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Gradient Method (gradient + method)
Selected AbstractsSimple preconditioners for the conjugate gradient method: experience with test day modelsJOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 3 2002I. STRANDÉN Preconditioned conjugate gradient method can be used to solve large mixed model equations quickly. Convergence of the method depends on the quality of the preconditioner. Here, the effect of simple preconditioners on the number of iterations until convergence was studied by solving breeding values for several test day models. The test day records were from a field data set, and several simulated data sets with low and high correlations among regression coefficients. The preconditioner matrices had diagonal or block diagonal parts. Transformation of the mixed model equations by diagonalization of the genetic covariance matrix was studied as well. Preconditioner having the whole block of the fixed effects was found to be advantageous. A block diagonal preconditioner for the animal effects reduced the number of iterations the higher the correlations among animal effects, but increased memory usage of the preconditioner. Diagonalization of the animal genetic covariance matrix often reduced the number of iterations considerably without increased memory usage. Einfache Preconditioners für die `Conjugate Gradient Method': Erfahrungen mit Testtagsmodellen Die `Preconditioned Conjugate Gradient Methode' kann benutzt werden um große `Mixed Model' Gleichungssysteme schnell zu lösen. In diesem Beitrag wurde der Einfluss von einfachen Preconditioners auf die Anzahl an Iterationen bis zur Konvergenz bei der Schätzung von Zuchtwerten bei verschiedenen Testtagsmodellen untersucht. Die Testtagsdaten stammen aus einem Felddatensatz und mehreren simulierten Datensätzen mit unterschiedlichen Korrelationen zwischen den Regressionskoeffizienten. Die Preconditioner Matrix bestand aus Diagonalen oder Blockdiagonalen Teilen. Eine Transformation der Mixed Modell Gleichungen durch Diagonalisierung der genetischen Kovarianzmatrix wurde ebenfalls untersucht. Preconditioners mit dem Block der fixen Effekte zeigten sich immer überlegen. Ein Blockdiagonaler Preconditioner für den Tiereffekt reduzierte die Anzahl an Iterationen mit höher werden Korrelationen zwischen den Tiereffekten, aber erhöhte den Speicherbedarf. Eine Diagonalisierung der genetischen Kovarianzmatrix reduzierte sehr oft die Anzahl an Iterationen erheblich ohne den Speicherbedarf zu erhöhen. [source] NMR diffusion measurements under chemical exchange between sites involving a large chemical shift differenceCONCEPTS IN MAGNETIC RESONANCE, Issue 2 2010S. Leclerc Abstract This study concerns the thallium-205 cation in aqueous solution in the presence of a calixarene molecule. Although the measurement of the self-diffusion coefficient of pure thallium (without calixarene in the aqueous solution) does not pose any particular problem, major difficulties are encountered with the standard method using gradient strength increment as soon as thallium is partly complexed by calixarene. With static magnetic field gradients, the NMR signal is so weak that it prevents any reliable measurement, whereas radio frequency (rf) field gradients lead to an unrealistic value of the diffusion coefficient. This failure is explained by the fact that thallium is in fast exchange between two sites (complexed and free thallium) thus exhibiting a single NMR signal although, in the course of the experiment, two signals, with an important difference in resonance frequencies (due to the large thallium chemical shift range), are effectively involved. With the objective to understand these quite unexpected observations, the theory underlying NMR diffusion experiments is first reviewed, and criteria of fast exchange are discussed for three parameters: chemical shifts, relaxation rates, and diffusion coefficients. It turns out that off-resonance effects are responsible for unwanted defocusing due to rf pulses in the static magnetic field gradient method and for time-dependent gradients in the rf field gradient method. Concerning the latter, a remedy is proposed which consists in applying the stronger gradient and incrementing the gradient pulse durations. After correction for relaxation, the expected value of the diffusion coefficient is retrieved. © 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part A 36A: 127,137, 2010. [source] Techniques to measure the dry aeolian deposition of dust in arid and semi-arid landscapes: a comparative study in West NigerEARTH SURFACE PROCESSES AND LANDFORMS, Issue 2 2008Dirk Goossens Abstract Seven techniques designed to measure the dry aeolian deposition of dust on a desert surface were tested during field experiments in Niger, central-west Africa. Deposition fluxes were measured during eight periods of 3,4 days each. Experimental techniques tested were the MDCO (marble dust collector) method, the Frisbee method, the glass plate method (optical analysis of dust deposited on glass surfaces using particle imaging software), the soil surface method (deposition on a simulated desert floor) and the