Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods
NASA Astrophysics Data System (ADS)
Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco
2015-04-01
The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface
NASA Astrophysics Data System (ADS)
Cirpka, Olaf A.; Kitanidis, Peter K.
Including tracer data into geostatistically based methods of inverse modeling is computationally very costly when all concentration measurements are used and the sensitivities of many observations are calculated by the direct differentiation approach. Harvey and Gorelick (Water Resour Res 1995;31(7):1615-26) have suggested the use of the first temporal moment instead of the complete concentration record at a point. We derive a computationally efficient adjoint-state method for the sensitivities of the temporal moments that require the solution of the steady-state flow equation and two steady-state transport equations for the forward problem and the same number of equations for each first-moment measurement. The efficiency of the method makes it feasible to evaluate the sensitivity matrix many times in large domains. We incorporate our approach for the calculation of sensitivities in the quasi-linear geostatistical method of inversing ("iterative cokriging"). The application to an artificial example of a tracer introduced into an injection well shows good convergence behavior when both head and first-moment data are used for inversing, whereas inversing of arrival times alone is less stable.
Mesh-free adjoint methods for nonlinear filters
NASA Astrophysics Data System (ADS)
Daum, Fred
2005-09-01
We apply a new industrial strength numerical approximation, called the "mesh-free adjoint method", to solve the nonlinear filtering problem. This algorithm exploits the smoothness of the problem, unlike particle filters, and hence we expect that mesh-free adjoints are superior to particle filters for many practical applications. The nonlinear filter problem is equivalent to solving the Fokker-Planck equation in real time. The key idea is to use a good adaptive non-uniform quantization of state space to approximate the solution of the Fokker-Planck equation. In particular, the adjoint method computes the location of the nodes in state space to minimize errors in the final answer. This use of an adjoint is analogous to optimal control algorithms, but it is more interesting. The adjoint method is also analogous to importance sampling in particle filters, but it is better for four reasons: (1) it exploits the smoothness of the problem; (2) it explicitly minimizes the errors in the relevant functional; (3) it explicitly models the dynamics in state space; and (4) it can be used to compute a corrected value for the desired functional using the residuals. We will attempt to make this paper accessible to normal engineers who do not have PDEs for breakfast.
Hekmat, Mohamad Hamed; Mirzaei, Masoud
2015-01-01
In the present research, we tried to improve the performance of the lattice Boltzmann (LB) -based adjoint approach by utilizing the mesoscopic inherent of the LB method. In this regard, two macroscopic discrete adjoint (MADA) and microscopic discrete adjoint (MIDA) approaches are used to answer the following two challenging questions. Is it possible to extend the concept of the macroscopic and microscopic variables of the flow field to the corresponding adjoint ones? Further, similar to the conservative laws in the LB method, is it possible to find the comparable conservation equations in the adjoint approach? If so, then a definite framework, similar to that used in the flow solution by the LB method, can be employed in the flow sensitivity analysis by the MIDA approach. This achievement can decrease the implementation cost and coding efforts of the MIDA method in complicated sensitivity analysis problems. First, the MADA and MIDA equations are extracted based on the LB method using the duality viewpoint. Meanwhile, using an elementary case, inverse design of a two-dimensional unsteady Poiseuille flow in a periodic channel with constant body forces, the procedure of analytical evaluation of the adjoint variables is described. The numerical results show that similar correlations between the distribution functions can be seen between the corresponding adjoint ones. Besides, the results are promising, emphasizing the flow field adjoint variables can be evaluated via the adjoint distribution functions. Finally, the adjoint conservative laws are introduced. PMID:25679735
NASA Astrophysics Data System (ADS)
Anis, Fatima; Lou, Yang; Conjusteau, André; Su, Richard; Oruganti, Tanmayi; Ermilov, Sergey A.; Oraevsky, Alexander A.; Anastasio, Mark A.
2014-03-01
In this work, we investigate a novel reconstruction method for laser-induced ultrasound computed tomography (USCT) breast imaging that circumvents limitations of existing methods that rely on ray-tracing. There is currently great interest in developing hybrid imaging systems that combine optoacoustic tomography (OAT) and USCT. There are two primary motivations for this: (1) the speed-of-sound (SOS) distribution reconstructed by USCT can provide complementary diagnostic information; and (2) the reconstructed SOS distribution can be incorporated in the OAT reconstruction algorithm to improve OAT image quality. However, image reconstruction in USCT remains challenging. The majority of existing approaches for USCT breast imaging involve ray-tracing to establish the imaging operator. This process is cumbersome and can lead to inaccuracies in the reconstructed SOS images in the presence of multiple ray-paths and/or shadow zones. To circumvent these problems, we implemented a partial differential equation-based Eulerian approach to USCT that was proposed in the mathematics literature but never investigated for medical imaging applications. This method operates by directly inverting the Eikonal equation without ray-tracing. A numerical implementation of this method was developed and compared to existing reconstruction methods for USCT breast imaging. We demonstrated the ability of the new method to reconstruct SOS maps from TOF data obtained by a hybrid OAT/USCT imager built by our team.
Wing planform optimization via an adjoint method
NASA Astrophysics Data System (ADS)
Leoviriyakit, Kasidit
This dissertation focuses on the problem of wing planform optimization for transonic aircraft based on flow simulation using Computational Fluid Dynamics (CFD) combined with an adjoint-gradient based numerical optimization procedure. The adjoint method, traditionally used for wing section design has been extended to cover planform variations and to compute the sensitivities of the structural weight of both the wing section and planform variations. The two relevant disciplines accounted for are the aerodynamics and structural weight. A simplified structural weight model is used for the optimization. Results of a variety of long range transports indicate that significant improvement in both aerodynamics and structures can be achieved simultaneously. The proof-of-concept optimal results indicate large improvements for both drag and structural weight. The work is an "enabling step" towards a realistic automated wing designed by a computer.
NASA Astrophysics Data System (ADS)
Virieux, J.; Bretaudeau, F.; Metivier, L.; Brossier, R.
2013-12-01
Simultaneous inversion of seismic velocities and source parameters have been a long standing challenge in seismology since the first attempts to mitigate trade-off between very different parameters influencing travel-times (Spencer and Gubbins 1980, Pavlis and Booker 1980) since the early development in the 1970s (Aki et al 1976, Aki and Lee 1976, Crosson 1976). There is a strong trade-off between earthquake source positions, initial times and velocities during the tomographic inversion: mitigating these trade-offs is usually carried empirically (Lemeur et al 1997). This procedure is not optimal and may lead to errors in the velocity reconstruction as well as in the source localization. For a better simultaneous estimation of such multi-parametric reconstruction problem, one may take benefit of improved local optimization such as full Newton method where the Hessian influence helps balancing between different physical parameter quantities and improving the coverage at the point of reconstruction. Unfortunately, the computation of the full Hessian operator is not easily computed in large models and with large datasets. Truncated Newton (TCN) is an alternative optimization approach (Métivier et al. 2012) that allows resolution of the normal equation H Δm = - g using a matrix-free conjugate gradient algorithm. It only requires to be able to compute the gradient of the misfit function and Hessian-vector products. Traveltime maps can be computed in the whole domain by numerical modeling (Vidale 1998, Zhao 2004). The gradient and the Hessian-vector products for velocities can be computed without ray-tracing using 1st and 2nd order adjoint-state methods for the cost of 1 and 2 additional modeling step (Plessix 2006, Métivier et al. 2012). Reciprocity allows to compute accurately the gradient and the full Hessian for each coordinates of the sources and for their initial times. Then the resolution of the problem is done through two nested loops. The model update Δm is
Adjoint methods for external beam inverse treatment planning
NASA Astrophysics Data System (ADS)
Kowalok, Michael E.
Forward and adjoint radiation transport methods may both be used to determine the dosimetric relationship between source parameters and voxel elements of a phantom. Forward methods consider one specific tuple of source parameters and calculate the response in all voxels of interest. This response is often cast as the dose delivered per unit source-weight. Adjoint transport methods, conversely, consider one particular voxel and calculate the response of that voxel in relation to all possible source parameters. In this regard, adjoint methods provide an "adjoint function" in addition to a dose value. Although the dose is for a single voxel only, the adjoint function illustrates the source parameters, (e.g. beam positions and directions) that are most important to delivering the dose to that voxel. In this regard, adjoint methods of analysis lend themselves in a natural way to optimization problems and perturbation studies. This work investigates the utility of adjoint analytic methods for treatment planning and for Monte Carlo dose calculations. Various methods for implementing this approach are discussed, along with their strengths and weaknesses. The complementary nature of adjoint and forward techniques is illustrated and exploited. Also, several features of the Monte Carlo codes MCNP and MCNPX are reviewed for treatment planning applications.
Aerodynamic design optimization by using a continuous adjoint method
NASA Astrophysics Data System (ADS)
Luo, JiaQi; Xiong, JunTao; Liu, Feng
2014-07-01
This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows. General formulation of the continuous adjoint equations and the corresponding boundary conditions are derived. With the adjoint method, the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function, regardless of the number of design parameters. An inverse design of airfoil is firstly performed to study the accuracy of the adjoint gradient and the effectiveness of the adjoint method as an inverse design method. Then the method is used to perform a series of single and multiple point design optimization problems involving the drag reduction of airfoil, wing, and wing-body configuration, and the aerodynamic performance improvement of turbine and compressor blade rows. The results demonstrate that the continuous adjoint method can efficiently and significantly improve the aerodynamic performance of the design in a shape optimization problem.
Sensitivity of Lumped Constraints Using the Adjoint Method
NASA Technical Reports Server (NTRS)
Akgun, Mehmet A.; Haftka, Raphael T.; Wu, K. Chauncey; Walsh, Joanne L.
1999-01-01
Adjoint sensitivity calculation of stress, buckling and displacement constraints may be much less expensive than direct sensitivity calculation when the number of load cases is large. Adjoint stress and displacement sensitivities are available in the literature. Expressions for local buckling sensitivity of isotropic plate elements are derived in this study. Computational efficiency of the adjoint method is sensitive to the number of constraints and, therefore, the method benefits from constraint lumping. A continuum version of the Kreisselmeier-Steinhauser (KS) function is chosen to lump constraints. The adjoint and direct methods are compared for three examples: a truss structure, a simple HSCT wing model, and a large HSCT model. These sensitivity derivatives are then used in optimization.
Adjoint sensitivity analysis of plasmonic structures using the FDTD method.
Zhang, Yu; Ahmed, Osman S; Bakr, Mohamed H
2014-05-15
We present an adjoint variable method for estimating the sensitivities of arbitrary responses with respect to the parameters of dispersive discontinuities in nanoplasmonic devices. Our theory is formulated in terms of the electric field components at the vicinity of perturbed discontinuities. The adjoint sensitivities are computed using at most one extra finite-difference time-domain (FDTD) simulation regardless of the number of parameters. Our approach is illustrated through the sensitivity analysis of an add-drop coupler consisting of a square ring resonator between two parallel waveguides. The computed adjoint sensitivities of the scattering parameters are compared with those obtained using the accurate but computationally expensive central finite difference approach. PMID:24978258
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
NASA Astrophysics Data System (ADS)
Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.
2015-03-01
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space-time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge-Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.
2015-03-15
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that
Adjoint Formulation for an Embedded-Boundary Cartesian Method
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.; Murman, Scott M.; Pulliam, Thomas H.
2004-01-01
Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code
Comparison of the Monte Carlo adjoint-weighted and differential operator perturbation methods
Kiedrowski, Brian C; Brown, Forrest B
2010-01-01
Two perturbation theory methodologies are implemented for k-eigenvalue calculations in the continuous-energy Monte Carlo code, MCNP6. A comparison of the accuracy of these techniques, the differential operator and adjoint-weighted methods, is performed numerically and analytically. Typically, the adjoint-weighted method shows better performance over a larger range; however, there are exceptions.
Use of adjoint methods in the probabilistic finite element approach to fracture mechanics
NASA Technical Reports Server (NTRS)
Liu, Wing Kam; Besterfield, Glen; Lawrence, Mark; Belytschko, Ted
1988-01-01
The adjoint method approach to probabilistic finite element methods (PFEM) is presented. When the number of objective functions is small compared to the number of random variables, the adjoint method is far superior to the direct method in evaluating the objective function derivatives with respect to the random variables. The PFEM is extended to probabilistic fracture mechanics (PFM) using an element which has the near crack-tip singular strain field embedded. Since only two objective functions (i.e., mode I and II stress intensity factors) are needed for PFM, the adjoint method is well suited.
NASA Technical Reports Server (NTRS)
Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe
2013-01-01
This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.
Multigrid methods for bifurcation problems: The self adjoint case
NASA Technical Reports Server (NTRS)
Taasan, Shlomo
1987-01-01
This paper deals with multigrid methods for computational problems that arise in the theory of bifurcation and is restricted to the self adjoint case. The basic problem is to solve for arcs of solutions, a task that is done successfully with an arc length continuation method. Other important issues are, for example, detecting and locating singular points as part of the continuation process, switching branches at bifurcation points, etc. Multigrid methods have been applied to continuation problems. These methods work well at regular points and at limit points, while they may encounter difficulties in the vicinity of bifurcation points. A new continuation method that is very efficient also near bifurcation points is presented here. The other issues mentioned above are also treated very efficiently with appropriate multigrid algorithms. For example, it is shown that limit points and bifurcation points can be solved for directly by a multigrid algorithm. Moreover, the algorithms presented here solve the corresponding problems in just a few work units (about 10 or less), where a work unit is the work involved in one local relaxation on the finest grid.
Introduction to Adjoint Models
NASA Technical Reports Server (NTRS)
Errico, Ronald M.
2015-01-01
In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.
Adjoint-Based Methods for Estimating CO2 Sources and Sinks from Atmospheric Concentration Data
NASA Technical Reports Server (NTRS)
Andrews, Arlyn E.
