the touched object from the information obtained by the proposed sensor.