CAPYR (capteur pyramidal) method. Theoretical techniques tested were the inferential method and the combination method (gradient method extended with a deposition term for coarse dust particles). The results obtained by the MDCO, Frisbee, inferential and combination methods could be directly compared by converting the data to identical standard conditions (deposition on a water surface producing no resuspension). The results obtained by the other methods (glass plate, soil surface, CAPYR) were compared relatively. The study shows that the crude (unconverted) deposition fluxes of the five experimental techniques were similar, while the crude deposition fluxes calculated by the two theoretical techniques were substantially higher, of the order of four to five times as high as for the experimental techniques. Recalculation of the data to identical environmental conditions (the standard water surface) resulted in nearly identical deposition fluxes for the MDCO, Frisbee, inferential and combination techniques, although the latter two still had slightly higher values (but the differences remained small). The measurements illustrate the need to include a grain shape factor in theoretical dust deposition models. Without such a factor, theoretical models overestimate the deposition. The paper also discusses the advantages and disadvantages of the techniques tested. Copyright © 2007 John Wiley & Sons, Ltd. [source] Characterization of voltage degradation in dynamic field gradient focusingELECTROPHORESIS, Issue 5 2008Jeffrey M. Burke Abstract Dynamic field gradient focusing (DFGF) is an equilibrium gradient method that utilizes an electric field gradient to simultaneously separate and concentrate charged analytes based on their individual electrophoretic mobilities. This work describes the use of a 2-D nonlinear, numerical simulation to examine the impact of voltage loss from the electrodes to the separation channel, termed voltage degradation, and distortions in the electric field on the performance of DFGF. One of the design parameters that has a large impact on the degree of voltage degradation is the placement of the electrodes in relation to the separation channel. The simulation shows that a distance of about 3,mm from the electrodes to the separation channel gives the electric field profile with least amount of voltage degradation. The simulation was also used to describe the elution of focused protein peaks. The simulation shows that elution under constant electric field gradient gives better performance than elution through shallowing of the electric field. Qualitative agreement between the numerical simulation and experimental results is shown. The simulation also illustrates that the presence of a defocusing region at the cathodic end of the separation channel causes peak dispersion during elution. The numerical model is then used to design a system that does not suffer from a defocusing region. Peaks eluted under this design experienced no band broadening in our simulations. Preliminary experimental results using the redesigned chamber are shown. [source] Re-Dating the Moraines at Skálafellsjökull and Heinabergsjökull using different Lichenometric Methods: Implications for the Timing of the Icelandic Little Ice Age MaximumGEOGRAFISKA ANNALER SERIES A: PHYSICAL GEOGRAPHY, Issue 4 2004Krista M. Mckinzey Abstract Little Ice Age (LIA) moraines along the margins of Skálafellsjökull and Heinabergsjökull, two neighbouring outlet glaciers flowing from the Vatnajökull ice-cap, have been re-dated to test the reliability of different lichenometric approaches. During 2003, 12 000 lichens were measured on 40 moraine fragments at Skálafellsjökull and Heinabergsjökull to provide surface age proxies. The results are revealing. Depending on the chosen method of analysis, Skálafellsjökull either reached its LIA maximum in the early 19th century (population gradient) or the late 19th century (average of five largest lichens), whereas the LIA maximum of Heinabergsjökull occurred by the mid-19th century (population gradient) or late-19th century (average of 5 largest lichens). Discrepancies (c. 80 years for Skálafellsjökull and c. 40 years for Heinabergsjökull) suggest that the previously cited AD 1887 LIA maxima for both glaciers should be reassessed. Dates predicted by the lichen population gradient method appear to be the most appropriate, as mounting evidence from other geochronological reconstructions and sea-ice records throughout Iceland tends to support an earlier LIA glacier maximum (late 18th to mid-19th century) and probably reflects changes in the North Atlantic Oscillation. These revised chronologies shed further light on the precise timing of the Icelandic LIA glacier maximum, whilst improving our understanding of glacier-climate interactions in the North Atlantic. [source] A quantitative identification technique for a two-dimensional subsurface defect based on surface temperature measurementHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2009Chunli Fan Abstract The inverse identification of a subsurface defect boundary is an important part of an inverse heat conduction problem, and is also the basis