MELVIN LEOK THESIS

Journal of Dynamical and Control Systems 14 4 , , Discrete exterior calculus is modeled on a primal simplicial complex, and a dual circumcentric cell complex. Mathematical and General 39 19 , , Citation Leok, Melvin Foundations of computational geometric mechanics. Variational Runge-Kutta discretizations are considered in detail, including the extent to which symmetry reduction and discretization commute. Discrete connections on principal bundles are obtained by introducing the discrete Atiyah sequence, and considering splittings of the sequence.

Get my own profile Cited by View all All Since Citations h-index 27 19 iindex 61 Their combined citations are counted only for the first article. International Journal for Numerical Methods in Engineering 79 9 , , In addition, we obtain the Reduced Symplectic Runge-Kutta algorithm, which is a discrete analogue of cotangent bundle reduction. Journal of Dynamical and Control Systems 15 3 , , Discrete connections provide an intrinsic coordinatization of the reduced discrete space, and the necessary discrete geometry to develop more general discrete symmetry reduction techniques. Mathematical and General 39 19 , ,

In examples tbesis as harmonic maps and electromagnetism, discretizations arising from discrete exterior calculus commute with taking variations in Hamilton’s principle, which implies that directly discretizing these equations yield numerical schemes that have the structure-preserving properties associated with variational schemes. Journal of Dynamical and Control Systems 14 4, The following articles are merged in Scholar.

Melvin Leok, Ph.D.

New perspective on the U n Wigner-Racah calculus. New articles by this author. Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques. Equivalent representations of a discrete connection are considered, and an extension of the pair groupoid composition that takes into account the principal bundle structure is introduced. International Journal for Numerical Methods in Engineering 79 9, Get my own profile Cited by View all All Since Citations h-index 27 19 iindex 61 In particular, we develop discrete theories of reduction by symmetry, exterior calculus, connections on principal bundles, as well as generalizations of variational melcin.

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Discrete exterior calculus is modeled on a primal simplicial peok, and a dual circumcentric cell complex. My profile My library Metrics Alerts. Abstract Geometric mechanics involves thesia study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques.

Melvin Leok

This “Cited by” count includes citations to the following articles in Scholar. Computational algorithms obtained from a discrete Hamilton’s principle yield a discrete analogue of Lagrangian mechanics, and they exhibit excellent structure-preserving properties that can be ascribed to their variational derivation.

Celestial Mechanics and Dynamical Astronomy 98 2, Generalized Galerkin variational integrators are obtained by discretizing the action integral through appropriate choices of finite-dimensional function space and numerical quadrature. Tesis and General 39 19, Discrete connections on principal bundles leko obtained by introducing the discrete Atiyah sequence, and considering splittings of the sequence. More information and software credits.

A Caltech Library Service. The system can’t perform the operation now. Foundations of thesiz geometric mechanics Citation Leok, Melvin Foundations of computational geometric mechanics. Mathematical and General 20 14, Scheeres University of Colorado Verified email at colorado.

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New citations to this author. Variational Runge-Kutta discretizations are considered in detail, including the extent to which symmetry reduction and discretization commute.

Foundations of computational geometric mechanics – CaltechTHESIS

Adrian Sandu Virginia Tech Verified email at vt. We construct discrete analogues of the geometric and symmetry methods underlying geometric mechanics to enable the systematic development of computational geometric mechanics.

melvin leok thesis

Leok, Melvin Foundations of computational geometric mechanics. New articles related to this author’s research.

melvin leok thesis

Journal of Dynamical and Control Systems 15 3, Discrete connections provide an intrinsic coordinatization of the reduced discrete space, and the necessary discrete geometry to develop more general discrete symmetry reduction techniques.

Computer Methods in Applied Mechanics and Engineering, Articles Cited by Co-authors. No commercial reproduction, distribution, display or performance rights in this work are provided.

Explicit expressions for Lie group, higher-order Euler-Poincar?