Computation Of Jacobian Matrix Research Articles

Periodic states of adsorption cycles III. Convergence acceleration for direct determination

This paper describes several enhancements to accelerate the direct determination of the periodic states of fixed-bed adsorption cycles. The new methods make it possible to calculate the periodic states up to 40 times faster than our original formulation (Croft & LeVan, Chem. Eng. Sci. 49 (1994) 1821) and in many cases 100–1000s of times faster than by just running cycle after cycle. We have tested the methods on several examples and have obtained fast, stable, robust convergence. The enhancements are (i) the use of a hybrid Newton–Broyden method to reduce some of the Jacobian matrix calculation processes required by Newton's method, (ii) the initial application of a novel iterative-secant approach to increase stability and to avoid the calculation of the first Jacobian matrix for the hybrid Newton–Broyden method, (iii) the implementation of a sensitivity interpolation technique with dynamic grid allocation, and (iv) the dynamic specification of integration error tolerances.

EM2INV — A finite difference based algorithm for two-dimensional inversion of geoelectromagnetic data

The paper presents an efficient finite difference based 2D-inversion algorithm, EM2INV, for geoelectromagnetic data. The special features of the algorithm are • optimal grid generation based on grid design thumb rules, • finite domain boundary conditions, • interpolation matrix that permits generation of response at observation points different from grid points, • Gaussian elimination forward matrix solver, that enables reuse of already decomposed coefficient matrix, • super-block notion that reduces the number of blocks with unknown resistivities and, in turn, the size of Jacobian matrix and • bi-conjugate gradient matrix solver for inverse problem which circumvents the need of explicit Jacobian matrix computation.

Cost-effective parallel processing for H /H∞ controller synthesis

A distributed version of a homotopy algorithm for solving the H /H∞ mixed-norm controller synthesis problem is presented. The main purpose of the study is to explore the possibility of achieving high performance with low cost. Existing UNIX workstations running PVM (Parallel Virtual Machine) are utilized. Only the jacobian matrix computation is distributed and therefore the modification to the original sequential code is minimal. The same algorithm has also been implemented on an Intel Paragon parallel machine. Our implementation shows that acceptable speed-up is achieved and the larger the problem sizes, the higher the speed-up. Compared with the results from the Intel Paragon, the study concludes that utilizing the existing UNIX workstations can be a very cost-effective approach to shorten computation time. Furthermore, this economical way to achieve high performance computation can easily be realized and incorporated in a practical industrial design environment.

Linearization of the Dynamics of Closed-Chain Mechanical Systems*

ABSTRACT This paper presents an analytical-numerical method for linearizing the equations of motion of mechanical systems with closed chains. The algorithm developed here linearizes basic recursive kinematic relationships and then applies the chain rule to the derivation of the equations of motion under the framework of recursive formulation. This method can be incorporated into the formulation of recursive equations of motion for general multibody dynamic systems to handle large-scale systems. The method is directly applicable to system Jacobian matrix computation. Since the proposed algorithm uses no numerical differentiation, its accuracy is comparable to a symbolic, closed-form linearization. Moreover, without needing repetition computation in search of proper perturbation quantity, this method is computationally more efficient than the finite difference method

A space marching inversion algorithm for pulsed borehole radar in the time-domain

An iterative algorithm is developed to reconstruct the image of formation conductivity surrounding a borehole using time-domain data. The forward modeling employed in the algorithm is derived from the transmission line matrix (TLM) method, which is used to simulate electromagnetic waves propagating in formations with two-dimensional variations in cylindrical coordinates. A new structure of a transmission line mode is used to simulate a coil-type transmitter antenna in a borehole. Since the inversion algorithm proceeds iteratively and the part of the formation involved in the inversion marches in space step by step, no optimization is necessary, and problems caused by optimization procedure such as inverting large-scale matrix and computation of Jacobian matrix numerically, are avoided. This method is especially useful in cases where the analytic gradient is not available. The inversion algorithm is tested in formations having both one- and two-dimensional conductivity variations with coil-type transmitters. Investigation depth and resolution for noise-free cases are also discussed. >

Local identifiability of linear systems in a general input-output configuration

The study of local identifiability of models by calculation of the jacobian matrix of the system of equations is a theoretical method that is well known but whose practical use is often restricted to simple models because the necessary analytical calculations are lengthy and difficult. By a suitable choice of variables, an analytical expression is found for the jacobian and its determinant in linear models, valid for any particular model considered. As it can easily be programmed, the use of the criterion put forward should make possible a study of the local identifiability of complex models.