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Showing 1 to 20 of 63 for “"Jacobian matrix"”.
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An augmented Jacobian matrix algorithm for tracking homotopy zero curves
… the zero set of this homotopy map. The augmented Jacobian matrix algorithm is part of the software package HOMPACK, and is based on an algorithm developed by W.C. Rheinboldt. The algorithm exists in two forms-one for dense Jacobian matrices, and the other for sparse Jacobian matrices.
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Parallel homotopy curve tracking on a hypercube
… kernel of the full rank n x (n + 1) Jacobian matrix Dρ<sub>α</sub>(λ,x). Hence, tracking a zero curve of a homotopy map involves evaluating the Jacobian matrix and finding the one-dimensional kernel of the n x (n + 1) Jacobian matrix with rank n. Since accuracy is important, an …
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Location of stable and unstable equilibrium configurations using a model trust region quasi-Newton method and tunnelling
… turning points and exploiting sparsity of the Jacobian matrix at the same time. A quasi-Newton method in conjunction with a deflation technique is proposed here as an alternative to the hybrid method. The proposed method not only exploits sparsity and symmetry, but also represents an …
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Parameter estimation in reconstructing temperature fields during hyperthermia.
… and used to determine the elements in the Jacobian matrix associated with the inverse problem of estimating the blood perfusion and temperature fields during hyperthermia cancer treatments. These methods and a previously developed influence coefficient method for obtaining that matrix are …
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Preconditioned sequential and parallel conjugate gradient algorithms for homotopy curve tracking
… and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. …
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Least squares spectral element method for laminar and turbulent flows, –continuous and discontinuous approaches–
… To improve and condition number of the Jacobian matrix, as well as the convergence of the nonlinear system, a weighting for the least squares spectral method is introduced. This modification is essential for systems that include different scales in the formulation. Least squares …
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Measurement-based tools for power system monitoring and operations
… linear distribution factors and the power flow Jacobian matrix. Improvements and extensions to the general methodology are developed: (i) the number of required measurements is reduced in distribution factor estimation, (ii) distributed computation is described in the context of Jacobian matrix …
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Robust Mahalanobis distance in power systems state estimation
… of the data points associated with the weighted Jacobian matrix in power system state estimation. These distances, called robust Mahalanobis distances, can be used as weight functions to robustify the residuals of both the M-estimators and the least median of squares estimators for outlier …
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The unstructured grid incompressible Navier-Stokes algorithm for convective heat transfer based on artificial compressibility
… flux. An eigensystem is derived for the flux Jacobian matrix, which is used in the evaluation of the numerical flux and the characteristic variable boundary conditions. The resulting algorithm is validated by simulating canonical test cases from the three regimes of convective heat transfer. …
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Workspace Generation for Wire-Actuated Parallel Manipulators
… a geometric analysis of the manipulator’s Jacobian matrix, can be extended to manipulators that have an external wrench and/or gravity applied to the mobile platform. The convex hull method is applied to the example manipulators investigated with the null space method. The workspace …
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Digital load flow analysis using general matrix storage and non-zero element storage
… the corrections to the bus voltages are general matrix storage and nonzero element storage. In the general matrix all matrices are used with every element represented. In the non-zero routine, only nonzero entries in the YBUS and the Jacobian matrix are stored. Along with the non-zero routine, a …
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Comparison of modified Riks/Wempner and homotopy methods
… has been carried out based on the number of Jacobian matrix evaluations and the CPU time used by the programs. The Riks/Wempner program successfully traced the equilibrium path through the limit points and bifurcation points for all the four structures analyzed while the homotopy program …
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Defect correction based domain decomposition methods for some nonlinear problems
… problem must have a strongly diagonal dominant Jacobian matrix with a very small condition number. Yet its advantage can be of high signicance in the computational cost where it simply needs a scalar as the approximation of Jacobian matrix. Other nonlinear solvers employed for the schemes are a …
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A heuristic approach for path planning for redundant robots
… of the end effector and the elements of the jacobian matrix that correspond to the considered joint, while the output is the angle magnitude of the joint needed to reach the target point; An algorithm is used to determine the sign of the output from the fuzzy logic controller. Inverse …
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Innovative Methods for Solving Multicomponent Biogeochemical Groundwater Transport on Supercomputers
To evaluate the performance of the Jacobian-Free Newton-Krylov method, PARTRAN was used to simulate enhanced in situ bioremediation of subsurface NAPL (non-aqueous phase liquid) contamination on the ASCI Q supercomputer at Los Alamos National Laboratory, on which a study of parallel …
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A homotopy approach to the solutions of minimum-fuel space-flight rendezvous problems
… requires a fairly accurate computation of the Jacobian matrix, analytical representation of the system of equations is desired. Consequently, equations obtained using the true anomaly regularization of the governing equations were employed for the above purpose. A homotopy map suited for the …
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Mechanical Simulation of Articular Cartilage Based on Experimental Results
… through (1) implementation of an exact material Jacobian matrix definition using the Jaumann-Kirchhoff (J-K) method and (2) quantification of elastic material parameters based upon research findings of the Cal Poly Cartilage Biomechanics Group (CPGBG). The J-K method was successfully implemented …
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Robust optimization, game theory, and variational inequalities
… the associated cost function has an asymmetric Jacobian matrix. We give sufficient conditions for the convexity of this reformulation and thereby identify a class of VIs, of which monotone affine (and possibly asymmetric) VIs are a special case, which may be solved using widely-available and …
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Design of 3-DOF parallel manipulators for micro-motion applications
… In this thesis, the inverse kinematic, Jacobian matrix and stiffness analyses have been conducted, followed by the design optimization for structures. Finally, the FEA (Finite Element Analysis) and dynamic analysis have also been performed. There are many practical applications for …
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Design and optimization of a macro-micro manipulator featuring a 3-UPS compliant parallel mechanism
… and inverse kinematic analysis, formulation of Jacobian matrix; micromanipulator-focused stiffness evaluation, workspace analysis and structural optimization of stiffness and workspace properties.
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