for the quantitative development of a nondestructive thermographic inspection technique. For the commonly encountered quantitative thermographic defect identification problem when the test piece is heated from one part of the outer boundary, our previous study showed that some parts of the defect boundary are sensitive to the initial defect boundary prediction of the conjugate gradient method. In this paper, the heat transfer mechanism inside a test piece with this problem is analyzed by building a two-dimensional model. A new method, the multiple measurements combination method (MMCM), is also presented which combines the identification algorithm study with the optimization of the thermographic detection technique to solve the problem. Numerical experiments certified the effectiveness of the present method. The temperature measurement error and the initial prediction of the defect boundary shape have little effect on the identification result. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20251 [source] Optimization of Train Speed Profile for Minimum Energy ConsumptionIEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, Issue 3 2010Masafumi Miyatake Member Abstract The optimal operation of railway systems minimizing total energy consumption is discussed in this paper. Firstly, some measures of finding energy-saving train speed profiles are outlined. After the characteristics that should be considered in optimizing train operation are clarified, complete optimization based on optimal control theory is reviewed. Their basic formulations are summarized taking into account most of the difficult characteristics peculiar to railway systems. Three methods of solving the formulation, dynamic programming (DP), gradient method, and sequential quadratic programming (SQP), are introduced. The last two methods can also control the state of charge (SOC) of the energy storage devices. By showing some numerical results of simulations, the significance of solving not only optimal speed profiles but also optimal SOC profiles of energy storage are emphasized, because the numerical results are beyond the conventional qualitative studies. Future scope for applying the methods to real-time optimal control is also mentioned. Copyright © 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source] Determining elastic constants of transversely isotropic rocks using Brazilian test and iterative procedureINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2008Yen-Chin Chou Abstract The elastic constants of rocks are the basic parameters for rock mechanics, and play a very important role in engineering design. There are many laboratory methods to determine the elastic constants of transversely isotropic rocks, and the Brazilian test is a popular method. This paper presented a method combination of the Brazilian test, back calculation, and iterative procedure to evaluate the five independent elastic constants of transversely isotropic rocks in laboratory. The strain data at the centre of discs were obtained using Brazilian test. The stresses at the centre of discs were computed using numerical programs. By using back calculation, the temporary elastic constants were computed after the stresses and stains were substituted into elastic mechanics equations. After iterative procedure, the convergent values of the elastic constants can be obtained. One numerical example and three experimental cases were proposed to show the applicability of this method. The convergent values of the five independent elastic constants can be obtained in no more than 10 iterative cycles. The results coming from numerical analysis method exhibited satisfactory outcome in accordance with those of generalized reduced gradient method. The merits of this method include convenient specimen preparation of the Brazilian test, simple iterative procedure, and readily available commercially numerical programs, so that this method can be easily popularized in research and engineering analysis. Copyright © 2007 John Wiley & Sons, Ltd. [source] Efficient finite element simulation of crack propagation using adaptive iterative solversINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2006A. Meyer Abstract This paper delivers an efficient solution technique for the numerical simulation of crack propagation of 2D linear elastic formulations based on finite elements together with the conjugate gradient method in order to solve the corresponding linear equation systems. The developed iterative numerical approach using hierarchical preconditioners has the interesting feature that the hierarchical data structure will not be destroyed during crack propagation. Thus, it is possible to simulate crack advance in a very effective numerical manner, including adaptive mesh refinement and mesh coarsening. Test examples are presented to illustrate the efficiency of the given approach. Numerical simulations of crack propagation are compared with experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [source] Application of the additive Schwarz method to large scale Poisson problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2004K. M. Singh Abstract This