Semi-implicit Integration Method Research Articles

Chaotic Communication System with Symmetry-Based Modulation

Communication systems based on chaotic synchronization are gaining interest in the area of secure and covert data transmission. In this paper, a novel digital communication technique based on a coherent chaotic data transmission approach is proposed. In general, this technique resembles the well-known approach based on the modulation of nonlinearity parameters. The key idea of this study is to modulate a signal by varying not the system parameter but the symmetry coefficient in discrete chaotic models obtained by the special numerical integration method. For this purpose, the self-adjoint semi-implicit integration method of order 2 is used to obtain discrete master and slave models of the considered chaotic oscillator. The experimental results explicitly show that, like during parameter modulation, transmitting and receiving oscillators may completely synchronize only if the symmetry coefficients are equal in both systems. The architecture of the communication system based on the proposed modulation is presented. The practical applicability of the approach is confirmed by transmitting a test binary sequence between the transmitter and receiver models and preliminary benchmarking of the obtained communication system. Since the symmetry coefficient modulation does not significantly impact the chaotic behavior of the transmitting digital system, its better suitability for covert messaging was experimentally confirmed by comparing it with the parameter modulation technique.

Non-Iterative Semi-Implicit Integration Method for Active Distribution Networks With a High Penetration of Distributed Generations

With the increasing penetration of distributed generations (DGs), the equations governing active distribution networks (ADNs) exhibit stronger nonlinearity and greater stiffness. Additionally, the uncertainties associated with DGs mean that ADNs face more frequent and diversified disturbances. The novel properties of ADNs exacerbate the instabilities and computational burdens on iterations of time-domain simulation when using traditional explicit and implicit integration algorithms. This article proposes a novel semi-implicit integration method incorporating an adaptive Jacobian matrix to solve the differential equations (DEs) governing ADNs, resulting in a non-iterative technique with good numerical stability. The proposed approach simultaneously combines the advantages of both explicit and implicit methods. Moreover, a parameter optimization strategy that comprehensively considers stability, efficiency, and accuracy conditions and an adaptive Jacobian matrix update strategy are developed to further improve the numerical performance of the proposed method. Finally, the proposed method is validated using a modified 33-node system and a practical 436-node distribution system. The simulation results demonstrate the prominent advantages of the proposed method in terms of stability and efficiency compared with the modified Euler and trapezoidal methods.

Semi-Implicit and Semi-Explicit Adams-Bashforth-Moulton Methods

Multistep integration methods are widespread in the simulation of high-dimensional dynamical systems due to their low computational costs. However, the stability of these methods decreases with the increase of the accuracy order, so there is a known room for improvement. One of the possible ways to increase stability is implicit integration, but it consequently leads to sufficient growth in computational costs. Recently, the development of semi-implicit techniques achieved great success in the construction of highly efficient single-step ordinary differential equations (ODE) solvers. Thus, the development of multistep semi-implicit integration methods is of interest. In this paper, we propose the simple solution to increase the numerical efficiency of Adams-Bashforth-Moulton predictor-corrector methods using semi-implicit integration. We present a general description of the proposed methods and explicitly show the superiority of ODE solvers based on semi-implicit predictor-corrector methods over their explicit and implicit counterparts. To validate this, performance plots are given for simulation of the van der Pol oscillator and the Rossler chaotic system with fixed and variable stepsize. The obtained results can be applied in the development of advanced simulation software.

Implications of the choice of predictors for semi-implicit Picard integral deferred correction methods

High-order semi-implicit Picard integral deferred correction (SIPIDC) methods have previously been proposed for the time-integration of partial differential equations with two or more disparate time scales. The SIPIDC methods studied to date compute a high-order approximation byfirst computing a provisional solution with a first-order semi-implicit method and then using a similar semi-implicit method to solve a series of correction equations, each of which raises the order of accuracy of the solution by one. This study assesses the efficiency of SIPIDC methods that instead use standard semi-implicit methods with orders two through four to compute the provisional solution. Numerical results indicate that using a method with more than first-order accuracy in the computation of the provisional solution increases the efficiency of SIPIDC methods in some cases. First-order PIDC corrections can improve the efficiency of semi-implicit integration methods based on backward difference formulae (BDF) or Runge‐Kutta methods while maintaining desirable stability properties. Finally, the phenomenon of order reduction, which may be encountered in the integration of stiff problems, can be partially alleviated by the use of BDF methods in the computation of the provisional solution.

