6533b7d4fe1ef96bd1261ebf

RESEARCH PRODUCT

Path integral solution handled by Fast Gauss Transform

Roberta SantoroM. Di Paola

subject

Mechanical EngineeringMathematical analysisMathematicsofComputing_NUMERICALANALYSISAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsProbability density functionWhite noiseCondensed Matter Physicssymbols.namesakeNuclear Energy and EngineeringKronecker deltaComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONPath integral formulationsymbolsTwo-sided Laplace transformApplied mathematicsGauss–Seidel methodSettore ICAR/08 - Scienza Delle CostruzioniPath integral solution Fast Gauss Transform Symmetric Fast Gauss Transform Fokker-Planck equation Ito calculusS transformGaussian processCivil and Structural EngineeringMathematics

description

Abstract The path integral solution method is an effective tool for evaluating the response of non-linear systems under Normal White Noise, in terms of probability density function (PDF). In this paper it has been observed that, using short-time Gaussian approximation, the PDF at a given time instant is the Gauss Transform of the PDF at an earlier close time instant. Taking full advantage of the so-called Fast Gauss Transform a new integration method is proposed. In order to overcome some unsatisfactory trends of the classical Fast Gauss Transform, a new version termed as Symmetric Fast Gauss Transform is also proposed. Moreover, extensions to the two Fast Gauss Transform to MDOF systems are provided taking full advantage of Kronecker algebra.

yearjournalcountryeditionlanguage
2009-07-01Probabilistic Engineering Mechanics
https://doi.org/10.1016/j.probengmech.2008.07.008