نتایج جستجو برای: discrete variational theory
تعداد نتایج: 937936 فیلتر نتایج به سال:
We study variational problems involving the measure of level sets, or more precisely the push-forward of the Lebegue measure. This problem generalizes variational problems with finitely many (discrete) volume constraints. We obtain existence results for this general framework. Moreover, we show the surprising existence of asymmetric solutions to symmetric variational problems with this type of ...
We present a variational theory of integrable differential-difference equations (semi-discrete systems). This is natural extension the ideas known by names "Lagrangian multiforms" and "Pluri-Lagrangian systems", which have previously been established in both fully discrete continuous cases. The main feature these to capture hierarchy commuting single principle. Our example illustrate new semi-d...
We develop a semi-discrete version of discrete variational mechanics with applications to numerical integration of classical field theories. The geometric preservation properties are studied.
Variational integrators are a class of discretizations for mechanical systems which are derived by discretizing Hamilton’s principle of stationary action. They are applicable to both ordinary and partial differential equations, and to both conservative and forced problems. In the absence of forcing they conserve (multi-)symplectic structures, momenta arising from symmetries, and energy up to a ...
For the elastodynamic simulation of a geometrically exact beam, a variational integrator is derived from a PDE viewpoint. Variational integrators are symplectic and conserve discrete momentum maps and since the presented integrator is derived in the Lie group setting (unit quaternions for the representation of rotational degrees of freedom), it intrinsically preserves the group structure withou...
Parabolic variational inequalities of Allen-Cahn and CahnHilliard type are solved using methods involving constrained optimization. Time discrete variants are formulated with the help of Lagrange multipliers for local and non-local equality and inequality constraints. Fully discrete problems resulting from finite element discretizations in space are solved with the help of a primal-dual active ...
We show that transport in high contrast, conductive media has a discrete behavior. In the asymptotic limit of innnitely high contrast, the eeective impedance and the magnetic eld in such media are given by discrete min-max variational principles. Furthermore, we show that the transport problem has an asymptotic, resistor-inductor-capacitor network approximation. We use new variational formulati...
Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational discretizations is often the set of configuration pairs, analogously corresponding to initial and terminal points of a tangent vector. We develop alternative discrete an...
Undirected graphical models are applied in genomics, protein structure prediction, and neuroscience to identify sparse interactions that underlie discrete data. Although Bayesian methods for inference would be favorable in these contexts, they are rarely used because they require doubly intractable Monte Carlo sampling. Here, we develop a framework for scalable Bayesian inference of discrete un...
Variational integrators have traditionally been constructed from the perspective of Lagrangian mechanics, but there recent efforts to adopt discrete variational approaches symplectic discretization Hamiltonian mechanics using integrators. In this paper, we will extend these results setting multisymplectic field theories. We demonstrate that one can use notion Type II generating functionals for ...
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