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Geometric Discretization of Lagrangian Mechanics and Field Theories [PDF]
, 2009 This thesis presents a unified framework for geometric discretization of highly oscillatory mechanics and classical field theories, based on Lagrangian variational principles and discrete differential forms. For highly oscillatory problems in mechanics,
Stern, Ari Joshua
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Universe, 2021 A small deformation to the Schwarzschild metric controlled by four free parameters could be referred to as a nonspinning black hole solution in alternative theories of gravity.
Hongxing Zhang +3 more
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Novel Fractional order Integrators Using Traditional Rules Interpolation
Algerian Journal of Signals and Systems, 2020 This work proposes a new IIR integer order digital, so a new IIR fractional order integrators. The followed method includes two stages. First, the integer order integrator is obtained by interpolating well-known integration rulesnamely, Euler, bilinear ...
Chafia MEKHNACHE +2 more
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On Iterated Numerical Integration [PDF]
, 2005 We revisit the iterated numerical integration method and show that it is extremely efficient in solving certain classes of problems. A multidimensional integral can be approximated by a combination of lower-dimensional or one-dimensional adaptive methods iteratively. When an integrand contains sharp ridges which are not parallel with any axis, iterated
Shujun Li +2 more
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A Numerical Study of Quantization-Based Integrators
ITM Web of Conferences, 2014 Adaptive step size solvers are nowadays considered fundamental to achieve efficient ODE integration. While, traditionally, ODE solvers have been designed based on discrete time machines, new approaches based on discrete event systems have been proposed ...
Barros Fernando
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The role of numerical integration in numerical homogenization [PDF]
ESAIM: Proceedings and Surveys, 2015 Summary: Finite elements methods (FEMs) with numerical integration play a central role in numerical homogenization methods for partial differential equations with multiple scales, as the effective data in a homogenization problem can only be recovered from a microscopic solver at a finite number of points in the computational domain.
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Multisymplectic formulation of fluid dynamics using the inverse map [PDF]
, 2007 13.02.14 KB. Ok to add accepted version to spiral, embargo expired. RS policyWe construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map.
Cotter, CJ +5 more
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Variational Methods for Nonsmooth Mechanics [PDF]
, 2003 In this thesis we investigate nonsmooth classical and continuum mechanics and its discretizations by means of variational numerical and geometric methods.
Fetecau, Razvan Constantin
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Numerical Integration of Peak Functions
Journal of Complexity, 1996 Numerical integration of monotone and unimodal positive functions is considered. Adaptive and nonadaptive methods are studied in the worst case setting. Adaptation significantly helps for the class of unimodal functions, but not for the class of monotone functions. The methods are reliable for nonsmooth and discontinuous functions as well.
Erich Novak, Ingo Roschmann
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Modeling, Simulation, and Design of Self-Assembling Space Systems: Accurate Collision Detection, Robust Time Integration, and Optimal Control [PDF]
, 2013 Motivated by issues inherent in modeling and designing self-assembling systems (e.g. multiple collisions, collisions between non-smooth bodies, clumping and jamming behaviors, etc.), the goal of this thesis is to develop robust numerical tools that ...
Gwendolyn B. Johnson +1 more
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