Home About us Contact
|
Home About us Contact | ||
|
|
||
Arbitrary Order (arbitrary + order)
Selected AbstractsNumerical modelling method for wave propagation in a linear viscoelastic medium with singular memoryGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2004Jian-Fei Lu SUMMARY A numerical modelling method for wave propagation in a linear viscoelastic medium with singular memory is developed in this paper. For a demonstration of the method, the Cole,Cole model of viscoelastic relaxation is adopted here. A formulation of the Cole,Cole model based on internal variables satisfying fractional relaxation equations is applied. In order to avoid integrating and storing of the entire history of the variables, a new method for solving fractional differential equations of arbitrary order based on a set of secondary internal variables is developed. Using the new method, the velocity,stress equations and the fractional relaxation equations are reduced to a system of first-order ordinary differential equations for the velocities, stresses, primary internal variables as well as the secondary internal variables. The horizontal spatial derivatives involved in the governing equations are calculated by the Fourier pseudo-spectral (PS) method, while the vertical ones are calculated by the Chebychev PS method. The physical boundary conditions and the non-reflecting conditions for the Chebychev PS method are also discussed. The global solution of the first-order system of ordinary differential equations is advanced in time by the Euler predictor,corrector methods. For the demonstration of our method, some numerical results are presented. [source] Polynomial basis functions on pyramidal elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008M. J. Bluck Abstract Pyramidal elements are necessary to effect the transition from tetrahedral to hexahedral elements, a common requirement in practical finite element applications. However, existing pyramidal transition elements suffer from degeneracy or other numerical difficulties, requiring, at the least, warnings and care in their use. This paper presents a general technique for the construction of nodal basis functions on pyramidal finite elements. General forms for basis functions of arbitrary order are presented. The basis functions so derived are fully conformal and free of degeneracy. Copyright © 2007 John Wiley & Sons, Ltd. [source] Energy,momentum consistent finite element discretization of dynamic finite viscoelasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010M. Groß Abstract This paper is concerned with energy,momentum consistent time discretizations of dynamic finite viscoelasticity. Energy consistency means that the total energy is conserved or dissipated by the fully discretized system in agreement with the laws of thermodynamics. The discretization is energy,momentum consistent if also momentum maps are conserved when group motions are superimposed to deformations. The performed approximation is based on a three-field formulation, in which the deformation field, the velocity field and a strain-like viscous internal variable field are treated as independent quantities. The new non-linear viscous evolution equation satisfies a non-negative viscous dissipation not only in the continuous case, but also in the fully discretized system. The initial boundary value problem is discretized by using finite elements in space and time. Thereby, the temporal approximation is performed prior to the spatial approximation in order to preserve the stress objectivity for finite rotation increments (incremental objectivity). Although the present approach makes possible to design schemes of arbitrary order, the focus is on finite elements relying on linear Lagrange polynomials for the sake of clearness. The discrete energy,momentum consistency is based on the collocation property and an enhanced second Piola,Kirchhoff stress tensor. The obtained coupled non-linear algebraic equations are consistently linearized. The corresponding iterative solution procedure is associated with newly proposed convergence criteria, which take the discrete energy consistency into account. The iterative solution procedure is therefore not complicated by different scalings in the independent variables, since the motion of the element is taken into account for solving the viscous evolution equation. Representative numerical simulations with various boundary conditions show the superior stability of the new time-integration algorithm in comparison with the ordinary midpoint rule. Both the quasi-rigid deformations during a free flight, and large deformations arising in a dynamic tensile test are considered. Copyright © 2009 John Wiley & Sons, Ltd. [source] A Hermite reproducing kernel approximation for thin-plate analysis with sub-domain stabilized conforming integrationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2008Dongdong Wang Abstract A Hermite reproducing kernel (RK) approximation and a sub-domain stabilized conforming integration (SSCI) are proposed for solving thin-plate problems in which second-order differentiation is involved in the weak form. Although the standard RK approximation can be constructed with an arbitrary order of continuity, the proposed approximation based on both deflection and rotation variables is shown to be more effective in solving plate problems. By imposing the Kirchhoff mode reproducing conditions on deflectional and rotational degrees of freedom simultaneously, it is demonstrated that the minimum normalized support size (coverage) of kernel functions can be significantly reduced. With this proposed approximation, the Galerkin meshfree framework for thin plates is then formulated and the integration constraint for bending exactness is also derived. Subsequently, an SSCI method is developed to achieve the exact pure bending solution as well as to maintain spatial stability. Numerical examples demonstrate that the proposed formulation offers superior convergence rates, accuracy and efficiency, compared with those based on higher-order Gauss quadrature rule. Copyright © 2007 John Wiley & Sons, Ltd. [source] Fully hierarchical divergence-conforming basis functions on tetrahedral cells, with applicationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007Matthys M. Botha Abstract A new set of hierarchical, divergence-conforming, vector basis functions on curvilinear tetrahedrons is presented. The basis can model both mixed- and full-order polynomial spaces to arbitrary order, as defined by Raviart and Thomas, and Nédélec. Solenoidal- and non-solenoidal components are separately represented on the element, except in the case of the mixed first-order space, for which a decomposition procedure on the global, mesh-wide level is presented. Therefore, the hierarchical aspect of the basis can be made to extend down to zero polynomial order. The basis can be used to model divergence-conforming quantities, such as electromagnetic flux- and current density, fluid velocity, etc., within numerical methods such as the finite element method (FEM) or integral equation-based methods. The basis is ideally suited to p -adaptive analysis. The paper concludes with two example applications. The