The Experts below are selected from a list of 2121 Experts worldwide ranked by ideXlab platform
Adam M Oberman - One of the best experts on this subject based on the ideXlab platform.
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convergent finite difference solvers for viscosity solutions of the elliptic monge ampere equation in dimensions two and higher
SIAM Journal on Numerical Analysis, 2011Co-Authors: Brittany D Froese, Adam M ObermanAbstract:The elliptic Monge-Ampere equation is a fully nonlinear partial differential equation that originated in geometric surface theory and has been applied in Dynamic Meteorology, elasticity, geometric optics, image processing, and image registration. Solutions can be singular, in which case standard numerical approaches fail. Novel solution methods are required for stability and convergence to the weak (viscosity) solution. In this article we build a wide stencil finite difference discretization for the Monge-Ampere equation. The scheme is monotone, so the Barles-Souganidis theory allows us to prove that the solution of the scheme converges to the unique viscosity solution of the equation. Solutions of the scheme are found using a damped Newton's method. We prove convergence of Newton's method and provide a systematic method to determine a starting point for the Newton iteration. Computational results are presented in two and three dimensions, which demonstrates the speed and accuracy of the method on a number of exact solutions, which range in regularity from smooth to nondifferentiable.
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fast finite difference solvers for singular solutions of the elliptic monge ampere equation
Journal of Computational Physics, 2011Co-Authors: Brittany D Froese, Adam M ObermanAbstract:The elliptic Monge-Ampere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in Dynamic Meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. In this article we build a finite difference solver for the Monge-Ampere equation, which converges even for singular solutions. Regularity results are used to select a priori between a stable, provably convergent monotone discretization and an accurate finite difference discretization in different regions of the computational domain. This allows singular solutions to be computed using a stable method, and regular solutions to be computed more accurately. The resulting nonlinear equations are then solved by Newton's method. Computational results in two and three-dimensions validate the claims of accuracy and solution speed. A computational example is presented which demonstrates the necessity of the use of the monotone scheme near singularities.
Adam P. Showman - One of the best experts on this subject based on the ideXlab platform.
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Dynamic Meteorology at the photosphere of hd 209458b
The Astrophysical Journal, 2005Co-Authors: Curtis S. Cooper, Adam P. ShowmanAbstract:We calculate the Meteorology of the close-in transiting extrasolar planet HD 209458b using a global, three-dimensional atmospheric circulation model. Dynamics are driven by perpetual irradiation of one hemisphere of this tidally locked planet. The simulation predicts global temperature contrasts of ~500 K at the photosphere and the development of a steady superrotating jet. The jet extends from the equator to midlatitudes and from the top model layer at 1 mbar down to 10 bar at the base of the heated region. Wind velocities near the equator exceed 4 km s-1 at 300 mbar. The hottest regions of the atmosphere are blown downstream from the substellar point by ~60° of longitude. We predict from these results a factor of ~2 ratio between the maximum and minimum observed radiation from the planet over a full orbital period, with peak infrared emission preceding the time of the secondary eclipse by ~14 hr.
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Dynamic Meteorology at the Photosphere of HD 209458b
The Astrophysical Journal, 2005Co-Authors: Curtis S. Cooper, Adam P. ShowmanAbstract:We calculate the Meteorology of the close-in transiting extrasolar planet HD 209458b using a global, three-dimensional atmospheric circulation model. Dynamics are driven by perpetual irradiation of one hemisphere of this tidally locked planet. The simulation predicts global temperature contrasts of ~500 K at the photosphere and the development of a steady superrotating jet. The jet extends from the equator to mid-latitudes and from the top model layer at 1 mbar down to 10 bars at the base of the heated region. Wind velocities near the equator exceed 4 km/s at 300 mbar. The hottest regions of the atmosphere are blown downstream from the substellar point by 60 degrees of longitude. We predict from these results a factor of ~2 ratio between the maximum and minimum observed radiation from the planet over a full orbital period, with peak infrared emission preceding the time of the secondary eclipse by ~14 hours.
Brittany D Froese - One of the best experts on this subject based on the ideXlab platform.