2003-01-01
Work to develop adjoint-based methods for estimating CO2 sources and sinks from atmospheric concentration data was initiated in preparation for last year's summer institute on Carbon Data Assimilation (CDAS) at the National Center for Atmospheric Research in Boulder, CO. The workshop exercises used the GSFC Parameterized Chemistry and Transport Model and its adjoint. Since the workshop, a number of simulations have been run to evaluate the performance of the model adjoint. Results from these simulations will be presented, along with an outline of challenges associated with incorporating a variety of disparate data sources, from sparse, but highly precise, surface in situ observations to less accurate, global future satellite observations.
NASA Astrophysics Data System (ADS)
Hermand, Jean-Pierre; Berrada, Mohamed; Meyer, Matthias; Asch, Mark
2005-09-01
Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937-2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a spectral integral representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. The paper further discusses the application of the numerical adjoint PE method for ocean acoustic tomography. To show the effectiveness of the implemented numerical adjoint, preliminary inversion results of water sound-speed profile and bottom acoustic properties will be shown for the YELLOW SHARK '94 experimental conditions.
Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.
2004-01-01
Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented
Reconstruction of ocean circulation from sparse data using the adjoint method: LGM and the present
NASA Astrophysics Data System (ADS)
Kurahashi-Nakamura, T.; Losch, M. J.; Paul, A.; Mulitza, S.; Schulz, M.
2010-12-01
Understanding the behavior of the Earth's climate system under different conditions in the past is the basis for more robust projections of future climate. It is thought that the ocean circulation plays a very important role in the climate system, because it can greatly affect climate by dynamic-thermodynamic (as a medium of heat transport) and biogeochemical processes (by affecting the global carbon cycle). In this context, studying the period of the Last Glacial Maximum (LGM) is particularly promising, as it represents a climate state that is very different from today. Furthermore the LGM, compared to other paleoperiods, is characterized by a relatively good paleo-data coverage. Unfortunately, the ocean circulation during the LGM is still uncertain, with a range of climate models estimating both a stronger and a weaker formation rate of North Atlantic Deep Water (NADW) as compared to the present rate. Here, we present a project aiming at reducing this uncertainty by combining proxy data with a numerical ocean model using variational techniques. Our approach, the so-called adjoint method, employs a quadratic cost function of model-data differences weighted by their prior error estimates. We seek an optimal state estimate at the global minimum of the cost function by varying the independent control variables such as initial conditions (e.g. temperature), boundary conditions (e.g. surface winds, heat flux), or internal parameters (e.g. vertical diffusivity). The adjoint or dual model computes the gradient of the cost function with respect to these control variables and thus provides the information required by gradient descent algorithms. The gradients themselves provide valuable information about the sensitivity of the system to perturbations in the control variables. We use the Massachusetts Institute of Technology ocean general circulation model (MITgcm) with a cubed-sphere grid system that avoids converging grid lines and pole singularities. This model code is
Sensitivity analysis of numerically-simulated convective storms using direct and adjoint methods
Park, S.K.; Droegemeier, K.K.; Bischof, C.; Knauff, T.
1994-06-01
The goal of this project is to evaluate the sensitivity of numerically modeled convective storms to control parameters such as the initial conditions, boundary conditions, environment, and various physical and computational parameters. In other words, the authors seek the gradient of the solution vector with respect to specified parameters. One can use two approaches to accomplish this task. In the first or so-called brute force method, one uses a fully nonlinear model to generate a control forecast starting from a specified initial state. Then, a number of other forecasts are made in which chosen parameters (e.g., initial conditions) are systematically varied. The obvious drawback is that a large number of full model predictions are needed to examine the effects of only a single parameter. The authors describe herein an alternative, essentially automated method (ADIFOR, or Automatic DIfferentiation of FORtran) for obtaining the solution gradient that bypasses the adjoint altogether yet provides even more information about the gradient. (ADIFOR, like the adjoint technique, is constrained by the linearity assumption.) Applied to a 1-D moist cloud model, the authors assess the utility of ADIFOR relative to the brute force approach and evaluate the validity of the tangent linear approximation in the context of deep convection.
NASA Astrophysics Data System (ADS)
Clemo, T. M.; Ramarao, B.; Kelly, V. A.; Lavenue, M.
2011-12-01
Capture is a measure of the impact of groundwater pumping upon groundwater and surface water systems. The computation of capture through analytical or numerical methods has been the subject of articles in the literature for several decades (Bredehoeft et al., 1982). Most recently Leake et al. (2010) described a systematic way to produce capture maps in three-dimensional systems using a numerical perturbation approach in which capture from streams was computed using unit rate pumping at many locations within a MODFLOW model. The Leake et al. (2010) method advances the current state of computing capture. A limitation stems from the computational demand required by the perturbation approach wherein days or weeks of computational time might be required to obtain a robust measure of capture. In this paper, we present an efficient method to compute capture in three-dimensional systems based upon adjoint states. The efficiency of the adjoint method will enable uncertainty analysis to be conducted on capture calculations. The USGS and INTERA have collaborated to extend the MODFLOW Adjoint code (Clemo, 2007) to include stream-aquifer interaction and have applied it to one of the examples used in Leake et al. (2010), the San Pedro Basin MODFLOW model. With five layers and 140,800 grid blocks per layer, the San Pedro Basin model, provided an ideal example data set to compare the capture computed from the perturbation and the adjoint methods. The capture fraction map produced from the perturbation method for the San Pedro Basin model required significant computational time to compute and therefore the locations for the pumping wells were limited to 1530 locations in layer 4. The 1530 direct simulations of capture require approximately 76 CPU hours. Had capture been simulated in each grid block in each layer, as is done in the adjoint method, the CPU time would have been on the order of 4 years. The MODFLOW-Adjoint produced the capture fraction map of the San Pedro Basin model
Adaptive mesh refinement and adjoint methods in geophysics simulations
NASA Astrophysics Data System (ADS)
Burstedde, Carsten
2013-04-01
required by human intervention and analysis. Specifying an objective functional that quantifies the misfit between the simulation outcome and known constraints and then minimizing it through numerical optimization can serve as an automated technique for parameter identification. As suggested by the similarity in formulation, the numerical algorithm is closely related to the one used for goal-oriented error estimation. One common point is that the so-called adjoint equation needs to be solved numerically. We will outline the derivation and implementation of these methods and discuss some of their pros and cons, supported by numerical results.
Martien, Philip T; Harley, Robert A; Cacuci, Dan G
2006-04-15
Photochemical air pollution forms when emissions of nitrogen oxides (NO(x)) and volatile organic compounds (VOC) react in the atmosphere in the presence of sunlight. The goal of applying three-dimensional photochemical air quality models is usually to conduct sensitivity analysis: for example, to predict changes in an ozone response due to changes in NO(x) and VOC emissions or other model data. Forward sensitivity analysis methods are best suited to investigating sensitivities of many model responses to changes in a few inputs or parameters. Here we develop a continuous adjoint model and demonstrate an adjoint sensitivity analysis procedure that is well-suited to the complementary case of determining sensitivity of a small number of model responses to many parameters. Sensitivities generated using the adjoint method agree with those generated using other methods. Compared to the forward method, the adjoint method had large disk storage requirements but was more efficient in terms of computer processor time for receptor-based investigations focused on a single response at a specified site and time. The adjoint method also generates sensitivity apportionment fields, which reveal when and where model data are important to the target response. PMID:16683606
NASA Technical Reports Server (NTRS)
Pulliam, T. H.; Nemec, M.; Holst, T.; Zingg, D. W.; Kwak, Dochan (Technical Monitor)
2002-01-01
A comparison between an Evolutionary Algorithm (EA) and an Adjoint-Gradient (AG) Method applied to a two-dimensional Navier-Stokes code for airfoil design is presented. Both approaches use a common function evaluation code, the steady-state explicit part of the code,ARC2D. The parameterization of the design space is a common B-spline approach for an airfoil surface, which together with a common griding approach, restricts the AG and EA to the same design space. Results are presented for a class of viscous transonic airfoils in which the optimization tradeoff between drag minimization as one objective and lift maximization as another, produces the multi-objective design space. Comparisons are made for efficiency, accuracy and design consistency.
Assessing the Impact of Observations on Numerical Weather Forecasts Using the Adjoint Method
NASA Technical Reports Server (NTRS)
Gelaro, Ronald
2012-01-01
The adjoint of a data assimilation system provides a flexible and efficient tool for estimating observation impacts on short-range weather forecasts. The impacts of any or all observations can be estimated simultaneously based on a single execution of the adjoint system. The results can be easily aggregated according to data type, location, channel, etc., making this technique especially attractive for examining the impacts of new hyper-spectral satellite instruments and for conducting regular, even near-real time, monitoring of the entire observing system. This talk provides a general overview of the adjoint method, including the theoretical basis and practical implementation of the technique. Results are presented from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. When performed in conjunction with standard observing system experiments (OSEs), the adjoint results reveal both redundancies and dependencies between observing system impacts as observations are added or removed from the assimilation system. Understanding these dependencies may be important for optimizing the use of the current observational network and defining requirements for future observing systems
Pappin, Amanda Joy
2013-01-01
Background: Decision making regarding air pollution can be better informed if air quality impacts are traced back to individual emission sources. Adjoint or backward sensitivity analysis is a modeling tool that can achieve this goal by allowing for quantification of how emissions from sources in different locations influence human health metrics. Objectives: We attributed short-term mortality (valuated as an overall “health benefit”) in Canada and the United States to anthropogenic nitrogen oxides (NOx) and volatile organic compound (VOC) emissions across North America. Methods: We integrated epidemiological data derived from Canadian and U.S. time-series studies with the adjoint of an air quality model and also estimated influences of anthropogenic emissions at each location on nationwide health benefits. Results: We found significant spatiotemporal variability in estimated health benefit influences of NOx and VOC emission reductions on Canada and U.S. mortality. The largest estimated influences on Canada (up to $250,000/day) were from emissions originating in the Quebec City–Windsor Corridor, where population centers are concentrated. Estimated influences on the United States tend to be widespread and more substantial owing to both larger emissions and larger populations. The health benefit influences calculated using 24-hr average ozone (O3) concentrations are lower in magnitude than estimates calculated using daily 1-hr maximum O3 concentrations. Conclusions: Source specificity of the adjoint approach provides valuable information for guiding air quality decision making. Adjoint results suggest that the health benefits of reducing NOx and VOC emissions are substantial and highly variable across North America. PMID:23434744
NASA Technical Reports Server (NTRS)
Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.
2009-01-01
.We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation.
Eulerian-Lagrangian localized adjoint methods for reactive transport in groundwater
Ewing, R.E.; Wang, Hong
1996-12-31
In this paper, we present Eulerian-Lagrangian localized adjoint methods (ELLAM) to solve convection-diffusion-reaction equations governing contaminant transport in groundwater flowing through an adsorbing porous medium. These ELLAM schemes can treat various combinations of boundary conditions and conserve mass. Numerical results are presented to demonstrate the strong potential of ELLAM schemes.
NASA Astrophysics Data System (ADS)
Ren, L.; Liu, Q.
2012-12-01
We present multiple moment-tensor solution of the December 26, 2004 Sumatra earthquake based upon adjoint methods. An objective function Φ that measures the goodness of waveform fit between data and synthetics is minimized. Synthetics are calculated by spectral-element simulations (SPECFEM3D_GLOBE) in a 3D global earth model S362ANI to reduce the effect of heterogeneous structures. The Fréchet derivatives of Φ in the form δΦ = ∫T ∫VI(ɛ †ij)(x,T-t) δ(m_dot)ij(x,t)d3xdt, where δmij is the perturbation of moment density function and I(ɛ†ij)(x,T-t) denotes the time-integrated adjoint strain tensor, are calculated based upon adjoint methods implemented in SPECFEM3D_GLOBE. Our initial source model is obtained by monitoring the time-integrated adjoint strain tensors in the vicinity of the presumed source region. Source model parameters are iteratively updated by a preconditioned conjugate-gradient method to iteratively utilizing the calculated Φ and δΦ values. Our final inversion results show both similarities to and differences from previous source inversion results based on 1D background models.
NASA Astrophysics Data System (ADS)
Ren, L.; Liu, Q.; Hjörleifsdóttir, V.
2010-12-01
We present multiple moment-tensor solution of the Dec 26, 2004 Sumatra earthquake based upon the adjoint methods. An objective function Φ(m), where m is the multiple source model, measures the goodness of waveform fit between data and synthetics. The Fréchet derivatives of Φ in the form δΦ = ∫∫I(ɛ†)(x,T-t)δmij_dot(x,t)dVdt, where δmij is the source model perturbation and I(ɛ†)(x,T-t) denotes the time-integrated adjoint strain tensor, are calculated based upon adjoint methods and spectral-element simulations (SPECFEM3D_GLOBE) in a 3D global earth model S362ANI. Our initial source model is obtained independently by monitoring the time-integrated adjoint strain tensors around the presumed source region. We then utilize the Φ and δΦ calculations in a conjugate-gradient method to iteratively invert for the source model. Our final inversion results show both similarities with and differences to previous source inversion results based on 1D earth models.
NASA Astrophysics Data System (ADS)
Sikarwar, Nidhi
multiple experiments or numerical simulations. Alternatively an inverse design method can be used. An adjoint optimization method can be used to achieve the optimum blowing rate. It is shown that the method works for both geometry optimization and active control of the flow in order to deflect the flow in desirable ways. An adjoint optimization method is described. It is used to determine the blowing distribution in the diverging section of a convergent-divergent nozzle that gives a desired pressure distribution in the nozzle. Both the direct and adjoint problems and their associated boundary conditions are developed. The adjoint method is used to determine the blowing distribution required to minimize the shock strength in the nozzle to achieve a known target pressure and to achieve close to an ideally expanded flow pressure. A multi-block structured solver is developed to calculate the flow solution and associated adjoint variables. Two and three-dimensional calculations are performed for internal and external of the nozzle domains. A two step MacCormack scheme based on predictor- corrector technique is was used for some calculations. The four and five stage Runge-Kutta schemes are also used to artificially march in time. A modified Runge-Kutta scheme is used to accelerate the convergence to a steady state. Second order artificial dissipation has been added to stabilize the calculations. The steepest decent method has been used for the optimization of the blowing velocity after the gradients of the cost function with respect to the blowing velocity are calculated using adjoint method. Several examples are given of the optimization of blowing using the adjoint method.