paper presents an application of the additive Schwarz method to large scale Poisson problems on parallel computers. Domain decomposition in rectangular blocks with matching grids on a structured rectangular mesh has been used together with a stepwise approximation to approximate sloping sides and complicated geometric features. A seven-point stencil based on central difference scheme has been used for the discretization of the Laplacian for both interior and boundary grid points, and this results in a symmetric linear algebraic system for any type of boundary conditions. The preconditioned conjugate gradient method has been used as an accelerator for the additive Schwarz method, and three different methods have been assessed for the solution of subdomain problems. Numerical experiments have been performed to determine the most suitable set of subdomain solvers and the optimal accuracy of subdomain solutions; to assess the effect of different decompositions of the problem domain; and to evaluate the parallel performance of the additive Schwarz preconditioner. Application to a practical problem involving complicated geometry is presented which establishes the efficiency and robustness of the method. Copyright © 2004 John Wiley & Sons, Ltd. [source] A non-linear fin design problem in determining the optimum shape of spine and longitudinal finsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2003Cheng-Hung Huang Abstract A non-linear fin design algorithm is applied to estimate the optimum shapes for the spine and longitudinal fins by using the conjugate gradient method (CGM) based on the desired fin efficiency and fin volume. One of the advantages in using CGM in the inverse design problem lies in that it can handle problems having a large number of unknown parameters easily and converges very fast. The validity of the present algorithm by using the CGM to solve the non-linear fin design problem is justified based on numerical experiments. Results show that the optimum fin shapes can always be obtained. Copyright © 2003 John Wiley & Sons, Ltd. [source] Hybrid domain decomposition algorithms for compressible and almost incompressible elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2010Clark R. Dohrmann Abstract Overlapping Schwarz methods are considered for mixed finite element approximations of linear elasticity, with discontinuous pressure spaces, as well as for compressible elasticity approximated by standard conforming finite elements. The coarse components of the preconditioners are based on spaces, with a number of degrees of freedom per subdomain which are uniformly bounded, which are similar to those previously developed for scalar elliptic problems and domain decomposition methods of iterative substructuring type, i.e. methods based on nonoverlapping decompositions of the domain. The local components of the new preconditioners are based on solvers on a set of overlapping subdomains. In the current study, the dimension of the coarse spaces is smaller than in recently developed algorithms; in the compressible case all independent face degrees of freedom have been eliminated while in the almost incompressible case five out of six are not needed. In many cases, this will result in a reduction of the dimension of the coarse space by about one half compared with that of the algorithm previously considered. In addition, in spite of using overlapping subdomains to define the local components of the preconditioner, values of the residual and the approximate solution need only to be retained on the interface between the subdomains in the iteration of the new hybrid Schwarz algorithm. The use of discontinuous pressures makes it possible to work exclusively with symmetric, positive-definite problems and the standard preconditioned conjugate gradient method. Bounds are established for the condition number of the preconditioned operators. The bound for the almost incompressible case grows in proportion to the square of the logarithm of the number of degrees of freedom of individual subdomains and the third power of the relative overlap between the overlapping subdomains, and it is independent of the Poisson ratio as well as jumps in the Lamé parameters across the interface between the subdomains. Numerical results illustrate the findings. Copyright © 2009 John Wiley & Sons, Ltd. [source] The identification of a Robin coefficient by a conjugate gradient methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009Fenglian Yang Abstract This paper investigates a non-linear inverse problem associated with the heat conduction problem of identifying a Robin coefficient from boundary temperature measurement. The variational formulation of the problem is given. The conjugate gradient method combining with the discrepancy principle for choosing the suitable stop step are proposed for solving the optimization problem, in which the finite difference method is used to solve the direct problems. The performance of the method is verified by simulating four examples. The convergence with respect to the grid refinement and the amount of noise in the data is also investigated. Copyright © 2008 John Wiley & Sons, Ltd. [source] Optimal design and optimal control of structures undergoing finite rotations and elastic deformationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004A. Ibrahimbegovic Abstract In this work, we deal with the optimal design and optimal control of structures undergoing large rotations and large elastic deformations. In other words, we show how to find the corresponding initial configuration through optimal design or the corresponding set of multiple load parameters through optimal control, in order to recover a desired deformed configuration or some desirable features of the deformed configuration as specified more precisely by the objective or cost function. The model problem chosen to illustrate the proposed optimal design and optimal control methodologies is the one of geometrically exact beam. First, we present a non-standard formulation of the optimal design and optimal control problems, relying on the method of Lagrange multipliers in order to make the mechanics state variables independent from either design or control variables and thus provide the most general basis for developing the best possible solution procedure. Two different solution procedures are then explored, one based on the diffuse approximation of response function and gradient method and the other one based on genetic algorithm. A number of numerical examples are given in order to illustrate both the advantages and potential drawbacks of each of the presented procedures. Copyright © 2004 John Wiley & Sons, Ltd. [source] An inverse radiation problem of simultaneous estimation of heat transfer coefficient and absorption coefficient in participating mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2003H. M. Park Abstract An inverse radiation problem is investigated where the spatially varying heat transfer coefficient h(z) and the absorption coefficient , in the radiant cooler are estimated simultaneously from temperature measurements. The inverse radiation problem is solved through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature, using the conjugate gradient method. The gradient of the performance function is evaluated by means of the improved adjoint variable method that can take care of both the function estimation and the parameter estimation efficiently. The present method is found to estimate h(z) and , with reasonable accuracy even with noisy temperature measurements. Copyright © 2002 John Wiley & Sons, Ltd. [source] Inverse optimal design of cooling conditions for continuous quenching processesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2001Yimin Ruan Abstract This paper presents an inverse design methodology to obtain a required yield strength with an optimal cooling condition for the continuous quenching of precipitation hardenable sheet alloys. The yield strength of a precipitation hardenable alloy can be obtained by allowing solute to enter into solid solution at a proper temperature and rapidly cooling the alloy to hold the solute in the solid solution. An aging process may be needed for the alloy to develop the final mechanical property. The objective of the design is to optimize the quenching process so that the required yield strength can be achieved. With the inverse design method, the required yield strength is specified and the sheet thermal profile at the exit of the quenching chamber can also be specified. The conjugate gradient method is used to optimize the cooling boundary condition during quenching. The adjoint system is developed to compute the gradient of the objective functional. An aluminium sheet quenching problem is presented to demonstrate the inverse design method. Copyright © 2001 John Wiley & Sons, Ltd. [source] Inverse design of directional solidification processes in the presence of a strong external magnetic fieldINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001Rajiv Sampath Abstract A computational method for the design of directional alloy solidification processes is addressed such that a desired growth velocity ,f under stable growth conditions is achieved. An externally imposed magnetic field is introduced to facilitate the design process and to reduce macrosegregation by the damping of melt flow. The design problem is posed as a functional optimization problem. The unknowns of the design problem are the thermal boundary conditions. The cost functional is taken as the square of the L2 norm of an expression representing the deviation of the freezing interface thermal conditions from the conditions corresponding to local thermodynamic equilibrium. The adjoint method for the inverse design of continuum processes is adopted in this work. A continuum adjoint system is derived to calculate the adjoint temperature, concentration, velocity and electric potential fields such that the gradient of the L2 cost functional can be expressed analytically. The cost functional minimization process is realized by the conjugate gradient method via the FE solutions of the continuum direct, sensitivity and adjoint problems. The developed formulation is demonstrated with an example of designing the boundary thermal fluxes for the directional growth of a germanium