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Showing 1 to 13 of 13 for “"Jacobian matrices"”.
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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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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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Discrete Adjoints: Theoretical Analysis, Efficient Computation, and Applications
… a new algorithm for computing sparse Hessian matrices is presented including a complexity analysis and a report on practical experiments. Hence, the first two contributions of this thesis are dedicated to an efficient computation of discrete adjoints. The analysis of discrete adjoints with …
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Kinematics Analysis of Two Parallel Locomotion Mechanisms
… respectively. Based on the screw theory, the Jacobian matrices are assembled. Using Grassmann Line Geometry, each row of the Jacobian matrices is interpreted as a line in 3D space and the analytical conditions of the linear dependency cases are identified, which corresponds to the forward …
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Automatic simulation-driven reachability using matrix measures
… local bounds on the matrix measure of the Jacobian matrices. We discuss different techniques to compute the matrix measures under different norms: regular Euclidean norm or Euclidean norm under coordinate transformation, such that the exponential rate of the discrepancy function is locally …
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Chebyshev spectral method for incompressible viscous flow with boundary layer control via suction or blowing
… The appearance of spurious singularities in the Jacobian matrices associated with the system of equations and the vector of unknowns prevented this method from being implemented. Second, a Chebyshev spectral method using the wall function technique was applied to the defect form of the …
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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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A Thousand Bells: Acoustical implementation of bell spectra using the finite element method and its compositional realization
… transformation, FE shape functions, usages of Jacobian matrices, numerical integration of the stiffness matrix and the equivalent nodal force vector for the element by using the Gauss-Lagrange quadrature. In the fourth chapter, I create bell model geometry by using 2D bell nominal curve and …
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Development of a New Parallel In-Situ Combustion Simulator
… is introduced, and both numerical and analytical Jacobian matrices are applied. Due to the complexity of an ISC problem, an appropriate decoupling method must be considered. Thus the Gauss-Jordan transformation is raised. Then, with certain preconditioners and iterative solvers, a numerical …
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NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS
… Under suitable assumptions, the discretized Jacobian matrix is proved to have a uniformly bounded inverse with respect to mesh size. Different from current available approaches, a new strategy that leads to a robust multigrid solver is employed to define the coarse grid operator. Numerical …
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Analysing concerted criteria for local dynamic properties of metabolic systems
… a parameterised representation of the system's Jacobian matrix in which the model parameters encode information about the enzyme-metabolite interactions. Stability criteria can be derived by generating a large number of structural kinetic models (SK-models) with randomly sampled parameter sets …