first is the FEM-based solution of the linearized acoustic vector wave equation, where it is shown how the decomposition into solenoidal components and their complements can be used to stabilize the method at low frequencies. The second is the solution of the electric field, volume integral equation for electromagnetic scattering analysis, where the benefits of the decomposition are again demonstrated. Copyright © 2006 John Wiley & Sons, Ltd. [source] Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedraINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003Seppo Järvenpää Abstract A numerical solution of integral equations typically requires calculation of integrals with singular kernels. The integration of singular terms can be considered either by purely numerical techniques, e.g. Duffy's method, polar co-ordinate transformation, or by singularity extraction. In the latter method the extracted singular integral is calculated in closed form and the remaining integral is calculated numerically. This method has been well established for linear and constant shape functions. In this paper we extend the method for polynomial shape functions of arbitrary order. We present recursive formulas by which we can extract any number of terms from the singular kernel defined by the fundamental solution of the Helmholtz equation, or its gradient, and integrate the extracted terms times a polynomial shape function in closed form over plane triangles or tetrahedra. The presented formulas generalize the singularity extraction technique for surface and volume integral equation methods with high-order basis functions. Numerical experiments show that the developed method leads to a more accurate and robust integration scheme, and in many cases also a faster method than, for example, Duffy's transformation. Copyright © 2003 John Wiley & Sons, Ltd. [source] A general framework for evaluating nonlinearity, noise and dynamic range in continuous-time OTA-C filters for computer-aided design and optimizationINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 4 2007S. Koziel Abstract Efficient procedures for evaluating nonlinear distortion and noise valid for any OTA-C filter of arbitrary order are developed based on matrix description of a general OTA-C filter model. Since those procedures use OTA macromodels, they allow us to obtain the results significantly faster than transistor-level simulation. On the other hand, the general OTA-C filter model allows us to apply matrix transforms that manipulate (rescale) filter element values and/or change topology without changing its transfer function. Due to this, the proposed procedures can be used in direct optimization of OTA-C filters with respect to important characteristics such as noise performance, THD, IM3, DR or SNR. As an example, a simple optimization procedure using equivalence transformations is discussed. An application example of the proposed approach to optimal block sequencing and gain distribution of 8th order cascade Butterworth filter is given. Accuracy of the theoretical tools has been verified by comparing to transistor-level simulation results and to experimental results. Copyright © 2006 John Wiley & Sons, Ltd. [source] New perspectives on unitary coupled-cluster theoryINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2006Andrew G. Taube Abstract The advantages and possibilities of a unitary coupled-cluster (CC) theory are examined. It is shown that using a unitary parameterization of the wave function guarantees agreement between a sum-over-states polarization propagator and response theory calculation of properties of arbitrary order, as opposed to the case in conventional CC theory. Then, using the Zassenhaus expansion for noncommuting exponential operators, explicit diagrams for an extensive and variational method based on unitary CC theory are derived. Possible extensions to the approximations developed are discussed as well. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Numerical method to solve chemical differential-algebraic equationsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2002Ercan Çelik Abstract In this article, the solution of a chemical differential-algebraic equation model of general type F(y, y,, x) = 0 has been done using MAPLE computer algebra systems. The MAPLE program is given in the Appendix. First we calculate the Power series of the given equations system, then we transform it into Padé series form, which gives an arbitrary order for solving chemical differential-algebraic equation numerically. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] An efficient method for analyzing nonuniformly coupled microstrip linesINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 2 2005Dengpeng Chen Abstract This article presents an efficient method for analyzing nonuniformly coupled microstrip lines. By choosing a modal-transformation matrix, the coupled nonlinear differential equations describing the symmetric nonuniformly coupled microstrip lines are decoupled using even- and odd-mode parameters; the original problem is thus transformed into two single nonuniform transmission lines. A power-law function of arbitrary order and having two adjustable parameters is chosen to better approximate the equation coefficients. Closed-form ABCD matrix solutions are obtained and used to calculate the S -parameters of nonuniformly coupled microstrip lines. Numerical results for two examples are compared with those from a full-wave commercial package and experimental ones in the literature in order to demonstrate the accuracy and efficiency of this method. This highly efficient method is employed to optimize a cosine-shape 10-dB codirectional coupler, which has good return loss and high directivity performance over a wide frequency range. © 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2005. [source] A variable order constitutive relation for viscoelasticityANNALEN DER PHYSIK, Issue 7-8 2007L.E.S. Ramirez Abstract A constitutive relation for linear viscoelasticity of composite materials is formulated using the novel concept of Variable Order (VO) differintegrals. In the model proposed in this work, the order of the derivative is allowed to be a function of the independent variable (time), rather than a constant of arbitrary order. We generalize previous works that used fractional derivatives for the stress and strain relationship by allowing a continuous spectrum of non-integer dynamics to describe the physical problem. Starting with the assumption that the order of the derivative is a measure of the rate of change of disorder within the material, we develop a statistical mechanical model that is in agreement with experimental results for strain rates varying more than eight orders of magnitude in value. We use experimental data for an epoxy resin and a carbon/epoxy composite undergoing constant compression rates in order to derive a VO constitutive equation that accurately models the linear viscoelastic deformation in time. The resulting dimensionless constitutive equation agrees well with all the normalized data while using a much smaller number of empirical coefficients when compared to available models in the literature. [source] | ||||||||||