Sensitivity analysis of a model of CO2 exchange in tundra ecosystems by the adjoint method
NASA Technical Reports Server (NTRS)
Waelbroek, C.; Louis, J.-F.
1995-01-01
A model of net primary production (NPP), decomposition, and nitrogen cycling in tundra ecosystems has been developed. The adjoint technique is used to study the sensitivity of the computed annual net CO2 flux to perturbation in initial conditions, climatic inputs, and model's main parameters describing current seasonal CO2 exchange in wet sedge tundra at Barrow, Alaska. The results show that net CO2 flux is most sensitive to parameters characterizing litter chemical composition and more sensitive to decomposition parameters than to NPP parameters. This underlines the fact that in nutrient-limited ecosystems, decomposition drives net CO2 exchange by controlling mineralization of main nutrients. The results also indicate that the short-term (1 year) response of wet sedge tundra to CO2-induced warming is a significant increase in CO2 emission, creating a positive feedback to atmosphreic CO2 accumulation. However, a cloudiness increase during the same year can severely alter this response and lead to either a slight decrease or a strong increase in emitted CO2, depending on its exact timing. These results demonstrate that the adjoint method is well suited to study systems encountering regime changes, as a single run of the adjoint model provides sensitivities of the net CO2 flux to perturbations in all parameters and variables at any time of the year. Moreover, it is shown that large errors due to the presence of thresholds can be avoided by first delimiting the range of applicability of the adjoint results.
On the proper treatment of grid sensitivities in continuous adjoint methods for shape optimization
NASA Astrophysics Data System (ADS)
Kavvadias, I. S.; Papoutsis-Kiachagias, E. M.; Giannakoglou, K. C.
2015-11-01
The continuous adjoint method for shape optimization problems, in flows governed by the Navier-Stokes equations, can be formulated in two different ways, each of which leads to a different expression for the sensitivity derivatives of the objective function with respect to the control variables. The first formulation leads to an expression including only boundary integrals; it, thus, has low computational cost but, when used with coarse grids, its accuracy becomes questionable. The second formulation comprises a sum of boundary and field integrals; due to the field integrals, it has noticeably higher computational cost, obtaining though higher accuracy. In this paper, the equivalence of the two formulations is revisited from the mathematical and, particularly, the numerical point of view. Internal and external aerodynamics cases, in which the objective function is either the total pressure losses or the force exerted on a solid body, are examined and differences in the computed gradients are discussed. After identifying the reason behind these discrepancies, the adjoint formulation is enhanced by the adjoint to a (hypothetical) grid displacement model and the new approach is proved to reproduce the accuracy of the second adjoint formulation while maintaining the low cost of the first one.
NASA Astrophysics Data System (ADS)
Edwards, S.; Reuther, J.; Chattot, J. J.
The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjoint approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to a target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speeds.
Active adjoint modeling method in microwave induced thermoacoustic tomography for breast tumor.
Zhu, Xiaozhang; Zhao, Zhiqin; Wang, Jinguo; Chen, Guoping; Liu, Qing Huo
2014-07-01
To improve the model-based inversion performance of microwave induced thermoacoustic tomography for breast tumor imaging, an active adjoint modeling (AAM) method is proposed. It aims to provide a more realistic breast acoustic model used for tumor inversion as the background by actively measuring and reconstructing the structural heterogeneity of human breast environment. It utilizes the reciprocity of acoustic sensors, and adapts the adjoint tomography method from seismic exploration. With the reconstructed acoustic model of breast environment, the performance of model-based inversion method such as time reversal mirror is improved significantly both in contrast and accuracy. To prove the advantage of AAM, a checkerboard pattern model and anatomical realistic breast models have been used in full wave numerical simulations. PMID:24956614
NASA Astrophysics Data System (ADS)
Shi, Lei; Wang, Z. J.
2015-08-01
Adjoint-based mesh adaptive methods are capable of distributing computational resources to areas which are important for predicting an engineering output. In this paper, we develop an adjoint-based h-adaptation approach based on the high-order correction procedure via reconstruction formulation (CPR) to minimize the output or functional error. A dual-consistent CPR formulation of hyperbolic conservation laws is developed and its dual consistency is analyzed. Super-convergent functional and error estimate for the output with the CPR method are obtained. Factors affecting the dual consistency, such as the solution point distribution, correction functions, boundary conditions and the discretization approach for the non-linear flux divergence term, are studied. The presented method is then used to perform simulations for the 2D Euler and Navier-Stokes equations with mesh adaptation driven by the adjoint-based error estimate. Several numerical examples demonstrate the ability of the presented method to dramatically reduce the computational cost comparing with uniform grid refinement.
NASA Astrophysics Data System (ADS)
Fernández-López, Sheila; Carrera, Jesús; Ledo, Juanjo; Queralt, Pilar; Luquot, Linda; Martínez, Laura; Bellmunt, Fabián
2016-04-01
Seawater intrusion in aquifers is a complex phenomenon that can be characterized with the help of electric resistivity tomography (ERT) because of the low resistivity of seawater, which underlies the freshwater floating on top. The problem is complex because of the need for joint inversion of electrical and hydraulic (density dependent flow) data. Here we present an adjoint-state algorithm to treat electrical data. This method is a common technique to obtain derivatives of an objective function, depending on potentials with respect to model parameters. The main advantages of it are its simplicity in stationary problems and the reduction of computational cost respect others methodologies. The relationship between the concentration of chlorides and the resistivity values of the field is well known. Also, these resistivities are related to the values of potentials measured using ERT. Taking this into account, it will be possible to define the different resistivities zones from the field data of potential distribution using the basis of inverse problem. In this case, the studied zone is situated in Argentona (Baix Maresme, Catalonia), where the values of chlorides obtained in some wells of the zone are too high. The adjoint-state method will be used to invert the measured data using a new finite element code in C ++ language developed in an open-source framework called Kratos. Finally, the information obtained numerically with our code will be checked with the information obtained with other codes.
An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.
2003-01-01
An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.
NASA Technical Reports Server (NTRS)
Andrews, A.
2002-01-01
A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future COS levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an "inverse problem," where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from long-term surface monitoring stations with data from intensive field campaigns and with proposed future satellite observations. A major advantage of the adjoint approach is that meteorological and surface data, as well as data for other atmospheric constituents and pollutants can be efficiently included in addition to observations of CO2 mixing ratios. This presentation will provide an overview of potentially useful datasets for carbon cycle research in general with an emphasis on planning for the North American Carbon Project. Areas of overlap with ongoing and proposed work on air quality/air pollution issues will be highlighted.
Adjoint-based deviational Monte Carlo methods for phonon transport calculations
NASA Astrophysics Data System (ADS)
Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G.
2015-06-01
In the field of linear transport, adjoint formulations exploit linearity to derive powerful reciprocity relations between a variety of quantities of interest. In this paper, we develop an adjoint formulation of the linearized Boltzmann transport equation for phonon transport. We use this formulation for accelerating deviational Monte Carlo simulations of complex, multiscale problems. Benefits include significant computational savings via direct variance reduction, or by enabling formulations which allow more efficient use of computational resources, such as formulations which provide high resolution in a particular phase-space dimension (e.g., spectral). We show that the proposed adjoint-based methods are particularly well suited to problems involving a wide range of length scales (e.g., nanometers to hundreds of microns) and lead to computational methods that can calculate quantities of interest with a cost that is independent of the system characteristic length scale, thus removing the traditional stiffness of kinetic descriptions. Applications to problems of current interest, such as simulation of transient thermoreflectance experiments or spectrally resolved calculation of the effective thermal conductivity of nanostructured materials, are presented and discussed in detail.
Source attribution of particulate matter pollution over North China with the adjoint method
NASA Astrophysics Data System (ADS)
Zhang, Lin; Liu, Licheng; Zhao, Yuanhong; Gong, Sunling; Zhang, Xiaoye; Henze, Daven K.; Capps, Shannon L.; Fu, Tzung-May; Zhang, Qiang; Wang, Yuxuan
2015-08-01
We quantify the source contributions to surface PM2.5 (fine particulate matter) pollution over North China from January 2013 to 2015 using the GEOS-Chem chemical transport model and its adjoint with improved model horizontal resolution (1/4° × 5/16°) and aqueous-phase chemistry for sulfate production. The adjoint method attributes the PM2.5 pollution to emissions from different source sectors and chemical species at the model resolution. Wintertime surface PM2.5 over Beijing is contributed by emissions of organic carbon (27% of the total source contribution), anthropogenic fine dust (27%), and SO2 (14%), which are mainly from residential and industrial sources, followed by NH3 (13%) primarily from agricultural activities. About half of the Beijing pollution originates from sources outside of the city municipality. Adjoint analyses for other cities in North China all show significant regional pollution transport, supporting a joint regional control policy for effectively mitigating the PM2.5 air pollution.
Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.
2006-01-01
A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design
Imaging the slab beneath central Chile using the Spectral Elements Method and adjoint techniques
NASA Astrophysics Data System (ADS)
Mercerat, E. D.; Nolet, G.; Marot, M.; Deshayes, P.; Monfret, T.
2010-12-01
This work focuses on imaging the subducting slab beneath Central Chile using novel inversion techniques based on the adjoint method and accurate wave propagation simulations using the Spectral Elements Method. The study area comprises the flat slab portion of the Nazca plate between 29 S and 34 S subducting beneath South America. We will use a database of regional seismicity consisting of both crustal and deep slab earthquakes with magnitude 3 < Mw < 6 recorded by different temporary and permanent seismological networks. Our main goal is to determine both the kinematics and the geometry of the subducting slab in order to help the geodynamical interpretation of such particular active margin. The Spectral Elements Method (SPECFEM3D code) is used to generate the synthetic seismograms and it will be applied for the iterative minimization based on adjoint techniques. The numerical mesh is 600 km x 600 km in horizontal coordinates and 220 km depth. As a first step, we are faced to well-known issues concerning mesh generation (resolution, quality, absorbing boundary conditions). In particular, we must evaluate the influence of free surface topography, as well as the MOHO and other geological interfaces in the synthetic seismograms. The initial velocity model from a previous travel-time tomography study, is linearly interpolated to the Gauss-Lobatto-Legendre grid. The comparison between the first forward simulations (up to 4 seconds minimum period) validate the initial velocity model of the study area, although many features not reproduced by the initial model have already been identified. Next step will concentrate in the comparison between finite-frequency kernels calculated by travel-time methods with ones based on adjoint methods, in order to highlight advantages and disadvantages in terms of resolution, accuracy, but also computational cost.
Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis,Michael J.
2006-01-01
Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach
NASA Astrophysics Data System (ADS)
Gopalakrishnan, Ganesh; Cornuelle, Bruce D.; Hoteit, Ibrahim; Rudnick, Daniel L.; Owens, W. Brechner
2013-07-01
An ocean state estimate has been developed for the Gulf of Mexico (GoM) using the MIT general circulation model and its adjoint. The estimate has been tested by forecasting loop current (LC) evolution and eddy shedding in the GoM. The adjoint (or four-dimensional variational) method was used to match the model evolution to observations by adjusting model temperature and salinity initial conditions, open boundary conditions, and atmospheric forcing fields. The model was fit to satellite-derived along-track sea surface height, separated into temporal mean and anomalies, and gridded sea surface temperature for 2 month periods. The optimized state at the end of the assimilation period was used to initialize the forecast for 2 months. Forecasts explore practical LC predictability and provide a cross-validation test of the state estimate by comparing it to independent future observations. The model forecast was tested for several LC eddy separation events, including Eddy Franklin in May 2010 during the deepwater horizon oil spill disaster in the GoM. The forecast used monthly climatological open boundary conditions, atmospheric forcing, and run-off fluxes. The model performance was evaluated by computing model-observation root-mean-square difference (rmsd) during both the hindcast and forecast periods. The rmsd metrics for the forecast generally outperformed persistence (keeping the initial state fixed) and reference (forecast initialized using assimilated Hybrid Coordinate Ocean Model 1/12° global analysis) model simulations during LC eddy separation events for a period of 1˜2 months.
Pricing of American style options with an adjoint process correction method
NASA Astrophysics Data System (ADS)
Jaekel, Uwe
2005-07-01
Pricing of American options is a more complicated problem than pricing of European options. In this work a formula is derived that allows the computation of the early exercise premium, i.e. the price difference between these two option types in terms of an adjoint process evolving in the reversed time direction of the original process determining the evolution of the European price. We show how this equation can be utilised to improve option price estimates from numerical schemes like finite difference or Monte Carlo methods.
Source attribution of PM2.5 pollution over North China using the adjoint method
NASA Astrophysics Data System (ADS)
Zhang, L.; Liu, L.; Zhao, Y.; Gong, S.; Henze, D. K.
2014-12-01
Conventional methods for source attribution of air pollution are based on measurement statistics (such as Positive Matrix Factorization) or sensitivity simulations with a chemical transport model (CTM). These methods generally ignore the nonlinear chemistry associated with the pollution formation or require unaffordable computational time. Here we use the adjoint of GEOS-Chem CTM at 0.25x0.3125 degree resolution to examine the sources contributing to the PM2.5 pollution over North China in winter 2013. We improved the model sulfate simulation by implementing the aqueous-phase oxidation of S(IV) by nitrogen dioxide. The adjoint results provide detailed source information at the model underlying grid resolution including source types and sectors. We show that PM2.5 pollution over Beijing and Baoding (Hebei) in winter was largely contributed by the large-scale residential and industrial burnings, and ammonia (NH3) emissions from agriculture activities. Nearly half of pollution was transported from outside of the city domains, and accumulated over 2-3 days. We also show under the current emission conditions, the PM2.5 concentrations over North China are more sensitive to NH3 emissions than NOx and SO2 emissions.
Ocean acoustic tomography from different receiver geometries using the adjoint method.