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Convergent finite difference solvers for viscosity solutions of the elliptic Monge-Ampère equation in dimensions two and higher
2016Co-Authors: Brittany D Froese, M. ObermanAbstract:Abstract. The elliptic Monge-Ampère equation is a fully nonlinear Partial Differential Equation that originated in geometric surface theory and has been applied in Dynamic Meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. Novel solution methods are required for stability and convergence to the weak (viscosity) solution. In this article we build a wide stencil finite difference discretization for the Monge-Ampère equation. The scheme is monotone, so the Barles-Souganidis theory allows us to prove that the solution of the scheme converges to the unique viscosity solution of the equation. Solutions of the scheme are found using a damped Newton’s method. We prove convergence of Newton’s method and provide a systematic method to determine a starting point for the Newton iteration. Computational results are presented in two and three dimensions, which demonstrates the speed and accuracy of the method on a number of exact solutions, which range in regularity from smooth to non-differentiable. 1
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convergent finite difference solvers for viscosity solutions of the elliptic monge ampere equation in dimensions two and higher
SIAM Journal on Numerical Analysis, 2011Co-Authors: Brittany D Froese, Adam M ObermanAbstract:The elliptic Monge-Ampere equation is a fully nonlinear partial differential equation that originated in geometric surface theory and has been applied in Dynamic Meteorology, elasticity, geometric optics, image processing, and image registration. Solutions can be singular, in which case standard numerical approaches fail. Novel solution methods are required for stability and convergence to the weak (viscosity) solution. In this article we build a wide stencil finite difference discretization for the Monge-Ampere equation. The scheme is monotone, so the Barles-Souganidis theory allows us to prove that the solution of the scheme converges to the unique viscosity solution of the equation. Solutions of the scheme are found using a damped Newton's method. We prove convergence of Newton's method and provide a systematic method to determine a starting point for the Newton iteration. Computational results are presented in two and three dimensions, which demonstrates the speed and accuracy of the method on a number of exact solutions, which range in regularity from smooth to nondifferentiable.
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fast finite difference solvers for singular solutions of the elliptic monge ampere equation
Journal of Computational Physics, 2011Co-Authors: Brittany D Froese, Adam M ObermanAbstract:The elliptic Monge-Ampere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in Dynamic Meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. In this article we build a finite difference solver for the Monge-Ampere equation, which converges even for singular solutions. Regularity results are used to select a priori between a stable, provably convergent monotone discretization and an accurate finite difference discretization in different regions of the computational domain. This allows singular solutions to be computed using a stable method, and regular solutions to be computed more accurately. The resulting nonlinear equations are then solved by Newton's method. Computational results in two and three-dimensions validate the claims of accuracy and solution speed. A computational example is presented which demonstrates the necessity of the use of the monotone scheme near singularities.
Curtis S. Cooper - One of the best experts on this subject based on the ideXlab platform.
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Dynamic Meteorology at the photosphere of hd 209458b
The Astrophysical Journal, 2005Co-Authors: Curtis S. Cooper, Adam P. ShowmanAbstract:We calculate the Meteorology of the close-in transiting extrasolar planet HD 209458b using a global, three-dimensional atmospheric circulation model. Dynamics are driven by perpetual irradiation of one hemisphere of this tidally locked planet. The simulation predicts global temperature contrasts of ~500 K at the photosphere and the development of a steady superrotating jet. The jet extends from the equator to midlatitudes and from the top model layer at 1 mbar down to 10 bar at the base of the heated region. Wind velocities near the equator exceed 4 km s-1 at 300 mbar. The hottest regions of the atmosphere are blown downstream from the substellar point by ~60° of longitude. We predict from these results a factor of ~2 ratio between the maximum and minimum observed radiation from the planet over a full orbital period, with peak infrared emission preceding the time of the secondary eclipse by ~14 hr.
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Dynamic Meteorology at the Photosphere of HD 209458b
The Astrophysical Journal, 2005Co-Authors: Curtis S. Cooper, Adam P. ShowmanAbstract:We calculate the Meteorology of the close-in transiting extrasolar planet HD 209458b using a global, three-dimensional atmospheric circulation model. Dynamics are driven by perpetual irradiation of one hemisphere of this tidally locked planet. The simulation predicts global temperature contrasts of ~500 K at the photosphere and the development of a steady superrotating jet. The jet extends from the equator to mid-latitudes and from the top model layer at 1 mbar down to 10 bars at the base of the heated region. Wind velocities near the equator exceed 4 km/s at 300 mbar. The hottest regions of the atmosphere are blown downstream from the substellar point by 60 degrees of longitude. We predict from these results a factor of ~2 ratio between the maximum and minimum observed radiation from the planet over a full orbital period, with peak infrared emission preceding the time of the secondary eclipse by ~14 hours.
Ronald M Errico - One of the best experts on this subject based on the ideXlab platform.
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the workshop on applications of adjoint models in Dynamic Meteorology
Bulletin of the American Meteorological Society, 2003Co-Authors: Ronald M ErricoAbstract:The Fifth International Workshop on the Applications of Adjoint Models in Dynamic Meteorology was convened in Mount Bethel, Pennsylvania, 21–26 April 2002. There were 62 participants from 12 countries. Topics included adjoint model development, sensitivity and stability analysis, ensemble forecasting, and several aspects of data assimilation.
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workshop on adjoint applications in Dynamic Meteorology 23 28 august 1992 pacific grove california meeting review
Bulletin of the American Meteorological Society; (United States), 1993Co-Authors: Ronald M Errico, T Vukicevic, P Courtier, J DerberAbstract:A workshop on the development and application of ajoint models in the field of Dynamic Meteorology was held in Pacific Grove, California, during 23--28 August 1992. Topics addressed included sensitivity analysis, consideration of discontinuous processes in models, data assimilation, stability analysis, optimal evaluation of model parameters, and Kalman filtering.
