Research and Application on the Visualization Algorithm of Wheel-Rail Contact

A visualization algorithm was presented for the optimization of geometrical shape matching in the wheel-rail contact system. The algorithm of the subsection cubic spline interpolation was adopted to fit the wheel-rail profiles curves, and curve boundary was got by the finite difference method; furthermore, the wheel-rail contact positions were figured out by computing the roll angles of wheelset iteratively with the dichotomy. Based on MATLAB and Visual C++, the wheel-rail contact geometrical parameters were calculated and visualized, the simulation results show the algorithm has the strong robustness.

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Numerical Simulation of Consolidation Test Considering Different Drainage Height

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.170-173.2325 ◽

2012 ◽

Vol 170-173 ◽

pp. 2325-2328

Author(s):

Yang Liu ◽

Zhe Wang

Keyword(s):

Numerical Simulation ◽

Finite Difference ◽

Finite Difference Method ◽

Soil Sample ◽

Difference Method ◽

Simulation Method ◽

Test Apparatus ◽

Consolidation Test ◽

Simulation Results ◽

The Finite Difference Method

Numerical simulation of the consolidation test was developed in different drainage conditions using the finite difference method. Soil sample was divided into layers to determine the time-steps of the test. A series of simulation tests were carried out to study the influence of drainage height on the coefficient ratio. Finally, some experiments data were compared with the numerical simulation results. Numerical results indicate that the simulation method broke through the limitation of test apparatus, and made it possible to conduct big size specimen consolidation test under certain conditions.

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Fast numerical method for pricing of variable annuities with guaranteed minimum withdrawal benefit under optimal withdrawal strategy

International Journal of Financial Engineering ◽

10.1142/s2424786315500243 ◽

2015 ◽

Vol 02 (03) ◽

pp. 1550024 ◽

Cited By ~ 12

Author(s):

Xiaolin Luo ◽

Pavel V. Shevchenko

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Close Agreement ◽

Spline Interpolation ◽

Transition Density ◽

Portfolio Performance ◽

Variable Annuities ◽

The Finite Difference Method ◽

Gauss Hermite Quadrature

A variable annuity contract with guaranteed minimum withdrawal benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the policy life plus the remaining account balance at maturity, regardless of the portfolio performance. Under the optimal withdrawal strategy of a policyholder, the pricing of variable annuities with GMWB becomes an optimal stochastic control problem. So far in the literature these contracts have only been evaluated by solving partial differential equations (PDE) using the finite difference method. The well-known least-squares or similar Monte Carlo methods cannot be applied to pricing these contracts because the paths of the underlying wealth process are affected by optimal cash withdrawals (control variables) and thus cannot be simulated forward in time. In this paper, we present a very efficient new algorithm for pricing these contracts in the case when transition density of the underlying asset between withdrawal dates or its moments are known. This algorithm relies on computing the expected contract value through a high order Gauss–Hermite quadrature applied on a cubic spline interpolation. Numerical results from the new algorithm for a series of GMWB contract are then presented, in comparison with results using the finite difference method solving corresponding PDE. The comparison demonstrates that the new algorithm produces results in very close agreement with those of the finite difference method, but at the same time it is significantly faster; virtually instant results on a standard desktop PC.

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