Browsing by Author "Constantinescu, Emil M."

Now showing 1 - 9 of 9
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    Achieving Very High Order for Implicit Explicit Time Stepping: Extrapolation Methods
    Constantinescu, Emil M.; Sandu, Adrian (Department of Computer Science, Virginia Polytechnic Institute & State University, 2008-07-01)
    In this paper we construct extrapolated implicit-explicit time stepping methods that allow to efficiently solve problems with both stiff and non-stiff components. The proposed methods can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method of lines framework. These methods are simple to construct, easy to implement and parallelize. We establish the existence of perturbed asymptotic expansions of global errors, explain the convergence orders of these methods, and explore their linear stability properties. Numerical results with stiff ODEs, DAEs, and PDEs illustrate the theoretical findings and the potential of these methods to solve multiphysics multiscale problems.
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    Autoregressive Models of Background Errors for Chemical Data Assimilation
    Constantinescu, Emil M.; Chai, Tianfeng; Sandu, Adrian; Carmichael, Gregory R. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2006-10-01)
    The task of providing an optimal analysis of the state of the atmosphere requires the development of dynamic data-driven systems that efficiently integrate the observational data and the models. Data assimilation (DA) is the process of adjusting the states or parameters of a model in such a way that its outcome (prediction) is close, in some distance metric, to observed (real) states. It is widely accepted that a key ingredient of successful data assimilation is a realistic estimation of the background error distribution. This paper introduces a new method for estimating the background errors which are modeled using autoregressive processes. The proposed approach is computationally inexpensive and captures the error correlations along the flow lines.
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    Ensemble-based chemical data assimilation I: An idealized setting
    Constantinescu, Emil M.; Sandu, Adrian; Chai, Tianfeng; Carmichael, Gregory R. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2006-03-01)
    Data assimilation is the process of integrating observational data and model predictions to obtain an optimal representation of the state of the atmosphere. As more chemical observations in the troposphere are becoming available, chemical data assimilation is expected to play an essential role in air quality forecasting, similar to the role it has in numerical weather prediction. Considerable progress has been made recently in the development of variational tools for chemical data assimilation. In this paper we assess the performance of the ensemble Kalman filter (EnKF). Results in an idealized setting show that EnKF is promising for chemical data assimilation.
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    Ensemble-based chemical data assimilation II: Real observations
    Constantinescu, Emil M.; Sandu, Adrian; Chai, Tianfeng; Carmichael, Gregory R. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2006-03-01)
    Data assimilation is the process of integrating observational data and model predictions to obtain an optimal representation of the state of the atmosphere. As more chemical observations in the troposphere are becoming available, chemical data assimilation is expected to play an essential role in air quality forecasting, similar to the role it has in numerical weather prediction. Considerable progress has been made recently in the development of variational tools for chemical data assimilation. In this paper we assess the performance of the ensemble Kalman filter (EnKF) and compare it with a state of the art 4D-Var approach. We analyze different aspects that affect the assimilation process, investigate several ways to avoid filter divergence, and investigate the assimilation of emissions. Results with a real model and real observations show that EnKF is a promising approach for chemical data assimilation. The results also point to several issues on which further research is necessary.
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    Ensemble-based Chemical Data Assimilation III: Filter Localization
    Constantinescu, Emil M.; Sandu, Adrian; Chai, Tianfeng; Carmichael, Gregory R. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2006-03-01)
    Data assimilation is the process of integrating observational data and model predictions to obtain an optimal representation of the state of the atmosphere. As more chemical observations in the troposphere are becoming available, chemical data assimilation is expected to play an essential role in air quality forecasting, similar to the role it has in numerical weather prediction. Considerable progress has been made recently in the development of variational tools for chemical data assimilation. In this paper we implement and assess the performance of a localized ``perturbed observations'' ensemble Kalman filter (LEnKF). We analyze different settings of the ensemble localization, and investigate the joint assimilation of the state, emissions and boundary conditions. Results with a real model and real observations show that LEnKF is a promising approach for chemical data assimilation. The results also point to several issues on which future research is necessary.
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    Multirate explicit Adams methods for time integration of conservation laws
    Sandu, Adrian; Constantinescu, Emil M. (Department of Computer Science, Virginia Polytechnic Institute & State University, 2007-08-01)
    This paper constructs multirate linear multistep time discretizations based on Adams-Bashforth methods. These methods are aimed at solving conservation laws and allow different timesteps to be used in different parts of the spatial domain. The proposed family of discretizations is second order accurate in time and has conservation and linear and nonlinear stability properties under local CFL conditions. Multirate timestepping avoids the necessity to take small global timesteps - restricted by the largest value of the Courant number on the grid - and therefore results in more efficient computations. Numerical results obtained for the advection and Burgers' equations confirm the theoretical findings.
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    Multirate timestepping methods for hyperbolic conservation laws
    Constantinescu, Emil M.; Sandu, Adrian (Department of Computer Science, Virginia Polytechnic Institute & State University, 2006)
    This paper constructs multirate time discretizations for hyperbolic conservation laws that allow different time-steps to be used in different parts of the spatial domain. The discretization is second order accurate in time and preserves the conservation and stability properties under local CFL conditions. Multirate timestepping avoids the necessity to take small global time-steps (restricted by the largest value of the Courant number on the grid) and therefore results in more efficient algorithms.
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    On Extrapolated Multirate Methods
    Constantinescu, Emil M.; Sandu, Adrian (Department of Computer Science, Virginia Polytechnic Institute & State University, 2008-07-01)
    In this manuscript we construct extrapolated multirate discretization methods that allow to efficiently solve problems that have components with different dynamics. This approach is suited for the time integration of multiscale ordinary and partial differential equations and provides highly accurate discretizations. We analyze the linear stability properties of the multirate explicit and linearly implicit extrapolated methods. Numerical results with multiscale ODEs illustrate the theoretical findings.
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    Update on Multirate Timestepping Methods for Hyperbolic Conservation Laws
    Constantinescu, Emil M.; Sandu, Adrian (Department of Computer Science, Virginia Polytechnic Institute & State University, 2007-03-01)
    This paper constructs multirate time discretizations for hyperbolic conservation laws that allow different timesteps to be used in different parts of the spatial domain. The proposed family of discretizations is second order accurate in time and has conservation and linear and nonlinear stability properties under local CFL conditions. Multirate timestepping avoids the necessity to take small global timesteps (restricted by the largest value of the Courant number on the grid) and therefore results in more efficient algorithms. Numerical results obtained for the advection and Burgers equations confirm the theoretical findings.