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Constant Coefficients (constant + coefficient)
Selected AbstractsThird-order methods for first-order hyperbolic partial differential equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2004T. A. Cheema Abstract In this paper numerical methods for solving first-order hyperbolic partial differential equations are developed. These methods are developed by approximating the first-order spatial derivative by third-order finite-difference approximations and a matrix exponential function by a third-order rational approximation having distinct real poles. Then parallel algorithms are developed and tested on a sequential computer for an advection equation with constant coefficient and a non-linear problem. Copyright © 2003 John Wiley & Sons, Ltd. [source] Identification of Time-Variant Modal Parameters Using Time-Varying Autoregressive with Exogenous Input and Low-Order Polynomial FunctionCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 7 2009C. S. Huang By developing the equivalent relations between the equation of motion of a time-varying structural system and the TVARX model, this work proves that instantaneous modal parameters of a time-varying system can be directly estimated from the TVARX model coefficients established from displacement responses. A moving least-squares technique incorporating polynomial basis functions is adopted to approximate the coefficient functions of the TVARX model. The coefficient functions of the TVARX model are represented by polynomials having time-dependent coefficients, instead of constant coefficients as in traditional basis function expansion approaches, so that only low orders of polynomial basis functions are needed. Numerical studies are carried out to investigate the effects of parameters in the proposed approach on accurately determining instantaneous modal parameters. Numerical analyses also demonstrate that the proposed approach is superior to some published techniques (i.e., recursive technique with a forgetting factor, traditional basis function expansion approach, and weighted basis function expansion approach) in accurately estimating instantaneous modal parameters of a structure. Finally, the proposed approach is applied to process measured data for a frame specimen subjected to a series of base excitations in shaking table tests. The specimen was damaged during testing. The identified instantaneous modal parameters are consistent with observed physical phenomena. [source] Stability analysis of the Crank,Nicholson method for variable coefficient diffusion equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2007Charles Tadjeran Abstract The Crank,Nicholson method is a widely used method to obtain numerical approximations to the diffusion equation due to its accuracy and unconditional stability. When the diffusion coefficient is not a constant, the general approach is to obtain a discretization for the PDE in the same manner as the case for constant coefficients. In this paper, we show that the manner of this discretization may impact the stability of the resulting method and could lead to instability of the numerical solution. It is shown that the classical Crank,Nicholson method will fail to be unconditionally stable if the diffusion coefficient is computed at the time gridpoints instead of at the midpoints of the temporal subinterval. A numerical example is presented and compared with the exact analytical solution to examine its divergence. Copyright © 2006 John Wiley & Sons, Ltd. [source] Evaluating recursive filters on distributed memory parallel computersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2006Przemys, aw Stpiczy, skiArticle first published online: 6 APR 200 Abstract The aim of this paper is to show that the recently developed high performance divide and conquer algorithm for solving linear recurrence systems with constant coefficients together with the new BLAS-based algorithm for narrow-banded triangular Toeplitz matrix,vector multiplication, allow to evaluate linear recursive filters efficiently on distributed memory parallel computers. We apply the BSP model of parallel computing to predict the behaviour of the algorithm and to find the optimal values of the method's parameters. The results of experiments performed on a cluster of twelve dual-processor Itanium 2 computers and Cray X1 are also presented and discussed. The algorithm allows to utilize up to 30% of the peak performance of 24 Itanium processors, while a simple scalar algorithm can only utilize about 4% of the peak performance of a single processor. Copyright © 2006 John Wiley & Sons, Ltd. [source] Delayed reflection of the energy flow at a potential step for dispersive wave packetsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2004F. Ali Mehmeti Abstract We study Klein,Gordon equations with constant coefficients and different dispersion relations on two one-dimensional semi-infinite media coupled with transmission conditions. We obtain lower and upper bounds of the reflected part of the energy flow at the connecting point when the frequency band involved in the initial signal is sufficiently narrow. We detect a phenomenon of delayed reflection for low frequency wave packets, which is in accordance with the recent experiments of Haibel and Nimtz. The result is then generalized for a star-shaped network of n semi-infinite branches connected at one point. Copyright © 2004 John Wiley & Sons, Ltd. [source] Local energy decay for a class of hyperbolic equations with constant coefficients near infinityMATHEMATISCHE NACHRICHTEN, Issue 5 2010Shintaro Aikawa Abstract A uniform local energy decay result is derived to a compactly perturbed hyperbolic equation with spatial vari¬able coefficients. We shall deal with this equation in an N -dimensional exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data and the equation includes anisotropic variable coefficients {ai(x): i = 1, 2, ,, N }, which are not necessarily equal to each other (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] An algebraic generalization of local Fourier analysis for grid transfer operators in multigrid based on Toeplitz matricesNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2010M. Donatelli Abstract Local Fourier analysis (LFA) is a classical tool for proving convergence theorems for multigrid methods (MGMs). In particular, we are interested in optimal convergence, i.e. convergence rates that are independent of the problem size. For elliptic partial differential equations (PDEs), a well-known optimality result requires that the sum of the orders of the grid transfer operators is not lower than the order of the PDE approximated. Analogously, when dealing with MGMs for Toeplitz matrices, a well-known optimality condition concerns the position and the order of the zeros of the symbols of the grid transfer operators. In this work we show that in the case of elliptic PDEs with constant coefficients, the two different approaches lead to an equivalent condition. We argue that the analysis for Toeplitz matrices is an algebraic generalization of the LFA, which allows to deal not only with differential problems but also for instance with integral problems. The equivalence of the two approaches gives the possibility of using grid transfer operators with different orders also for MGMs for Toeplitz matrices. We give also a class of grid transfer operators related to the B-spline's refinement equation and study their geometric properties. Numerical experiments confirm the correctness of the proposed analysis. Copyright © 2010 John Wiley & Sons, Ltd. [source] Material Modelling of Porous Media for Wave Propagation ProblemsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003M. Schanz PD Dr.-Ing. Under the assumption of a linear geometry description and linear constitutive equations, the governing equations are derived for two poroelastic theories, Biot's theory and Theory of Porous Media (TPM), using solid displacements and pore pressure as unknowns. In both theories, this is only possible in the Laplace domain. Comparing the sets of differential equations of Biot's theory and of TPM, they show different constant coefficients but the same structure of coupled differential equations. Identifying these coefficients with the material data and correlating them leads to the known problem with Biot's ,apparent mass density'. Further, in trying to find a correlation between Biot's stress coefficient to parameters used in TPM yet unsolved inconsistencies are found. For studying the numerical effect of these differences, wave propagation results of a one-dimensional poroelastic column are analysed. Differences between both theories are resolved only for compressible constituents. 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