melt with dopant impurities in the presence of an externally applied magnetic field. The design is shown to achieve a stable interface growth at a prescribed desired growth rate. Copyright © 2001 John Wiley & Sons, Ltd. [source] A cascadic conjugate gradient algorithm for mass conservative, semi-implicit discretization of the shallow water equations on locally refined structured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1-2 2002Luca Bonaventura Abstract A semi-implicit, mass conservative discretization scheme is applied to the two-dimensional shallow water equations on a hierarchy of structured, locally refined Cartesian grids. Different resolution grids are fully interacting and the discrete Helmholtz equation obtained from the semi-implicit discretization is solved by the cascadic conjugate gradient method. A flux correction is applied at the interface between the coarser and finer discretization grids, so as to ensure discrete mass conservation, along with symmetry and diagonal dominance of the resulting matrix. Two-dimensional idealized simulations are presented, showing the accuracy and the efficiency of the resulting method. Copyright © 2002 John Wiley & Sons, Ltd. [source] GENSMAC3D: a numerical method for solving unsteady three-dimensional free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2001M.F. Tomé Abstract A numerical method for solving three-dimensional free surface flows is presented. The technique is an extension of the GENSMAC code for calculating free surface flows in two dimensions. As in GENSMAC, the full Navier,Stokes equations are solved by a finite difference method; the fluid surface is represented by a piecewise linear surface composed of quadrilaterals and triangles containing marker particles on their vertices; the stress conditions on the free surface are accurately imposed; the conjugate gradient method is employed for solving the discrete Poisson equation arising from a velocity update; and an automatic time step routine is used for calculating the time step at every cycle. A program implementing these features has been interfaced with a solid modelling routine defining the flow domain. A user-friendly input data file is employed to allow almost any arbitrary three-dimensional shape to be described. The visualization of the results is performed using computer graphic structures such as phong shade, flat and parallel surfaces. Results demonstrating the applicability of this new technique for solving complex free surface flows, such as cavity filling and jet buckling, are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] Development of analytic energy gradient method in nuclear orbital plus molecular orbital theoryINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 14 2007Minoru Hoshino Abstract This study formulates the analytic energy gradients in the Hartree-Fock calculations of the NOMO theory, which simultaneously determines nuclear and electronic wave functions without the Born-Oppenheimer approximation. The formulations correspond to the translation- and rotation-contaminated (TRC), translation-free (TF), and translation- and rotation-free (TRF) treatments. The optimizations of the orbital centers for several diatomic molecules, which have been performed by using the analytic energy gradients, have given the averaged nuclear distances {R0} reflecting the quantum effects of nuclei and the anharmonicity of the potential energy surfaces. The numerical assessments have clarified that the effects of eliminating the translational and rotational contaminations, i.e., the TRF effects are important to improve the evaluations of {R0}, especially for the molecules including hydrogen atoms. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Adaptive integral method combined with the loose GMRES algorithm for planar structures analysisINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 1 2009W. Zhuang Abstract In this article, the adaptive integral method (AIM) is used to analyze large-scale planar structures. Discretization of the corresponding integral equations by method of moment (MoM) with Rao-Wilton-Glisson (RWG) basis functions can model arbitrarily shaped planar structures, but usually leads to a fully populated matrix. AIM could map these basis functions onto a rectangular grid, where the Toeplitz property of the Green's function would be utilized, which enables the calculation of the matrix-vector multiplication by use of the fast Fourier transform (FFT) technique. It reduces the memory requirement from O(N2) to O(N) and the operation complexity from O(N2) to O(N log N), where N is the number of unknowns. The resultant equations are then solved by the loose generalized minimal residual method (LGMRES) to accelerate iteration, which converges much faster than the conventional conjugate gradient method (CG). Furthermore, several preconditioning techniques are employed to enhance the computational efficiency of the LGMRES. Some typical microstrip circuits and microstrip antenna array are analyzed and numerical results show that the preconditioned LGMRES can converge much faster than conventional LGMRES. