Search results for "IMEX"
showing 6 items of 6 documents
NUMERICAL ALGORITHMS
2013
For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems implicit-explicit (IMEX) integration combines an explicit scheme for the non-stiff part with an implicit scheme for the stiff part. In a recent series of papers two of the authors (Sandu and Zhang) have developed IMEX GLMs, a family of implicit-explicit schemes based on general linear methods. It has been shown that, due to their high stage order, IMEX GLMs require no additional coupling order conditions, and are not marred by order reduction. This work develops a …
Stochastic Galerkin method for cloud simulation
2018
AbstractWe develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. The developed stochastic Galerkin method combines the space-time approximation obtained by a suitable finite volume method with a spectral-type approximation based on the generalized polynomial chaos expansion in the stochastic space. The resulting numerical scheme yields a second-order accurate approximation in both space and time and exponential convergence in the stochastic space. Our numerical results…
Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments
2013
Accepted by the Journal of Computational Physics Adaptive mesh refinement generally aims to increase computational efficiency without compromising the accuracy of the numerical solution. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result. This question is investigated for a specific example of dry atmospheric convection, namely the simulation of warm air bubbles. For this purpose a novel numerical model is developed that is tailored towards this specific application. The compressible Euler equations are solved with a Discontinuous Galerkin method. Time integration is done with an IMEXmethod and the dy…
Sensitivity of the SIMulation-EXtrapolation (SIMEX) methodology to mis-specification of the statistical properties of the measurement errors
2023
In hydrometeorological and environmental studies, it is common to seek relations between two variables (predictand and predictor), one of which (predictor) is affected by uncertainties. These errors unavoidably affect the results of the analyses by providing erroneous estimates of the parameters of the predictor-predictand model. A possible solution is represented by the SIMulation-EXtrapolation (SIMEX) methodology. This approach follows two steps: (1) perturbation of the predictor with increasing levels of uncertainties (multiples of the known error variance); and (2) finding a relation between the model's parameters and level of uncertainty, which allows their extrapolation to the error-f…
CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS
2018
We present an optimal control approach to the problem of model calibration for L\'evy processes based on a non parametric estimation procedure. The calibration problem is of considerable interest in mathematical finance and beyond. Calibration of L\'evy processes is particularly challenging as the jump distribution is given by an arbitrary L\'evy measure, which form a infinite dimensional space. In this work, we follow an approach which is related to the maximum likelihood theory of sieves. The sampling of the L\'evy process is modelled as independent observations of the stochastic process at some terminal time $T$. We use a generic spline discretization of the L\'evy jump measure and selec…
Cinètiques i mecanismes de la degradació atmosfèrica d'alguns pesticides
2016
Els plaguicides són amplament emprats actualment tant en agricultura com en usos domèstics o en industria. Tot i aportar importants beneficis a la societat actual, tant en temes relacionats amb la salut com amb l’economia, el seu ús també implica un riscos que s’han de conèixer. Un cop s’aplica un plaguicida, aquest es distribuirà entre els distints compartiments mediambientals –sòl, aigua i atmosfera- segons les seues propietats físico-químiques i el mode d’aplicació. L’atmosfera és un important medi de transport i reserva per als plaguicides i els seus productes de degradació. A l’arribar a l’atmosfera, el plaguicida es distribuirà entre les distintes fases aquosa, gasosa o particulada se…