Browsing by Author "Constantinescu, Emil M."

Now showing 1 - 10 of 10
  • Thumbnail Image
    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.
  • Thumbnail Image
    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.
  • Thumbnail Image
    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.
  • Thumbnail Image
    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.
  • Thumbnail Image
    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.
  • Thumbnail Image
    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.
  • Thumbnail Image
    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.
  • Thumbnail Image
    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.
  • Thumbnail Image
    Scalable Implicit Solvers with Dynamic Mesh Adaptation for a Relativistic Drift-Kinetic Fokker-Planck-Boltzmann Model
    Rudi, Johann; Heldman, Max; Constantinescu, Emil M.; Tang, Qi; Tang, Xian-Zhu (2023-03-10)
    In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker–Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. We develop a new scalable fully implicit solver utilizing finite volume and conservative finite difference schemes and dynamic mesh adaptivity. A new data management framework in the PETSc library based on the p4est library is developed to enable simulations with dynamic adaptive mesh refinement (AMR), distributed memory parallelization, and dynamic load balancing of computational work. This framework and the runaway electron solver building on the framework are able to dynamically capture both bulk Maxwellian at the low-energy region and a runaway tail at the high-energy region. To effectively capture features via the AMR algorithm, a new AMR indicator prediction strategy is proposed that is performed alongside the implicit time evolution of the solution. This strategy is complemented by the introduction of computationally cheap feature-based AMR indicators that are analyzed theoretically. Numerical results quantify the advantages of the prediction strategy in better capturing features compared with nonpredictive strategies; and we demonstrate trade-offs regarding computational costs. The robustness with respect to model parameters, algorithmic scalability, and parallel scalability are demonstrated through several benchmark problems including manufactured solutions and solutions of different physics models. We focus on demonstrating the advantages of using implicit time stepping and AMR for runaway electron simulations.
  • Thumbnail Image
    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.