Zhao, Xiaofeng; Wang, Dongxiao
2015-12-01
In this paper, an ocean acoustic tomography inversion using the adjoint method in a shallow water environment is presented. The propagation model used is an implicit Crank-Nicolson finite difference parabolic equation solver with a non-local boundary condition. Unlike previous matched-field processing works using the complex pressure fields as the observations, here, the observed signals are the transmission losses. Based on the code tests of the tangent linear model, the adjoint model, and the gradient, the optimization problem is solved by a gradient-based minimization algorithm. The inversions are performed in numerical simulations for two geometries: one in which hydrophones are sparsely distributed in the horizontal direction, and another in which the hydrophones are distributed vertically. The spacing in both cases is well beyond the half-wavelength threshold at which beamforming could be used. To deal with the ill-posedness of the inverse problem, a linear differential regularization operator of the sound-speed profile is used to smooth the inversion results. The L-curve criterion is adopted to select the regularization parameter, and the optimal value can be easily determined at the elbow of the logarithms of the residual norm of the measured-predicted fields and the norm of the penalty function. PMID:26723329
Using Adjoint Methods to Improve 3-D Velocity Models of Southern California
NASA Astrophysics Data System (ADS)
Liu, Q.; Tape, C.; Maggi, A.; Tromp, J.
2006-12-01
We use adjoint methods popular in climate and ocean dynamics to calculate Fréchet derivatives for tomographic inversions in southern California. The Fréchet derivative of an objective function χ(m), where m denotes the Earth model, may be written in the generic form δχ=int Km(x) δln m(x) d3x, where δln m=δ m/m denotes the relative model perturbation. For illustrative purposes, we construct the 3-D finite-frequency banana-doughnut kernel Km, corresponding to the misfit of a single traveltime measurement, by simultaneously computing the 'adjoint' wave field s† forward in time and reconstructing the regular wave field s backward in time. The adjoint wave field is produced by using the time-reversed velocity at the receiver as a fictitious source, while the regular wave field is reconstructed on the fly by propagating the last frame of the wave field saved by a previous forward simulation backward in time. The approach is based upon the spectral-element method, and only two simulations are needed to produce density, shear-wave, and compressional-wave sensitivity kernels. This method is applied to the SCEC southern California velocity model. Various density, shear-wave, and compressional-wave sensitivity kernels are presented for different phases in the seismograms. We also generate 'event' kernels for Pnl, S and surface waves, which are the Fréchet kernels of misfit functions that measure the P, S or surface wave traveltime residuals at all the receivers simultaneously for one particular event. Effectively, an event kernel is a sum of weighted Fréchet kernels, with weights determined by the associated traveltime anomalies. By the nature of the 3-D simulation, every event kernel is also computed based upon just two simulations, i.e., its construction costs the same amount of computation time as an individual banana-doughnut kernel. One can think of the sum of the event kernels for all available earthquakes, called the 'misfit' kernel, as a graphical
Full waveform seismic tomography of the Vrancea region using the adjoint method
NASA Astrophysics Data System (ADS)
Baron, J.; Danecek, P.; Morelli, A.; Tondi, R.
2013-12-01
constrained by the quantity of usable seismic data as well as a poor signal-to-noise ratio, which imposes to carry out the analysis in a frequency band of relatively high frequencies. The adjoint tomographic inversion is implemented with the SPECFEM3D solver (a community code applying the spectral element method) to generate synthetic data and traveltime misfit kernels in a fine computational mesh that satisfies the data frequency band requirements. The computation is run on a BlueGene/Q massively parallel computer available at the CINECA supercomputing centre. We show what information can be retrieved about the tomographic model applying the full-waveform inversion and adjoint methods even applied to a modest-quality, mostly high-frequency content, regional dataset.
NASA Astrophysics Data System (ADS)
Truchet, G.; Leconte, P.; Peneliau, Y.; Santamarina, A.; Malvagi, F.
2014-06-01
Pile-oscillation experiments are performed in the MINERVE reactor at the CEA Cadarache to improve nuclear data accuracy. In order to precisely calculate small reactivity variations (<10 pcm) obtained in these experiments, a reference calculation need to be achieved. This calculation may be accomplished using the continuous-energy Monte Carlo code TRIPOLI-4® by using the eigenvalue difference method. This "direct" method has shown limitations in the evaluation of very small reactivity effects because it needs to reach a very small variance associated to the reactivity in both states. To answer this problem, it has been decided to implement the exact perturbation theory in TRIPOLI-4® and, consequently, to calculate a continuous-energy adjoint flux. The Iterated Fission Probability (IFP) method was chosen because it has shown great results in some other Monte Carlo codes. The IFP method uses a forward calculation to compute the adjoint flux, and consequently, it does not rely on complex code modifications but on the physical definition of the adjoint flux as a phase-space neutron importance. In the first part of this paper, the IFP method implemented in TRIPOLI-4® is described. To illustrate the effciency of the method, several adjoint fluxes are calculated and compared with their equivalent obtained by the deterministic code APOLLO-2. The new implementation can calculate angular adjoint flux. In the second part, a procedure to carry out an exact perturbation calculation is described. A single cell benchmark has been used to test the accuracy of the method, compared with the "direct" estimation of the perturbation. Once again the method based on the IFP shows good agreement for a calculation time far more inferior to the "direct" method. The main advantage of the method is that the relative accuracy of the reactivity variation does not depend on the magnitude of the variation itself, which allows us to calculate very small reactivity perturbations with high
Comparison of adjoint and nudging methods to initialise ice sheet model basal conditions
NASA Astrophysics Data System (ADS)
Mosbeux, Cyrille; Gillet-Chaulet, Fabien; Gagliardini, Olivier
2016-07-01
Ice flow models are now routinely used to forecast the ice sheets' contribution to 21st century sea-level rise. For such short term simulations, the model response is greatly affected by the initial conditions. Data assimilation algorithms have been developed to invert for the friction of the ice on its bedrock using observed surface velocities. A drawback of these methods is that remaining uncertainties, especially in the bedrock elevation, lead to non-physical ice flux divergence anomalies resulting in undesirable transient effects. In this study, we compare two different assimilation algorithms based on adjoints and nudging to constrain both bedrock friction and elevation. Using synthetic twin experiments with realistic observation errors, we show that the two algorithms lead to similar performances in reconstructing both variables and allow the flux divergence anomalies to be significantly reduced.
NASA Technical Reports Server (NTRS)
Rozvany, G. I. N.; Sobieszczanski-Sobieski, J.
1992-01-01
In new, iterative continuum-based optimality criteria (COC) methods, the strain in the adjoint structure becomes non-unique if the number of active local constraints is greater than the number of design variables for an element. This brief note discusses the use of smooth envelope functions (SEFs) in overcoming economically computational problems caused by the above non-uniqueness.
NASA Astrophysics Data System (ADS)
Kocaogul, Ibrahim; Hu, Fang; Li, Xiaodong
2014-03-01
Radiation of acoustic waves at all frequencies can be obtained by Time Domain Wave Packet (TDWP) method in a single time domain computation. Other benefit of the TDWP method is that it makes possible the separation of acoustic and instability wave in the shear flow. The TDWP method is also particularly useful for computations in the ducted or waveguide environments where incident wave modes can be imposed cleanly without a potentially long transient period. The adjoint equations for the linearized Euler equations are formulated for the Cartesian coordinates. Analytical solution for adjoint equations is derived by using Green's function in 2D and 3D. The derivation of reciprocal relations is presented for closed and open ducts. The adjoint equations are then solved numerically in reversed time by the TDWP method. Reciprocal relation between the duct mode amplitudes and far field point sources in the presence of the exhaust shear flow is computed and confirmed numerically. Applications of the adjoint problem to closed and open ducts are also presented.
Seismic Imaging of VTI, HTI and TTI based on Adjoint Methods
NASA Astrophysics Data System (ADS)
Rusmanugroho, H.; Tromp, J.
2014-12-01
Recent studies show that isotropic seismic imaging based on adjoint method reduces low-frequency artifact caused by diving waves, which commonly occur in two-wave wave-equation migration, such as Reverse Time Migration (RTM). Here, we derive new expressions of sensitivity kernels for Vertical Transverse Isotropy (VTI) using the Thomsen parameters (ɛ, δ, γ) plus the P-, and S-wave speeds (α, β) as well as via the Chen & Tromp (GJI 2005) parameters (A, C, N, L, F). For Horizontal Transverse Isotropy (HTI), these parameters depend on an azimuthal angle φ, where the tilt angle θ is equivalent to 90°, and for Tilted Transverse Isotropy (TTI), these parameters depend on both the azimuth and tilt angles. We calculate sensitivity kernels for each of these two approaches. Individual kernels ("images") are numerically constructed based on the interaction between the regular and adjoint wavefields in smoothed models which are in practice estimated through Full-Waveform Inversion (FWI). The final image is obtained as a result of summing all shots, which are well distributed to sample the target model properly. The impedance kernel, which is a sum of sensitivity kernels of density and the Thomsen or Chen & Tromp parameters, looks crisp and promising for seismic imaging. The other kernels suffer from low-frequency artifacts, similar to traditional seismic imaging conditions. However, all sensitivity kernels are important for estimating the gradient of the misfit function, which, in combination with a standard gradient-based inversion algorithm, is used to minimize the objective function in FWI.
NASA Astrophysics Data System (ADS)
Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.
2014-12-01
Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.
MCNP: Multigroup/adjoint capabilities
Wagner, J.C.; Redmond, E.L. II; Palmtag, S.P.; Hendricks, J.S.
1994-04-01
This report discusses various aspects related to the use and validity of the general purpose Monte Carlo code MCNP for multigroup/adjoint calculations. The increased desire to perform comparisons between Monte Carlo and deterministic codes, along with the ever-present desire to increase the efficiency of large MCNP calculations has produced a greater user demand for the multigroup/adjoint capabilities. To more fully utilize these capabilities, we review the applications of the Monte Carlo multigroup/adjoint method, describe how to generate multigroup cross sections for MCNP with the auxiliary CRSRD code, describe how to use the multigroup/adjoint capability in MCNP, and provide examples and results indicating the effectiveness and validity of the MCNP multigroup/adjoint treatment. This information should assist users in taking advantage of the MCNP multigroup/adjoint capabilities.
High-resolution array imaging using teleseismic converted waves based on adjoint methods
NASA Astrophysics Data System (ADS)
Liu, Q.; Chen, C.
2011-12-01
Seismic coda waves and converted phases have been used extensively to image detailed subsurface structures underneath seismic arrays, based on methods such as receiver functions, Kirchhoff migration and generalized Radon transform (GRT). Utilizing the same coda and converted waves, we propose to image both discontinuity interfaces and 3D velocity anomalies by combining full numerical simulations of wave propagation with adjoint methods recently adopted in global and regional tomography inversions. The `sensitivities' of these coda/converted waves to density, P and S velocities are calculated based on the interaction of the forward wave field that produces the main P phase, and the adjoint wave field generated by injecting the coda/converted phases at array stations as virtual sources, similar to the computation of isochrons in previous techniques. The density kernels generally highlight discontinuity interfaces and sharp velocity contrasts, while P and S velocity kernels provide hints to the update of volumetric velocity structures. The application of numerical solvers also allows the incorporation of 3D regional tomography models as background velocity models, providing better focusing of velocity anomalies. We show the feasibility of this technique on a synthetic case built based on the imaging geometry for Slave craton in the northwestern Canadian Shield by the POLARIS broadband seismic network. The main challenge of this technique lies in reproducing the forward wave field generated by tele-seismic sources in a limited simulation domain encompassing only local heterogeneous structures underneath array receivers. For simple homogeneous and layer-over-half-space background models, this can be solved by setting the incoming plane waves as initial conditions based on analytical formulae. For more sophisticated background models, a hybrid spectral-element solver is implemented by defining a fictitious boundary encompassing all local heterogeneities within the
NASA Astrophysics Data System (ADS)
Hagedoorn, J. M.; Martinec, Z.
2012-12-01
Recent models of the Earth's geomagnetic field at the core-mantle boundary (CMB) are based on satellite measurements and/or observatory data, which are mostly harmonically downward continued to the CMB. One aim of the upcoming satellite mission Swarm is to determine the three-dimensional distribution of electric conductivity of the Earth's mantle. On this background, we developed an adjoint sensitivity downward continuation approach that is capable to consider three-dimensional electric conductivity distributions. Martinec (Geophys. J. Int., 136, 1999) developed a time-domain spectral-finite element approach for the forward modelling of vector electromagnetic induction data as measured on ground-based magnetic observatory or by satellites. We design a new method to compute the sensitivity of the magnetic induction data to a magnetic field prescribed at the core-mantle boundary, which we term the adjoint sensitivity method. The forward and adjoint initial boundary-value problems, both solved in the time domain, are identical, except for the specification of prescribed boundary conditions. The respective boundary-value data are the measured X magnetic component for the forward method and the difference between the measured and predicted Z magnetic component for the adjoint method. The squares of the differences in Z magnetic component summed up over the time of observation and all spatial positions of observations determine the misfit. Then the sensitivities of observed data, i.e. the partial derivatives of the misfit with respect to the parameters characterizing the magnetic field at the core-mantle boundary, are obtained by the surface integral over the core-mantle boundary of the product of the adjoint solution multiplied by the time-dependent functions describing the time variability of magnetic field at the core-mantle boundary, and integrated over the time of observation. The time variability of boundary data is represented in terms of locally supported B
Estimates of black carbon emissions in the western United States using the GEOS-Chem adjoint model
NASA Astrophysics Data System (ADS)
Mao, Y. H.; Li, Q. B.; Henze, D. K.; Jiang, Z.; Jones, D. B. A.; Kopacz, M.; He, C.; Qi, L.; Gao, M.; Hao, W.-M.; Liou, K.-N.
