New method for parallel computation of Hessian matrix of conformational energy function in internal coordinates

2002 ◽  
Vol 23 (4) ◽  
pp. 463-469
Author(s):  
Shugo Nakamura ◽  
Daisuke Kyono ◽  
Mitsunori Ikeguchi ◽  
Kentaro Shimizu
Keyword(s):  
Parallel Computation ◽  
Energy Function ◽  
Hessian Matrix ◽  
Conformational Energy ◽  
New Method ◽  
Internal Coordinates

scholarly journals A new entropy-variable-based discretization method for minimum entropy moment approximations of linear kinetic equations

2021 ◽  
Author(s):  
Tobias Leibner ◽  
Mario Ohlberger
Keyword(s):  
Optimization Problems ◽  
Hessian Matrix ◽  
Computational Cost ◽  
Kinetic Equations ◽  
New Method ◽  
Minimum Entropy ◽  
Reduced Basis ◽  
Simple Task ◽  
Wide Range ◽  
The Moment

In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic equations that conserve many of the fundamental physical properties of solutions. However, their practical use is limited by their high computational cost, as an optimization problem has to be solved for every cell in the space-time grid. In addition, implementation of numerical solvers for these models is hampered by the fact that the optimization problems are only well-defined if the moment vectors stay within the realizable set. For the same reason, further reducing these models by, e.g., reduced-basis methods is not a simple task. Our new method overcomes these disadvantages of classical approaches. The transformation is performed on the semi-discretized level which makes them applicable to a wide range of kinetic schemes and replaces the nonlinear optimization problems by inversion of the positive-definite Hessian matrix. As a result, the new scheme gets rid of the realizability-related problems. Moreover, a discrete entropy law can be enforced by modifying the time stepping scheme. Our numerical experiments demonstrate that our new method is often several times faster than the standard optimization-based scheme.

Eigenvalue Decomposition Based Modified Newton Algorithm

2013 ◽  
Vol 347-350 ◽  
pp. 2586-2589
Author(s):  
Wen Jun Wang ◽  
Ju Bo Zhu ◽  
Xiao Jun Duan
Keyword(s):  
Convergence Rate ◽  
Numerical Experiment ◽  
Hessian Matrix ◽  
New Method ◽  
Eigenvalue Decomposition ◽  
Newton Algorithm ◽  
Negative Eigenvalues ◽  
Classical Algorithm ◽  
Newton Direction ◽  
Modified Algorithm

When the Hessian matrix is not positive, the Newton direction maybe not the descending direction. A new method named eigenvalue decomposition based modified Newton algorithm is presented, which first takes eigenvalue decomposition on the Hessian matrix, then replaces the negative eigenvalues with their absolutely values, finally reconstruct Hessian matrix and modify searching direction. The new searching direction is always the descending direction, and the convergence of the algorithm is proved and conclusion on convergence rate is presented qualitatively. At last, a numerical experiment is given for comparing the convergence domains of modified algorithm and classical algorithm.

Excited vibrational states and potential energy function for OCS determined using generalized internal coordinates

2000 ◽  
Vol 113 (14) ◽  
pp. 5695-5704 ◽  
Author(s):  
José Zúñiga ◽  
Adolfo Bastida ◽  
Mercedes Alacid ◽  
Alberto Requena
Keyword(s):  
Potential Energy ◽  
Energy Function ◽  
Potential Energy Function ◽  
Vibrational States ◽  
Internal Coordinates

Time-Independent Plasticity Related to Critical Point of Free Energy Function and Functional

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Q. Yang ◽  
Y. R. Liu ◽  
X. Q. Feng ◽  
S. W. Yu
Keyword(s):  
Free Energy ◽  
Critical Point ◽  
Thermodynamic Equilibrium ◽  
Energy Function ◽  
Hessian Matrix ◽  
Energy Functional ◽  
Internal Variables ◽  
Free Energy Function ◽  
Free Energy Functional ◽  
Appl Math

In this paper, time-independent plasticity is addressed within the thermodynamic framework with internal variables by Rice (1971, “Inelastic Constitutive Relations for Solids: An Internal Variable Theory and Its Application to Metal Plasticity,” J. Mech. Phys. Solids, 19, pp. 433–455). It is shown in this paper that the existence of a free energy function along with thermodynamic equilibrium conditions directly leads to associated flow rules. The time-independent inelastic behaviors can be fully determined by the Hessian matrix at the nondegenerate critical point of the free energy function. The normality rule of Hill and Rice (1973, “Elastic Potentials and the Structure of Inelastic Constitutive Laws,” SIAM J. Appl. Math., 25, pp. 448–461) or the Il'yushin (1961, “On a Postulate of Plasticity,” J. Appl. Math. Mech. 25, pp. 746–750) postulate is just a stability requirement of the thermodynamic equilibrium. The existence of a free energy functional which is not a direct function of the internal variables, along with thermodynamic equilibrium conditions also leads to associated flow rules. The time-independent inelastic behaviors with the free energy functional can be fully determined by the quasi Hessian matrix at the quasi critical point of the free energy functional. With the free energy functional, the thermodynamic forces conjugate to the internal variables are nonconservative and are constructed based on Darboux theorem. Based on the constructed nonconservative forces, it is shown that there may exist several possible thermodynamic equilibrium mechanisms for the thermodynamic system of the material sample. Therefore, the associated flow rules based on free energy functionals may degenerate into nonassociated flow rules. The symmetry of the conjugate forces plays a central role for the characteristics of time-independent plasticity.

scholarly journals A generalized conformational energy function of DNA derived from molecular dynamics simulations

2009 ◽  
Vol 37 (20) ◽  
pp. e135-e135 ◽  
Author(s):  
S. Yamasaki ◽  
T. Terada ◽  
K. Shimizu ◽  
H. Kono ◽  
A. Sarai
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Energy Function ◽  
Conformational Energy ◽  
Dynamics Simulations
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