Low damped cloth simulation

This paper proposes a new implicit integration technique that reproduces a stable cloth without introducing excessive damping forces. Semi-implicit integration methods have been widely used in cloth simulations because of their high stability and speed. Artificial internal damping forces are generated during the linearization process of the semi-implicit integration. The simulations become extremely stable due to the artificial forces; however, the forces significantly degrade the realism of cloth simulations, since they are generated with respect to rotational rigid motions, as well as internal deformations. Hence, we propose a new method to decrease the damping artifacts. The artificial internal damping forces are computed solely for pure internal deformations, and are stably incorporated into the dynamical system. Experiments show that our simulator can reproduce various cloth materials without excessive damping artifacts even in real-time.

On the Use of Implicit Integration Methods and the Absolute Nodal Coordinate Formulation in the Analysis of Elasto-Plastic Deformation Problems

In the general theory of continuum mechanics, the state of rotation and deformation of material points can be uniquely defined from the displacement field by using the nine independent components of the displacement gradients. For this reason, the use of the absolute rotation parameters as nodal coordinates, without relating them to the displacement gradients, leads to coordinate redundancy that leads to numerical and fundamental problems in many existing large rotation finite element formulations. Because of this fundamental problem, special measures that require modifications of the numerical integration methods were proposed in the literature in order to satisfy the principle of work and energy. As demonstrated in this paper, no such measures need to be taken when the finite element absolute nodal coordinate formulation is used since the principle of work and energy are automatically satisfied. This formulation does not suffer from the problem of coordinate redundancy and ensures the continuity of stresses and strains at the nodal points. In this study, the use of the implicit integration methods with the consistent Lagrangian elasto-plastic tangent moduli is examined when the absolute nodal coordinate formulation is used. The performance of different numerical integration methods in the dynamic analysis of large elasto-plastic deformation problems is investigated. It is shown that all these methods, in the case of convergence, yield a solution that satisfies the principle of work and energy without the need of taking any special measures. Semi-implicit integration methods, however, can lead to numerical difficulties in the case of very stiff problems due to the linearization made in these methods in order to avoid the iterative Newton--Raphson procedure. It is also demonstrated that the use of the consistent Lagrangian-plastic tangent moduli derived in this investigation using the absolute nodal coordinate formulation leads to better convergence of the iterative Newton--Raphson procedure used in the implicit integration methods.

HFSM: HIERARCHICAL FACIAL SHAPE MODELING ALGORITHM FOR REALISTIC FACIAL EXPRESSION ANIMATION

We propose a hierarchical 3D facial modeling technique for realistic facial expression animation from the anatomical specification. We analyze the real human face to construct the facial model with a hierarchical biomechanical structure, incorporating a physically-based approximation to facial skin tissue, a set of anatomically-motivated facial muscle actuators and underlying skull structure. The deformable skin model has multi-layer structure to approximate different types of soft tissue. It takes into account the nonlinear stress-strain relationship of the skin and the fact that soft tissue is almost incompressible. Different kinds of muscle models have been developed to simulate the distribution of the muscle force exerted to the skin due to muscle contraction. The 3D face model incorporates a skull structure which extends the scope of facial motion and facilitates facial muscle construction. The facial muscle construction is achieved by a muscle mapping approach which efficiently locates facial muscles at the anatomically correct positions between the skin and skull layers. To generate facial expressions, the resulting hierarchical facial model is animated by solving the governing dynamic equation. For computational efficiency, we use a localized, semi-implicit integration method in the numerical simulation. The dynamic facial animation algorithm runs at an interactive rate and synthesizes various realistic facial expressions.