2015-07-01
We estimate black carbon (BC) emissions in the western United States for July-September 2006 by inverting surface BC concentrations from the Interagency Monitoring of Protected Visual Environments (IMPROVE) network using a global chemical transport model (GEOS-Chem) and its adjoint. Our best estimate of the BC emissions is 49.9 Gg at 2° × 2.5° (a factor of 2.1 increase) and 47.3 Gg at 0.5° × 0.667° (1.9 times increase). Model results now capture the observed major fire episodes with substantial bias reductions ( 35 % at 2° × 2.5° and 15 % at 0.5° × 0.667°). The emissions are 20-50 % larger than those from our earlier analytical inversions (Mao et al., 2014). The discrepancy is especially drastic in the partitioning of anthropogenic versus biomass burning emissions. The August biomass burning BC emissions are 4.6-6.5 Gg and anthropogenic BC emissions 8.6-12.8 Gg, varying with the model resolution, error specifications, and subsets of observations used. On average both anthropogenic and biomass burning emissions in the adjoint inversions increase 2-fold relative to the respective {a priori} emissions, in distinct contrast to the halving of the anthropogenic and tripling of the biomass burning emissions in the analytical inversions. We attribute these discrepancies to the inability of the adjoint inversion system, with limited spatiotemporal coverage of the IMPROVE observations, to effectively distinguish collocated anthropogenic and biomass burning emissions on model grid scales. This calls for concurrent measurements of other tracers of biomass burning and fossil fuel combustion (e.g., carbon monoxide and carbon isotopes). We find that the adjoint inversion system as is has sufficient information content to constrain the total emissions of BC on the model grid scales.
Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method
Dekeyser, W.; Reiter, D.; Baelmans, M.
2014-12-01
As magnetic confinement fusion progresses towards the development of first reactor-scale devices, computational tokamak divertor design is a topic of high priority. Presently, edge plasma codes are used in a forward approach, where magnetic field and divertor geometry are manually adjusted to meet design requirements. Due to the complex edge plasma flows and large number of design variables, this method is computationally very demanding. On the other hand, efficient optimization-based design strategies have been developed in computational aerodynamics and fluid mechanics. Such an optimization approach to divertor target shape design is elaborated in the present paper. A general formulation of the design problems is given, and conditions characterizing the optimal designs are formulated. Using a continuous adjoint framework, design sensitivities can be computed at a cost of only two edge plasma simulations, independent of the number of design variables. Furthermore, by using a one-shot method the entire optimization problem can be solved at an equivalent cost of only a few forward simulations. The methodology is applied to target shape design for uniform power load, in simplified edge plasma geometry.
Hep, J.; Konecna, A.; Krysl, V.; Smutny, V.
2011-07-01
This paper describes the application of effective source in forward calculations and the adjoint method to the solution of fast neutron fluence and activation detector activities in the reactor pressure vessel (RPV) and RPV cavity of a VVER-440 reactor. Its objective is the demonstration of both methods on a practical task. The effective source method applies the Boltzmann transport operator to time integrated source data in order to obtain neutron fluence and detector activities. By weighting the source data by time dependent decay of the detector activity, the result of the calculation is the detector activity. Alternatively, if the weighting is uniform with respect to time, the result is the fluence. The approach works because of the inherent linearity of radiation transport in non-multiplying time-invariant media. Integrated in this way, the source data are referred to as the effective source. The effective source in the forward calculations method thereby enables the analyst to replace numerous intensive transport calculations with a single transport calculation in which the time dependence and magnitude of the source are correctly represented. In this work, the effective source method has been expanded slightly in the following way: neutron source data were performed with few group method calculation using the active core calculation code MOBY-DICK. The follow-up neutron transport calculation was performed using the neutron transport code TORT to perform multigroup calculations. For comparison, an alternative method of calculation has been used based upon adjoint functions of the Boltzmann transport equation. Calculation of the three-dimensional (3-D) adjoint function for each required computational outcome has been obtained using the deterministic code TORT and the cross section library BGL440. Adjoint functions appropriate to the required fast neutron flux density and neutron reaction rates have been calculated for several significant points within the RPV
Comparison of Observation Impacts in Two Forecast Systems using Adjoint Methods
NASA Technical Reports Server (NTRS)
Gelaro, Ronald; Langland, Rolf; Todling, Ricardo
2009-01-01
An experiment is being conducted to compare directly the impact of all assimilated observations on short-range forecast errors in different operational forecast systems. We use the adjoint-based method developed by Langland and Baker (2004), which allows these impacts to be efficiently calculated. This presentation describes preliminary results for a "baseline" set of observations, including both satellite radiances and conventional observations, used by the Navy/NOGAPS and NASA/GEOS-5 forecast systems for the month of January 2007. In each system, about 65% of the total reduction in 24-h forecast error is provided by satellite observations, although the impact of rawinsonde, aircraft, land, and ship-based observations remains significant. Only a small majority (50- 55%) of all observations assimilated improves the forecast, while the rest degrade it. It is found that most of the total forecast error reduction comes from observations with moderate-size innovations providing small to moderate impacts, not from outliers with very large positive or negative innovations. In a global context, the relative impacts of the major observation types are fairly similar in each system, although regional differences in observation impact can be significant. Of particular interest is the fact that while satellite radiances have a large positive impact overall, they degrade the forecast in certain locations common to both systems, especially over land and ice surfaces. Ongoing comparisons of this type, with results expected from other operational centers, should lead to more robust conclusions about the impacts of the various components of the observing system as well as about the strengths and weaknesses of the methodologies used to assimilate them.
The adjoint method of data assimilation used operationally for shelf circulation
NASA Astrophysics Data System (ADS)
Griffin, David A.; Thompson, Keith R.
1996-02-01
A real-time shelf circulation model with data assimilation has been successfully used, possibly for the first time, on the outer Nova Scotian Shelf. The adjoint method was used to infer the time histories of flows across the four open boundaries of a 60 km × 60 km shallow-water equation model of Western Bank. The aim was to hindcast and nowcast currents over the bank so that a patch of water (initially 15 km in diameter) could be resampled over a 3-week period as part of a study of the early life history of Atlantic cod. Observations available in near real time for assimilation were from 14 drifting buoys, 2 telemetering moored current meters, the ship's acoustic Doppler current profiler and the local wind. For the postcruise hindcasts presented here, data from two bottom pressure gauges and two more current meters are also available. The experiment was successful, and the patch was sampled over a 19-day period that included two intense storms. In this paper we (1) document the model and how the data are assimilated, (2) present and discuss the observations, (3) demonstrate that the interpolative skill of the model exceeds that of simpler schemes that use just the current velocity data, and (4) provide examples of how particle tracking with the model enables asynoptically acquired data to be displayed as synoptic maps, greatly facilitating both underway cruise planning and postcruise data analysis. An interesting feature of the circulation on the bank was a nearly stationary eddy atop the bank crest. Larvae within the eddy were retained on the bank in a favorable environment until the onset of the storms. The variable integrity of the eddy may contribute to fluctuations of year-class success.
NASA Astrophysics Data System (ADS)
Morency, C.; Tromp, J.
2008-12-01
successfully performed. We present finite-frequency sensitivity kernels for wave propagation in porous media based upon adjoint methods. We first show that the adjoint equations in porous media are similar to the regular Biot equations upon defining an appropriate adjoint source. Then we present finite-frequency kernels for seismic phases in porous media (e.g., fast P, slow P, and S). These kernels illustrate the sensitivity of seismic observables to structural parameters and form the basis of tomographic inversions. Finally, we show an application of this imaging technique related to the detection of buried landmines and unexploded ordnance (UXO) in porous environments.
Adjoint Method and Predictive Control for 1-D Flow in NASA Ames 11-Foot Transonic Wind Tunnel
NASA Technical Reports Server (NTRS)
Nguyen, Nhan; Ardema, Mark
2006-01-01
This paper describes a modeling method and a new optimal control approach to investigate a Mach number control problem for the NASA Ames 11-Foot Transonic Wind Tunnel. The flow in the wind tunnel is modeled by the 1-D unsteady Euler equations whose boundary conditions prescribe a controlling action by a compressor. The boundary control inputs to the compressor are in turn controlled by a drive motor system and an inlet guide vane system whose dynamics are modeled by ordinary differential equations. The resulting Euler equations are thus coupled to the ordinary differential equations via the boundary conditions. Optimality conditions are established by an adjoint method and are used to develop a model predictive linear-quadratic optimal control for regulating the Mach number due to a test model disturbance during a continuous pitch
Healy, R.W.; Russell, T.F.
1993-01-01
Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods for solute transport problems that are dominated by advection. FVELLAM systematically conserves mass globally with all types of boundary conditions. Integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking of characteristic lines intersecting inflow boundaries. FVELLAM extends previous results by obtaining mass conservation locally on Lagrangian space-time elements. -from Authors
NASA Astrophysics Data System (ADS)
Wang, Brian; Goldstein, Moshe; Xu, X. George; Sahoo, Narayan
2005-03-01
Recently, the theoretical framework of the adjoint Monte Carlo (AMC) method has been developed using a simplified patient geometry. In this study, we extended our previous work by applying the AMC framework to a 3D anatomical model called VIP-Man constructed from the Visible Human images. First, the adjoint fluxes for the prostate (PTV) and rectum and bladder (organs at risk (OARs)) were calculated on a spherical surface of 1 m radius, centred at the centre of gravity of PTV. An importance ratio, defined as the PTV dose divided by the weighted OAR doses, was calculated for each of the available beamlets to select the beam angles. Finally, the detailed doses in PTV and OAR were calculated using a forward Monte Carlo simulation to include the electron transport. The dose information was then used to generate dose volume histograms (DVHs). The Pinnacle treatment planning system was also used to generate DVHs for the 3D plans with beam angles obtained from the AMC (3D-AMC) and a standard six-field conformal radiation therapy plan (3D-CRT). Results show that the DVHs for prostate from 3D-AMC and the standard 3D-CRT are very similar, showing that both methods can deliver prescribed dose to the PTV. A substantial improvement in the DVHs for bladder and rectum was found for the 3D-AMC method in comparison to those obtained from 3D-CRT. However, the 3D-AMC plan is less conformal than the 3D-CRT plan because only bladder, rectum and PTV are considered for calculating the importance ratios. Nevertheless, this study clearly demonstrated the feasibility of the AMC in selecting the beam directions as a part of a treatment planning based on the anatomical information in a 3D and realistic patient anatomy.
NASA Astrophysics Data System (ADS)
Chen, H.; Li, K.
2012-12-01
We applied a wave-equation based adjoint wavefield method for seismic illumination/resolution analyses and full waveform inversion. A two-way wave-equation is used to calculate directional and diffracted energy fluxes for waves propagating between sources and receivers to the subsurface target. The first-order staggered-grid pressure-velocity formulation, which lacks the characteristic of being self-adjoint is further validated and corrected to render the modeling operator before its practical application. Despite most published papers on synthetic kernel research, realistic applications to two field experiments are demonstrated and emphasize its practical needs. The Fréchet sensitivity kernels are used to quantify the target illumination conditions. For realistic illumination measurements and resolution analyses, two completely different survey geometries and nontrivial pre-conditioning strategies based on seismic data type are demonstrated and compared. From illumination studies, particle velocity responses are more sensitive to lateral velocity variations than pressure records. For waveform inversion, the more accurately estimated velocity model obtained the deeper the depth of investigation would be reached. To achieve better resolution and illumination, closely spaced OBS receiver interval is preferred. Based on the results, waveform inversion is applied for a gas hydrate site in Taiwan for shallow structure and BSR detection. Full waveform approach potentially provides better depth resolution than ray approach. The quantitative analyses, a by-product of full waveform inversion, are useful for quantifying seismic processing and depth migration strategies.llumination/resolution analysis for a 3D MCS/OBS survey in 2008. Analysis of OBS data shows that pressure (top), horizontal (middle) and vertical (bottom) velocity records produce different resolving power for gas hydrate exploration. ull waveform inversion of 8 OBS data along Yuan-An Ridge in SW Taiwan
NASA Astrophysics Data System (ADS)
Kopacz, Monika; Jacob, Daniel J.; Henze, Daven K.; Heald, Colette L.; Streets, David G.; Zhang, Qiang
2008-04-01
We apply the adjoint of an atmospheric chemical transport model (GEOS-Chem CTM) to constrain Asian sources of carbon monoxide (CO) with 2° × 2.5° spatial resolution using Measurement of Pollution in the Troposphere (MOPITT) satellite observations of CO columns in February-April 2001. Results are compared to the more common analytical method for solving the same Bayesian inverse problem and applied to the same data set. The analytical method is more exact but because of computational limitations it can only constrain emissions over coarse regions. We find that the correction factors to the a priori CO emission inventory from the adjoint inversion are consistent with those of the analytical inversion when averaged over the large regions of the latter. Unlike the analytical solution, the adjoint correction factors are not subject to compensating errors between adjacent regions (error anticorrelation). The adjoint solution also reveals fine-scale variability that the analytical inversion cannot resolve. For example, India shows both large emissions underestimates in the densely populated Ganges Valley and large overestimates in the eastern part of the country where springtime emissions are dominated by biomass burning. Correction factors to Chinese emissions are largest in central and eastern China, consistent with a recent bottom-up inventory though there are disagreements in the fine structure. Correction factors for biomass burning are consistent with a recent bottom-up inventory based on MODIS satellite fire data.
NASA Astrophysics Data System (ADS)
Al-Attar, D.; Woodhouse, J. H.
2011-12-01
Normal mode spectra provide a valuable data set for global seismic tomography, and, notably, are amongst the few geophysical observables that are sensitive to lateral variations in density structure within the Earth. Nonetheless, the effects of lateral density variations on mode spectra are rather subtle. In order, therefore, to reliably determine density variations with in the earth, it is necessary to make use of sufficiently accurate methods for calculating synthetic mode spectra. In particular, recent work has highlighted the need to perform 'full-coupling calculations' that take into account the interaction of large numbers of spherical earth multiplets. However, present methods for performing such full-coupling calculations require diagonalization of large coupling matrices, and so become computationally inefficient as the number of coupled modes is increased. In order to perform full-coupling calculations more efficiently, we describe a new implementation of the direct solution method for calculating synthetic spectra in laterally heterogeneous earth models. This approach is based on the solution of the inhomogeneous mode coupling equations in the frequency domain, and does not require the diagonalization of large matrices. Early implementations of the direct solution method used LU-decomposition to solve the mode coupling equations. However, as the number of coupled modes is increased, this method becomes impractically slow. To circumvent this problem, we solve the mode coupling equations iteratively using the preconditioned biconjugate gradient algorithm. We present a number of numerical tests to display the accuracy and efficiency of this method for performing large full-coupling calculations. In addition, we describe a frequency-domain formulation of the adjoint method for the calculation of Frechet kernels that show the sensitivity of normal mode observations to variations in earth structure. The calculation of such Frechet kernels involves one solution
Healy, R.W.; Russell, T.F.