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009. [source] Stabilization of invariant sets for nonlinear systems with applications to control of oscillationsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 3 2001Anton S. Shiriaev Abstract The existing results on stabilization of invariant sets for nonlinear systems based on speed,gradient method and the notion of V -detectability are overviewed and extended. Applications to control of oscillations in pendulum, cart,pendulum and spherical pendulum systems are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] Simple preconditioners for the conjugate gradient method: experience with test day modelsJOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 3 2002I. STRANDÉN Preconditioned conjugate gradient method can be used to solve large mixed model equations quickly. Convergence of the method depends on the quality of the preconditioner. Here, the effect of simple preconditioners on the number of iterations until convergence was studied by solving breeding values for several test day models. The test day records were from a field data set, and several simulated data sets with low and high correlations among regression coefficients. The preconditioner matrices had diagonal or block diagonal parts. Transformation of the mixed model equations by diagonalization of the genetic covariance matrix was studied as well. Preconditioner having the whole block of the fixed effects was found to be advantageous. A block diagonal preconditioner for the animal effects reduced the number of iterations the higher the correlations among animal effects, but increased memory usage of the preconditioner. Diagonalization of the animal genetic covariance matrix often reduced the number of iterations considerably without increased memory usage. Einfache Preconditioners für die `Conjugate Gradient Method': Erfahrungen mit Testtagsmodellen Die `Preconditioned Conjugate Gradient Methode' kann benutzt werden um große `Mixed Model' Gleichungssysteme schnell zu lösen. In diesem Beitrag wurde der Einfluss von einfachen Preconditioners auf die Anzahl an Iterationen bis zur Konvergenz bei der Schätzung von Zuchtwerten bei verschiedenen Testtagsmodellen untersucht. Die Testtagsdaten stammen aus einem Felddatensatz und mehreren simulierten Datensätzen mit unterschiedlichen Korrelationen zwischen den Regressionskoeffizienten. Die Preconditioner Matrix bestand aus Diagonalen oder Blockdiagonalen Teilen. Eine Transformation der Mixed Modell Gleichungen durch Diagonalisierung der genetischen Kovarianzmatrix wurde ebenfalls untersucht. Preconditioners mit dem Block der fixen Effekte zeigten sich immer überlegen. Ein Blockdiagonaler Preconditioner für den Tiereffekt reduzierte die Anzahl an Iterationen mit höher werden Korrelationen zwischen den Tiereffekten, aber erhöhte den Speicherbedarf. Eine Diagonalisierung der genetischen Kovarianzmatrix reduzierte sehr oft die Anzahl an Iterationen erheblich ohne den Speicherbedarf zu erhöhen. [source] A new method to locate saddle points for reactions in solution by using the free-energy gradient method and the mean field approximationJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 10 2004I. Fdez. Abstract A new method for calculating saddle points of reactions in solution is presented. The main characteristics of the method are: (1) the solute,solvent system is described by the averaged solvent electrostatic potential/molecular dynamics method (ASEP/MD). This is a quantum mechanics/molecular mechanics method (QM/MM) that makes use of the mean field approximation (MFA) and that permits one to simultaneously optimize the electronic structure and geometry of the solute molecule and the solvent structure around it. (2) The transition state is located by the joint use of the free-energy gradient method and the mean field approximation. An application to the study of the Menshutkin reaction between NH3 and CH3Cl in aqueous solution is discussed. The accuracy and usefulness of the proposed method is checked through comparison with other methods. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1227,1233, 2004 [source] Phenolic Acid Content and Composition in Leaves and Roots of Common Commercial Sweetpotato (Ipomea batatas L.) Cultivars in the United StatesJOURNAL OF FOOD SCIENCE, Issue 6 2007V.-D. Truong ABSTRACT:, Phenolic acids in commercially important sweet potato cultivars grown in the United States were analyzed using reversed-phase high-performance liquid chromatography (HPLC). Caffeic acid, chlorogenic acid, 4,5-di-O-caffeoylquinic acid, 3,5-di-O-caffeoylquinic acid, and 3,4-di-O-caffeoylquinic acid were well separated with an isocratic elution in less than 25 min compared to about 120 min for analyzing and re-equilibrating the column with a gradient method. The isocratic elution order of these caffeoylquinic acid derivatives was confirmed by LC-MS/MS. Chlorogenic acid was the highest in root tissues, while 3,5-di-O-caffeoylquinic acid and/or 4,5-di-O-caffeoylquinic acid were predominant in the leaves. Steam cooking resulted in statistically nonsignificant increases in the concentration of total phenolics and all the individual phenolic acids identified. Sweetpotato