1992-01-01
A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.
Wang, H.; Man, S.; Ewing, R.E.; Qin, G.; Lyons, S.L.; Al-Lawatia, M.
1999-06-10
Many difficult problems arise in the numerical simulation of fluid flow processes within porous media in petroleum reservoir simulation and in subsurface contaminant transport and remediation. The authors develop a family of Eulerian-Lagrangian localized adjoint methods for the solution of the initial-boundary value problems for first-order advection-reaction equations on general multi-dimensional domains. Different tracking algorithms, including the Euler and Runge-Kutta algorithms, are used. The derived schemes, which are full mass conservative, naturally incorporate inflow boundary conditions into their formulations and do not need any artificial outflow boundary conditions. Moreover, they have regularly structured, well-conditioned, symmetric, and positive-definite coefficient matrices, which can be efficiently solved by the conjugate gradient method in an optimal order number of iterations without any preconditioning needed. Numerical results are presented to compare the performance of the ELLAM schemes with many well studied and widely used methods, including the upwind finite difference method, the Galerkin and the Petrov-Galerkin finite element methods with backward-Euler or Crank-Nicolson temporal discretization, the streamline diffusion finite element methods, the monotonic upstream-centered scheme for conservation laws (MUSCL), and the Minmod scheme.
Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology
NASA Technical Reports Server (NTRS)
Rallabhandi, Siriam K.; Diskin, Boris; Nielsen, Eric J.
2012-01-01
This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.
Adjoint Error Estimation for Linear Advection
Connors, J M; Banks, J W; Hittinger, J A; Woodward, C S
2011-03-30
An a posteriori error formula is described when a statistical measurement of the solution to a hyperbolic conservation law in 1D is estimated by finite volume approximations. This is accomplished using adjoint error estimation. In contrast to previously studied methods, the adjoint problem is divorced from the finite volume method used to approximate the forward solution variables. An exact error formula and computable error estimate are derived based on an abstractly defined approximation of the adjoint solution. This framework allows the error to be computed to an arbitrary accuracy given a sufficiently well resolved approximation of the adjoint solution. The accuracy of the computable error estimate provably satisfies an a priori error bound for sufficiently smooth solutions of the forward and adjoint problems. The theory does not currently account for discontinuities. Computational examples are provided that show support of the theory for smooth solutions. The application to problems with discontinuities is also investigated computationally.
Heberton, C.I.; Russell, T.F.; Konikow, L.F.; Hornberger, G.Z.
2000-01-01
This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.
Ayyoubzadeh, Seyed Mohsen; Vosoughi, Naser
2011-09-14
Obtaining the set of algebraic equations that directly correspond to a physical phenomenon has been viable in the recent direct discrete method (DDM). Although this method may find its roots in physical and geometrical considerations, there are still some degrees of freedom that one may suspect optimize-able. Here we have used the information embedded in the corresponding adjoint equation to form a local functional, which in turn by its minimization, yield suitable dual mesh positioning.
D.L. Henderson; S. Yoo; M. Kowalok; T.R. Mackie; B.R. Thomadsen
2001-10-30
The goal of this project is to investigate the use of the adjoint method, commonly used in the reactor physics community, for the optimization of radiation therapy patient treatment plans. Two different types of radiation therapy are being examined, interstitial brachytherapy and radiotherapy. In brachytherapy radioactive sources are surgically implanted within the diseased organ such as the prostate to treat the cancerous tissue. With radiotherapy, the x-ray source is usually located at a distance of about 1-metere from the patient and focused on the treatment area. For brachytherapy the optimization phase of the treatment plan consists of determining the optimal placement of the radioactive sources, which delivers the prescribed dose to the disease tissue while simultaneously sparing (reducing) the dose to sensitive tissue and organs. For external beam radiation therapy the optimization phase of the treatment plan consists of determining the optimal direction and intensity of beam, which provides complete coverage of the tumor region with the prescribed dose while simultaneously avoiding sensitive tissue areas. For both therapy methods, the optimal treatment plan is one in which the diseased tissue has been treated with the prescribed dose and dose to the sensitive tissue and organs has been kept to a minimum.
Arnal, B; Pinton, G; Garapon, P; Pernot, M; Fink, M; Tanter, M
2013-10-01
Shear wave imaging (SWI) maps soft tissue elasticity by measuring shear wave propagation with ultrafast ultrasound acquisitions (10 000 frames s(-1)). This spatiotemporal data can be used as an input for an inverse problem that determines a shear modulus map. Common inversion methods are local: the shear modulus at each point is calculated based on the values of its neighbour (e.g. time-of-flight, wave equation inversion). However, these approaches are sensitive to the information loss such as noise or the lack of the backscattered signal. In this paper, we evaluate the benefits of a global approach for elasticity inversion using a least-squares formulation, which is derived from full waveform inversion in geophysics known as the adjoint method. We simulate an acoustic waveform in a medium with a soft and a hard lesion. For this initial application, full elastic propagation and viscosity are ignored. We demonstrate that the reconstruction of the shear modulus map is robust with a non-uniform background or in the presence of noise with regularization. Compared to regular local inversions, the global approach leads to an increase of contrast (∼+3 dB) and a decrease of the quantification error (∼+2%). We demonstrate that the inversion is reliable in the case when there is no signal measured within the inclusions like hypoechoic lesions which could have an impact on medical diagnosis. PMID:24018867
AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...
EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Many numerical methods use characteristic analysis to accommodate the advective component of transport. uch characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. eneralization of characteristic...
NASA Astrophysics Data System (ADS)
Martinec, Zdenek; Sasgen, Ingo; Velimsky, Jakub
2014-05-01
In this study, two new methods for computing the sensitivity of the glacial isostatic adjustment (GIA) forward solution with respect to the Earth's mantle viscosity are presented: the forward sensitivity method (FSM) and the adjoint sensitivity method (ASM). These advanced formal methods are based on the time-domain,spectral-finite element method for modelling the GIA response of laterally heterogeneous earth models developed by Martinec (2000). There are many similarities between the forward method and the FSM and ASM for a general physical system. However, in the case of GIA, there are also important differences between the forward and sensitivity methods. The analysis carried out in this study results in the following findings. First, the forward method of GIA is unconditionally solvable, regardless of whether or not a combined ice and ocean-water load contains the first-degree spherical harmonics. This is also the case for the FSM, however, the ASM must in addition be supplemented by nine conditions on the misfit between the given GIA-related data and the forward model predictions to guarantee the existence of a solution. This constrains the definition of data least-squares misfit. Second, the forward method of GIA implements an ocean load as a free boundary-value function over an ocean area with a free geometry. That is, an ocean load and the shape of ocean, the so-called ocean function, are being sought, in addition to deformation and gravity-increment fields, by solving the forward method. The FSM and ASM also apply the adjoint ocean load as a free boundary-value function, but instead over an ocean area with the fixed geometry given by the ocean function determined by the forward method. In other words, a boundary-value problem for the forward method of GIA is free with respect to determining (i) the boundary-value data over an ocean area and (ii) the ocean function itself, while the boundary-value problems for the FSM and ASM are free only with respect to
Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.
2006-01-01
Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.
NASA Astrophysics Data System (ADS)
Masson, Y.; Pierre, C.; Romanowicz, B. A.; French, S. W.; Yuan, H.
2014-12-01
Yuan et al. (2013) developed a 3D radially anisotropic shear wave model of North America (NA) upper mantle based on full waveform tomography, combining teleseismic and regional distance data sampling the NA. In this model, synthetic seismograms associated with regional events (i.e. events located inside in the region imaged NA) were computed exactly using the Spectral Element method (Cupillard et al., 2012), while, synthetic seismograms associated with teleseismic events were performed approximately using non-linear asymptotic coupling theory (NACT, Li and Romanowicz, 1995). Both the regional and the teleseismic dataset have been inverted using approximate sensitivity kernels based upon normal mode theory. Our objective is to improve our current model and to build the next generation model of NA by introducing new methodological developments (Masson et al., 2014) that allow us to compute exact synthetic seismograms as well as adjoint sensitivity kernels associated with teleseismic events, using mostly regional computations of wave propagation. The principle of the method is to substitute a teleseismic source (i.e. an earthquake) by an "equivalent" set of seismic sources acting on the boundaries of the region to be imaged that is producing exactly the same wavefield. Computing the equivalent set of sources associated with each one of the teleseismic events requires a few global simulations of the seismic wavefield that can be done once for all, prior to the regional inversion. Then, the regional full waveform inversion can be preformed using regional simulations only. We present a 3D model of NA demonstrating the advantages of the proposed method.
NASA Technical Reports Server (NTRS)
Edwards, S.; Reuther, J.; Chattot, J. J.
1997-01-01
The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjunct approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speed.
Design sensitivity analysis with Applicon IFAD using the adjoint variable method
NASA Technical Reports Server (NTRS)
Frederick, Marjorie C.; Choi, Kyung K.
1984-01-01
A numerical method is presented to implement structural design sensitivity analysis using the versatility and convenience of existing finite element structural analysis program and the theoretical foundation in structural design sensitivity analysis. Conventional design variables, such as thickness and cross-sectional areas, are considered. Structural performance functionals considered include compliance, displacement, and stress. It is shown that calculations can be carried out outside existing finite element codes, using postprocessing data only. That is, design sensitivity analysis software does not have to be imbedded in an existing finite element code. The finite element structural analysis program used in the implementation presented is IFAD. Feasibility of the method is shown through analysis of several problems, including built-up structures. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of a finite difference perturbation.
NASA Astrophysics Data System (ADS)
Yaremchuk, Max; Martin, Paul; Koch, Andrey; Beattie, Christopher
2016-01-01
Performance of the adjoint and adjoint-free 4-dimensional variational (4dVar) data assimilation techniques is compared in application to the hydrographic surveys and velocity observations collected in the Adriatic Sea in 2006. Assimilating the data into the Navy Coastal Ocean Model (NCOM) has shown that both methods deliver similar reduction of the cost function and demonstrate comparable forecast skill at approximately the same computational expense. The obtained optimal states were, however, significantly different in terms of distance from the background state: application of the adjoint method resulted in a 30-40% larger departure, mostly due to the excessive level of ageostrophic motions in the southern basin of the Sea that was not covered by observations.
Shape optimization governed by the Euler equations using an adjoint method
NASA Technical Reports Server (NTRS)
Iollo, Angelo; Salas, Manuel D.; Taasan, Shlomo
1993-01-01
A numerical approach for the treatment of optimal shape problems governed by the Euler equations is discussed. Focus is on flows with embedded shocks. A very simple problem is considered: the design of a quasi-one-dimensional Laval nozzle. A cost function and a set of Lagrange multipliers are introduced to achieve the minimum. The nature of the resulting costate equations is discussed. A theoretical difficulty that arises for cases with embedded shocks is pointed out and solved. Finally, some results are given to illustrate the effectiveness of the method.
NASA Astrophysics Data System (ADS)
Bozdag, Ebru; Lefebvre, Matthieu; Lei, Wenjie; Peter, Daniel; Smith, James; Komatitsch, Dimitri; Tromp, Jeroen
2015-04-01
We will present our initial results of global adjoint tomography based on 3D seismic wave simulations which is one of the most challenging examples in seismology in terms of intense computational requirements and vast amount of high-quality seismic data that can potentially be assimilated in inversions. Using a spectral-element method, we incorporate full 3D wave propagation in seismic tomography by running synthetic seismograms and adjoint simulations to compute exact sensitivity kernels in realistic 3D background models. We run our global simulations on the Oak Ridge National Laboratory's Cray XK7 "Titan" system taking advantage of the GPU version of the SPECFEM3D_GLOBE package. We have started iterations with initially selected 253 earthquakes within the magnitude range of 5.5 < Mw < 7.0 and numerical simulations having resolution down to ~27 s to invert for a transversely isotropic crust and mantle model using a non-linear conjugate gradient algorithm. The measurements are currently based on frequency-dependent traveltime misfits. We use both minor- and major-arc body and surface waves by running 200 min simulations where inversions are performed with more than 2.6 million measurements. Our initial results after 12 iterations already indicate several prominent features such as enhanced slab (e.g., Hellenic, Japan, Bismarck, Sandwich), plume/hotspot (e.g., the Pacific superplume, Caroline, Yellowstone, Hawaii) images, etc. To improve the resolution and ray coverage, particularly in the lower mantle, our aim is to increase the resolution of numerical simulations first going down to ~17 s and then to ~9 s to incorporate high-frequency body waves in inversions. While keeping track of the progress and illumination of features in our models with a limited data set, we work towards to assimilate all available data in inversions from all seismic networks and earthquakes in the global CMT catalogue.
NASA Technical Reports Server (NTRS)
Gelaro, Ron; Liu, Emily; Sienkiewicz, Meta
2011-01-01
The adjoint of a data assimilation system provides a flexible and efficient tool for estimating observation impacts on short-range weather forecasts. The impacts of any or all observations can be estimated simultaneously based on a single execution of the adjoint system. The results can be easily aggregated according to data type, location, channel, etc., making this technique especially attractive for examining the impacts of new hyper-spectral satellite instruments and for conducting regular, even near-real time, monitoring of the entire observing system. In this talk, we present results from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. The tool has been running in various off-line configurations for some time, and is scheduled to run as a regular part of the real-time forecast suite beginning in autumn 20 I O. We focus on the impacts of the newest components of the satellite observing system, including AIRS, IASI and GPS. For AIRS and IASI, it is shown that the vast majority of the channels assimilated have systematic positive impacts (of varying magnitudes), although some channels degrade the forecast. Of the latter, most are moisture-sensitive or near-surface channels. The impact of GPS observations in the southern hemisphere is found to be a considerable overall benefit to the system. In addition, the spatial variability of observation impacts reveals coherent patterns of positive and negative impacts that may point to deficiencies in the use of certain observations over, for example, specific surface types. When performed in conjunction with selected observing system experiments (OSEs), the adjoint results reveal both redundancies and dependencies between observing system impacts as observations are added or removed from the assimilation system. Understanding these dependencies appears to pose a major challenge for optimizing the use of the current observational network and
NASA Technical Reports Server (NTRS)
Martin, William G.; Cairns, Brian; Bal, Guillaume
2014-01-01
This paper derives an efficient procedure for using the three-dimensional (3D) vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties and improve their fit with multi-angle/multi-pixel radiometric and polarimetric measurements of scattered sunlight. The proposed adjoint method uses the 3D VRTE to compute the measurement misfit function and the adjoint 3D VRTE to compute its gradient with respect to all unknown parameters. In the remote sensing problems of interest, the scalar-valued misfit function quantifies agreement with data as a function of atmosphere and surface properties, and its gradient guides the search through this parameter space. Remote sensing of the atmosphere and surface in a three-dimensional region may require thousands of unknown parameters and millions of data points. Many approaches would require calls to the 3D VRTE solver in proportion to the number of unknown parameters or measurements. To avoid this issue of scale, we focus on computing the gradient of the misfit function as an alternative to the Jacobian of the measurement operator. The resulting adjoint method provides a way to adjust 3D atmosphere and surface properties with only two calls to the 3D VRTE solver for each spectral channel, regardless of the number of retrieval parameters, measurement view angles or pixels. This gives a procedure for adjusting atmosphere and surface parameters that will scale to the large problems of 3D remote sensing. For certain types of multi-angle/multi-pixel polarimetric measurements, this encourages the development of a new class of three-dimensional retrieval algorithms with more flexible parametrizations of spatial heterogeneity, less reliance on data screening procedures, and improved coverage in terms of the resolved physical processes in the Earth?s atmosphere.
Towards Global Adjoint Tomography
NASA Astrophysics Data System (ADS)
Bozdag, E.; Zhu, H.; Peter, D. B.; Tromp, J.
2012-12-01
Seismic tomography is at a stage where we can harness entire seismograms using the opportunities offered by advances in numerical wave propagation solvers and high-performance computing. Adjoint methods provide an efficient way for incorporating full nonlinearity of wave propagation and 3D Fréchet kernels in iterative seismic inversions which have so far given promising results at continental and regional scales. Our goal is to take adjoint tomography forward to image the entire planet. Using an iterative conjugate gradient scheme, we initially set the aim to obtain a global crustal and mantle model with confined transverse isotropy in the upper mantle. We have started with around 255 global CMT events having moment magnitudes between 5.8 and 7, and used GSN stations as well as some local networks such as USArray, European stations etc. Prior to the structure inversion, we reinvert global CMT solutions by computing Green functions in our 3D reference model to take into account effects of crustal variations on source parameters. Using the advantages of numerical simulations, our strategy is to invert crustal and mantle structure together to avoid any bias introduced into upper-mantle images due to "crustal corrections", which are commonly used in classical tomography. 3D simulations dramatically increase the usable amount of data so that, with the current earthquake-station setup, we perform each iteration with more than two million measurements. Multi-resolution smoothing based on ray density is applied to the gradient to better deal with the imperfect source-station distribution on the globe and extract more information underneath regions with dense ray coverage and vice versa. Similar to frequency domain approach, we reduce nonlinearities by starting from long periods and gradually increase the frequency content of data after successive model updates. To simplify the problem, we primarily focus on the elastic structure and therefore our measurements are based on
Improved Adjoint-Operator Learning For A Neural Network
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad; Barhen, Jacob
1995-01-01
Improved method of adjoint-operator learning reduces amount of computation and associated computational memory needed to make electronic neural network learn temporally varying pattern (e.g., to recognize moving object in image) in real time. Method extension of method described in "Adjoint-Operator Learning for a Neural Network" (NPO-18352).
Diagnositcs With Adjoint Modelling
NASA Astrophysics Data System (ADS)
Blessing, S.; Fraedrich, K.; Kirk, E.; Lunkeit, F.
The potential usefulness of an adjoint primitive equations global atmospheric circu- lation model for climate diagnostics is demonstrated in a feasibility study. A daily NAO-type index is calculated as one-point correlation of the 300 hPa streamfunction anomaly. By application of the adjoint model we diagnose its temperature forcing on short timescales in terms of spatial temperature sensitivity patterns at different time lags, which, in a first order approximation, induce growth of the index. The dynamical relevance of these sensitivity patterns is confirmed by lag-correlating the index time series and the projection time series of the model temperature on these sensitivity patterns.
NASA Astrophysics Data System (ADS)
Kano, Masayuki; Miyazaki, Shin'ichi; Ishikawa, Yoichi; Hiyoshi, Yoshihisa; Ito, Kosuke; Hirahara, Kazuro
2015-10-01
Data assimilation is a technique that optimizes the parameters used in a numerical model with a constraint of model dynamics achieving the better fit to observations. Optimized parameters can be utilized for the subsequent prediction with a numerical model and predicted physical variables are presumably closer to observations that will be available in the future, at least, comparing to those obtained without the optimization through data assimilation. In this work, an adjoint data assimilation system is developed for optimizing a relatively large number of spatially inhomogeneous frictional parameters during the afterslip period in which the physical constraints are a quasi-dynamic equation of motion and a laboratory derived rate and state dependent friction law that describe the temporal evolution of slip velocity at subduction zones. The observed variable is estimated slip velocity on the plate interface. Before applying this method to the real data assimilation for the afterslip of the 2003 Tokachi-oki earthquake, a synthetic data assimilation experiment is conducted to examine the feasibility of optimizing the frictional parameters in the afterslip area. It is confirmed that the current system is capable of optimizing the frictional parameters A-B, A and L by adopting the physical constraint based on a numerical model if observations capture the acceleration and decaying phases of slip on the plate interface. On the other hand, it is unlikely to constrain the frictional parameters in the region where the amplitude of afterslip is less than 1.0 cm d-1. Next, real data assimilation for the 2003 Tokachi-oki earthquake is conducted to incorporate slip velocity data inferred from time dependent inversion of Global Navigation Satellite System time-series. The optimized values of A-B, A and L are O(10 kPa), O(102 kPa) and O(10 mm), respectively. The optimized frictional parameters yield the better fit to the observations and the better prediction skill of slip
Adjoint affine fusion and tadpoles
NASA Astrophysics Data System (ADS)
Urichuk, Andrew; Walton, Mark A.
2016-06-01
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.
Double-difference adjoint seismic tomography
NASA Astrophysics Data System (ADS)
Yuan, Yanhua O.; Simons, Frederik J.; Tromp, Jeroen
2016-06-01
We introduce a `double-difference' method for the inversion for seismic wavespeed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systematic uncertainties. To alleviate the corresponding nonuniqueness in the inverse problem, we construct differential measurements between stations, thereby reducing the influence of the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of the differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and in practice. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relative (and thus higher-resolution) structural variations in areas close to the stations. Whereas in conventional tomography a measurement made on a single earthquake-station pair provides very limited structural information, in double-difference tomography one earthquake can actually resolve significant details of the structure. The double-difference methodology can be incorporated into the usual adjoint tomography workflow by simply pairing up all conventional measurements; the computational cost of the necessary adjoint simulations is largely unaffected. Rather than adding to the computational burden, the inversion of double-difference measurements merely modifies the construction of the adjoint sources for data assimilation.
The compressible adjoint equations in geodynamics: equations and numerical assessment
NASA Astrophysics Data System (ADS)
Ghelichkhan, Siavash; Bunge, Hans-Peter
2016-04-01
The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
ADGEN: ADjoint GENerator for computer models
Worley, B.A.; Pin, F.G.; Horwedel, J.E.; Oblow, E.M.
1989-05-01
This paper presents the development of a FORTRAN compiler and an associated supporting software library called ADGEN. ADGEN reads FORTRAN models as input and produces and enhanced version of the input model. The enhanced version reproduces the original model calculations but also has the capability to calculate derivatives of model results of interest with respect to any and all of the model data and input parameters. The method for calculating the derivatives and sensitivities is the adjoint method. Partial derivatives are calculated analytically using computer calculus and saved as elements of an adjoint matrix on direct assess storage. The total derivatives are calculated by solving an appropriate adjoint equation. ADGEN is applied to a major computer model of interest to the Low-Level Waste Community, the PRESTO-II model. PRESTO-II sample problem results reveal that ADGEN correctly calculates derivatives of response of interest with respect to 300 parameters. The execution time to create the adjoint matrix is a factor of 45 times the execution time of the reference sample problem. Once this matrix is determined, the derivatives with respect to 3000 parameters are calculated in a factor of 6.8 that of the reference model for each response of interest. For a single 3000 for determining these derivatives by parameter perturbations. The automation of the implementation of the adjoint technique for calculating derivatives and sensitivities eliminates the costly and manpower-intensive task of direct hand-implementation by reprogramming and thus makes the powerful adjoint technique more amenable for use in sensitivity analysis of existing models. 20 refs., 1 fig., 5 tabs.
NASA Astrophysics Data System (ADS)
Galanti, Eli; Kaspi, Yohai
2016-04-01
During 2016-17, the Juno and Cassini spacecraft will both perform close eccentric orbits of Jupiter and Saturn, respectively, obtaining high-precision gravity measurements for these planets. These data will be used to estimate the depth of the observed surface flows on these planets. All models to date, relating the winds to the gravity field, have been in the forward direction, thus only allowing the calculation of the gravity field from given wind models. However, there is a need to do the inverse problem since the new observations will be of the gravity field. Here, an inverse dynamical model is developed to relate the expected measurable gravity field, to perturbations of the density and wind fields, and therefore to the observed cloud-level winds. In order to invert the gravity field into the 3D circulation, an adjoint model is constructed for the dynamical model, thus allowing backward integration. This tool is used for the examination of various scenarios, simulating cases in which the depth of the wind depends on latitude. We show that it is possible to use the gravity measurements to derive the depth of the winds, both on Jupiter and Saturn, also taking into account measurement errors. Calculating the solution uncertainties, we show that the wind depth can be determined more precisely in the low-to-mid-latitudes. In addition, the gravitational moments are found to be particularly sensitive to flows at the equatorial intermediate depths. Therefore, we expect that if deep winds exist on these planets they will have a measurable signature by Juno and Cassini.
Energy Science and Technology Software Center (ESTSC)
2004-04-21
Version 04 NESTLE solves the few-group neutron diffusion equation utilizing the NEM. The NESTLE code can solve the eigenvalue (criticality), eigenvalue adjoint, external fixed-source steady-state, and external fixed-source or eigenvalue initiated transient problems. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two- ormore » four-energy groups can be utilized, with all energy groups being thermal groups (i.e., upscatter exits) if desired. Core geometries modeled include Cartesian and hexagonal. Three-, two-, and one-dimensional models can be utilized with various symmetries. The thermal conditions predicted by the thermal-hydraulic model of the core are used to correct cross sections for temperature and density effects. Cross sections are parameterized by color, control rod state (i.e., in or out), and burnup, allowing fuel depletion to be modeled. Either a macroscopic or microscopic model may be employed.« less
NASA Astrophysics Data System (ADS)
Galanti, E.; Finocchiaro, S.; Kaspi, Y.; Iess, L.
2013-12-01
The upcoming high precision measurements of the Juno flybys around Jupiter, have the potential of improving the estimation of Jupiter's gravity field. The analysis of the Juno Doppler data will provide a very accurate reconstruction of spacial gravity variations, but these measurements will be over a limited latitudinal and longitudinal range. In order to deduce the full gravity field of Jupiter, additional information needs to be incorporated into the analysis, especially with regards to the Jovian wind structure and its depth at high latitudes. In this work we propose a new iterative method for the estimation of the Jupiter gravity field, using the Juno expected measurements, a trajectory estimation model, and an adjoint based inverse thermal wind model. Beginning with an artificial gravitational field, the trajectory estimation model together with an optimization procedure is used to obtain an initial solution of the gravitational moments. As upper limit constraints, the model applies the gravity harmonics obtained from a thermal wind model in which the winds are assumed to penetrate barotropicaly along the direction of the spin axis. The solution from the trajectory model is then used as an initial guess for the thermal wind model, and together with an adjoint optimization method, the optimal penetration depth of the winds is computed. As a final step, the gravity harmonics solution from the thermal wind model is given back to the trajectory model, along with an uncertainties estimate, to be used as constraints for a new calculation of the gravity field. We test this method for several cases, some with zonal harmonics only, and some with the full gravity field including longitudinal variations that include the tesseral harmonics as well. The results show that using this method some of the gravitational moments are fitted better to the 'observed' ones, mainly due to the fact that the thermal wind model is taking into consideration the wind structure and depth
Healy, R.W.; Russell, T.F.
1998-01-01
We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.
Southern California Adjoint Source Inversions
NASA Astrophysics Data System (ADS)
Tromp, J.; Kim, Y.
2007-12-01
Southern California Centroid-Moment Tensor (CMT) solutions with 9 components (6 moment tensor elements, latitude, longitude, and depth) are sought to minimize a misfit function computed from waveform differences. The gradient of a misfit function is obtained based upon two numerical simulations for each earthquake: one forward calculation for the southern California model, and an adjoint calculation that uses time-reversed signals at the receivers. Conjugate gradient and square-root variable metric methods are used to iteratively improve the earthquake source model while reducing the misfit function. The square-root variable metric algorithm has the advantage of providing a direct approximation to the posterior covariance operator. We test the inversion procedure by perturbing each component of the CMT solution, and see how the algorithm converges. Finally, we demonstrate full inversion capabilities using data for real Southern California earthquakes.