leaves had the highest phenolic acid content followed by the peel, whole root, and flesh tissues. However, there was no significant difference in the total phenolic content and antioxidant activity between purees made from the whole and peeled sweet potatoes. [source] Comparison of real-time methods for maximizing power output in microbial fuel cellsAICHE JOURNAL, Issue 10 2010L. Woodward Abstract Microbial fuel cells (MFCs) constitute a novel power generation technology that converts organic waste to electrical energy using microbially catalyzed electrochemical reactions. Since the power output of MFCs changes considerably with varying operating conditions, the online optimization of electrical load (i.e., external resistance) is extremely important for maintaining a stable MFC performance. The application of several real-time optimization methods is presented, such as the perturbation and observation method, the gradient method, and the recently proposed multiunit method, for maximizing power output of MFCs by varying the external resistance. Experiments were carried out in two similar MFCs fed with acetate. Variations in substrate concentration and temperature were introduced to study the performance of each optimization method in the face of disturbances unknown to the algorithms. Experimental results were used to discuss advantages and limitations of each optimization method. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source] Rainfall-Runoff Model for Typhoons Making Landfall in Taiwan,JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, Issue 4 2007Ray-Shyan Wu Abstract:, In this study, we examine a physical raster-based distributed-parameter flood simulation model combining one-dimensional (1D) channel flow and two-dimensional (2D) overland flow. Continuity equations based on the water budget concept and momentum equations based on Manning's formula are included. The Shihmen reservoir watershed, situated in northern Taiwan, is selected as the study site, and data regarding the passage of Typhoons Xangsane [2000] and Nari [2001] are utilized to test the model. Comparative analysis shows that the description of the riverbed obtained by the gradient method is superior to that obtained by the GIS approach. This study suggests the Thiessen polygon method to interpolate spatial precipitation. The best calibrations are obtained at a spatial resolution of 160 m × 160 m, with a simulated time step of less than 5 s. The case study indicates that the proposed model has a good potential for inflow description, but does not accurately simulate the inflow amount. The proposed model is a flash reacting event-based watershed model. To improve simulation accuracy, a good infiltration model and soil moisture model are needed, and their formulation could be our next task. [source] New results on the convergence of the conjugate gradient methodNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 3 2009R. Bouyouli Abstract This paper is concerned with proving theoretical results related to the convergence of the conjugate gradient (CG) method for solving positive definite symmetric linear systems. Considering the inverse of the projection of the inverse of the matrix, new relations for ratios of the A -norm of the error and the norm of the residual are provided, starting from some earlier results of Sadok (Numer. Algorithms 2005; 40:201,216). The proofs of our results rely on the well-known correspondence between the CG method and the Lanczos algorithm. Copyright © 2008 John Wiley & Sons, Ltd. [source] Left conjugate gradient method for non-Hermitian linear systemsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 10 2008Li-Ping Wang Abstract Recently, Yuan et al. (BIT: Numer. Math. 2004; 44(1):189,207) proposed the left conjugate gradient (LCG) method for real positive-definite linear systems. This paper aims to generalize their method for solving complex non-Hermitian linear systems. To avoid the breakdown that possibly occurred in the LCG method, we also propose the block left conjugate direction method and the block LCG (BLCG) method. It is found that no breakdown occurs in the BLCG method and the block idea also applies to the real nonsymmetric case. Numerical experiments demonstrate the usefulness of the proposed LCG method. Copyright © 2008 John Wiley & Sons, Ltd. [source] Preconditioning CGNE iteration for inverse problemsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 3 2007H. Egger Abstract The conjugate gradient method applied to the normal equations (CGNE) is known as efficient method for the solution of non-symmetric linear equations. By stopping the iteration according to a discrepancy principle, CGNE can be turned into a regularization method, and thus can be applied to the solution of inverse, in particular, ill-posed problems. We show that CGNE for inverse problems can be further accelerated by preconditioning in Hilbert scales, derive (optimal) convergence rates with respect to data noise, and give tight bounds on the iteration numbers. The theoretical results are illustrated by numerical tests. Copyright © 2007 John Wiley & Sons, Ltd. [source] | ||||||||||||||||||||||