Adjoint Function: Physical Basis of Variational & Perturbation Theory in Transport
Energy Science and Technology Software Center (ESTSC)
2009-07-27
Version 00 Dr. J.D. Lewins has now released the following legacy book for free distribution: Importance: The Adjoint Function: The Physical Basis of Variational and Perturbation Theory in Transport and Diffusion Problems, North-Holland Publishing Company - Amsterdam, 582 pages, 1966 Introduction: Continuous Systems and the Variational Principle 1. The Fundamental Variational Principle 2. The Importance Function 3. Adjoint Equations 4. Variational Methods 5. Perturbation and Iterative Methods 6. Non-Linear Theory
NASA Astrophysics Data System (ADS)
Lee, E.; Chen, P.; Jordan, T. H.; Maechling, P. J.; Denolle, M.; Beroza, G. C.
2013-12-01
We apply a unified methodology for seismic waveform analysis and inversions to Southern California. To automate the waveform selection processes, we developed a semi-automatic seismic waveform analysis algorithm for full-wave earthquake source parameters and tomographic inversions. The algorithm is based on continuous wavelet transforms, a topological watershed method, and a set of user-adjustable criteria to select usable waveform windows for full-wave inversions. The algorithm takes advantages of time-frequency representations of seismograms and is able to separate seismic phases in both time and frequency domains. The selected wave packet pairs between observed and synthetic waveforms are then used for extracting frequency-dependent phase and amplitude misfit measurements, which are used in our seismic source and structural inversions. Our full-wave waveform tomography uses the 3D SCEC Community Velocity Model Version 4.0 as initial model, a staggered-grid finite-difference code to simulate seismic wave propagations. The sensitivity (Fréchet) kernels are calculated based on the scattering integral and adjoint methods to iteratively improve the model. We use both earthquake recordings and ambient noise Green's functions, stacking of station-to-station correlations of ambient seismic noise, in our full-3D waveform tomographic inversions. To reduce errors of earthquake sources, the epicenters and source parameters of earthquakes used in our tomographic inversion are inverted by our full-wave CMT inversion method. Our current model shows many features that relate to the geological structures at shallow depth and contrasting velocity values across faults. The velocity perturbations could up to 45% with respect to the initial model in some regions and relate to some structures that do not exist in the initial model, such as southern Great Valley. The earthquake waveform misfits reduce over 70% and the ambient noise Green's function group velocity delay time variance
Surface wave sensitivity: mode summation versus adjoint SEM
NASA Astrophysics Data System (ADS)
Zhou, Ying; Liu, Qinya; Tromp, Jeroen
2011-12-01
We compare finite-frequency phase and amplitude sensitivity kernels calculated based on frequency-domain surface wave mode summation and a time-domain adjoint method. The adjoint calculations involve a forward wavefield generated by an earthquake and an adjoint wavefield generated at a seismic receiver. We determine adjoint sources corresponding to frequency-dependent phase and amplitude measurements made using a multitaper technique, which may be applied to any single-taper measurement, including box car windowing. We calculate phase and amplitude sensitivity kernels using an adjoint method based on wave propagation simulations using a spectral element method (SEM). Sensitivity kernels calculated using the adjoint SEM are in good agreement with kernels calculated based on mode summation. In general, the adjoint SEM is more computationally expensive than mode summation in global studies. The advantage of the adjoint SEM lies in the calculation of sensitivity kernels in 3-D earth models. We compare surface wave sensitivity kernels computed in 1-D and 3-D reference earth models and show that (1) lateral wave speed heterogeneities may affect the geometry and amplitude of surface wave sensitivity; (2) sensitivity kernels of long-period surface waves calculated in 1-D model PREM and 3-D models S20RTS+CRUST2.0 and FFSW1+CRUST2.0 do not show significant differences, indicating that the use of a 1-D reference model is adequate in global inversions of long-period surface waves (periods of 50 s and longer); and (3) the differences become significant for short-period Love waves when mode coupling is sensitive to large differences in reference crustal structure. Finally, we show that sensitivity kernels in anelastic earth models may be calculated in purely elastic earth models provided physical dispersion is properly accounted for.
A new mathematical adjoint for the modified SAAF_{-SN} equations
Schunert, Sebastian; Wang, Yaqi; Martineau, Richard; DeHart, Mark D.
2015-01-01
We present a new adjoint FEM weak form, which can be directly used for evaluating the mathematical adjoint, suitable for perturbation calculations, of the self-adjoint angular flux SN equations (SAAF_{-SN}) without construction and transposition of the underlying coefficient matrix. Stabilization schemes incorporated in the described SAAF_{-SN} method make the mathematical adjoint distinct from the physical adjoint, i.e. the solution of the continuous adjoint equation with SAAF_{-SN} . This weak form is implemented into RattleSnake, the MOOSE (Multiphysics Object-Oriented Simulation Environment) based transport solver. Numerical results verify the correctness of the implementation and show its utility both for fixed source and eigenvalue problems.
Nonlinear self-adjointness and conservation laws of Klein-Gordon-Fock equation with central symmetry
NASA Astrophysics Data System (ADS)
Abdulwahhab, Muhammad Alim
2015-05-01
The concept of nonlinear self-adjointness, introduced by Ibragimov, has significantly extends approaches to constructing conservation laws associated with symmetries since it incorporates the strict self-adjointness, the quasi self-adjointness as well as the usual linear self-adjointness. Using this concept, the nonlinear self-adjointness condition for the Klein-Gordon-Fock equation was established and subsequently used to construct simplified but infinitely many nontrivial and independent conserved vectors. The Noether's theorem was further applied to the Klein-Gordon-Fock equation to explore more distinct first integrals, result shows that conservation laws constructed through this approach are exactly the same as those obtained under strict self-adjointness of Ibragimov's method.
Adjoint-Based Methodology for Time-Dependent Optimization
NASA Technical Reports Server (NTRS)
Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.
2008-01-01
This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.
NASA Astrophysics Data System (ADS)
Vich, M.; Romero, R.; Richard, E.; Arbogast, P.; Maynard, K.
2010-09-01
Heavy precipitation events occur regularly in the western Mediterranean region. These events often have a high impact on the society due to economic and personal losses. The improvement of the mesoscale numerical forecasts of these events can be used to prevent or minimize their impact on the society. In previous studies, two ensemble prediction systems (EPSs) based on perturbing the model initial and boundary conditions were developed and tested for a collection of high-impact MEDEX cyclonic episodes. These EPSs perturb the initial and boundary potential vorticity (PV) field through a PV inversion algorithm. This technique ensures modifications of all the meteorological fields without compromising the mass-wind balance. One EPS introduces the perturbations along the zones of the three-dimensional PV structure presenting the local most intense values and gradients of the field (a semi-objective choice, PV-gradient), while the other perturbs the PV field over the MM5 adjoint model calculated sensitivity zones (an objective method, PV-adjoint). The PV perturbations are set from a PV error climatology (PVEC) that characterizes typical PV errors in the ECMWF forecasts, both in intensity and displacement. This intensity and displacement perturbation of the PV field is chosen randomly, while its location is given by the perturbation zones defined in each ensemble generation method. Encouraged by the good results obtained by these two EPSs that perturb the PV field, a new approach based on a manual perturbation of the PV field has been tested and compared with the previous results. This technique uses the satellite water vapor (WV) observations to guide the correction of initial PV structures. The correction of the PV field intents to improve the match between the PV distribution and the WV image, taking advantage of the relation between dark and bright features of WV images and PV anomalies, under some assumptions. Afterwards, the PV inversion algorithm is applied to run
Adjoint sensitivity analysis of an ultrawideband antenna
Stephanson, M B; White, D A
2011-07-28
The frequency domain finite element method using H(curl)-conforming finite elements is a robust technique for full-wave analysis of antennas. As computers become more powerful, it is becoming feasible to not only predict antenna performance, but also to compute sensitivity of antenna performance with respect to multiple parameters. This sensitivity information can then be used for optimization of the design or specification of manufacturing tolerances. In this paper we review the Adjoint Method for sensitivity calculation, and apply it to the problem of optimizing a Ultrawideband antenna.
Probability density adjoint for sensitivity analysis of the Mean of Chaos
Blonigan, Patrick J. Wang, Qiqi
2014-08-01
Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. This paper presents a new method for sensitivity analysis of ergodic chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs.
Adjoint simulation of stream depletion due to aquifer pumping.
Neupauer, Roseanna M; Griebling, Scott A
2012-01-01
If an aquifer is hydraulically connected to an adjacent stream, a pumping well operating in the aquifer will draw some water from aquifer storage and some water from the stream, causing stream depletion. Several analytical, semi-analytical, and numerical approaches have been developed to estimate stream depletion due to pumping. These approaches are effective if the well location is known. If a new well is to be installed, it may be desirable to install the well at a location where stream depletion is minimal. If several possible locations are considered for the location of a new well, stream depletion would have to be estimated for all possible well locations, which can be computationally inefficient. The adjoint approach for estimating stream depletion is a more efficient alternative because with one simulation of the adjoint model, stream depletion can be estimated for pumping at a well at any location. We derive the adjoint equations for a coupled system with a confined aquifer, an overlying unconfined aquifer, and a river that is hydraulically connected to the unconfined aquifer. We assume that the stage in the river is known, and is independent of the stream depletion, consistent with the assumptions of the MODFLOW river package. We describe how the adjoint equations can be solved using MODFLOW. In an illustrative example, we show that for this scenario, the adjoint approach is as accurate as standard forward numerical simulation methods, and requires substantially less computational effort. PMID:22182421
Kim, Min-Geun; Jang, Hong-Lae; Cho, Seonho
2013-05-01
An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.
Adjoints and Low-rank Covariance Representation
NASA Technical Reports Server (NTRS)
Tippett, Michael K.; Cohn, Stephen E.
2000-01-01
Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.
RamaRao, B.S.; Reeves, M. )
1990-10-01
Calibration of a numerical model of the regional ground-water flow in the Culebra dolomite at the Waste Isolation Pilot Plant in southeastern New Mexico, has been performed by an interative parameter-fitting procedure. Parameterization has been secured by choosing to assign the transmissivity values at a limited number of selected locations, designated as pilot points. The transmissivity distribution in the model is derived by kriging the combined pool of measured and pilot-plant transmissivities. Iterating on the twin steps of sequentially adding additional pilot point(s) and kriging leads to the model of required accuracy, as judged by a weighted least-square-error objective function. At the end of calibration, it must be ensured that the correlation structure of the measured transmissivities is broadly preserved by the pilot-plant transmissivities. Adjoint-sensitivity analysis of the model has been coupled with kriging to provide objectively the optimal location of the pilot points during an iteration. The pilot-point transmissivities have been adjusted by modeler's judgement incorporating information, where available, on local geologic conditions and large-scale hydraulic interference tests, in order to minimize the objective function. 43 refs., 5 figs., 5 tabs.
Self-adjointness of deformed unbounded operators
Much, Albert
2015-09-15
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.
Adjoint Based Data Assimilation for an Ionospheric Model
NASA Astrophysics Data System (ADS)
Rosen, I. G.; Hajj, G. A.; Hajj, G. A.; Pi, X.; Pi, X.; Wang, C.; Wilson, B. D.
2001-05-01
The success of ionospheric modeling depends primarily on accurate knowledge of the forces (drivers) which enter into the collisional plasma hydrodynamic equations for the ionosphere and control the ionization as well as other dynamical and chemical processes. These include solar EUV and UV radiation, magnetospheric electric fields, particle precipitation, dynamo electric fields, thermospheric winds, neutral densities, and temperature. The determination of these model parameters from observational data is known as data assimilation. The data assimilation problem is formulated as a problem of minimizing a nonlinear functional, J (typically least squares) under a system of constraints consisting primarily of the underlying model equations. The performance index, J, can, in principle, be minimized using standard techniques such as the Newton's steepest decent method. There are however major technical challenges in practice. Since J is highly nonlinear and each evaluation of the functional requires the integration of the ionospheric model equations, computing the gradient vector of J with respect to the unknown parameters is time consuming. This problem is solved by use of the adjoint method. The ionospheric model used in this effort is for mid- and low-latitudes and consists of solving the continuity and momentum partial differential equations in four dimensional (three spatial dimensions and time) to compute the O+ density in the ionosphere and plasmasphere. We have developed codes for solving the forward model on a fixed grid. This makes it relatively straight forward to apply the adjoint method for computing gradients when doing nonlinear least squares based data assimilation. Because of the significant cost (in computational effort and CPU time) involved in performing a forward integration of the underlying 3-D model at any reasonable grid resolution, the use of the adjoint method for computing the gradients is indispensable. The adjoint method provides an elegant
MS S4.03.002 - Adjoint-Based Design for Configuration Shaping
NASA Technical Reports Server (NTRS)
Nemec, Marian; Aftosmis, Michael J.
2009-01-01
This slide presentation discusses a method of inverse design for low sonic boom using adjoint-based gradient computations. It outlines a method for shaping a configuration in order to match a prescribed near-field signature.
Adjoint operator approach to shape design for internal incompressible flows
NASA Technical Reports Server (NTRS)
Cabuk, H.; Sung, C.-H.; Modi, V.
1991-01-01
The problem of determining the profile of a channel or duct that provides the maximum static pressure rise is solved. Incompressible, laminar flow governed by the steady state Navier-Stokes equations is assumed. Recent advances in computational resources and algorithms have made it possible to solve the direct problem of determining such a flow through a body of known geometry. It is possible to obtain a set of adjoint equations, the solution to which permits the calculation of the direction and relative magnitude of change in the diffuser profile that leads to a higher pressure rise. The solution to the adjoint problem can be shown to represent an artificially constructed flow. This interpretation provides a means to construct numerical solutions to the adjoint equations that do not compromise the fully viscous nature of the problem. The algorithmic and computational aspects of solving the adjoint equations are addressed. The form of these set of equations is similar but not identical to the Navier-Stokes equations. In particular some issues related to boundary conditions and stability are discussed.
Numerical Computation of Sensitivities and the Adjoint Approach
NASA Technical Reports Server (NTRS)
Lewis, Robert Michael
1997-01-01
We discuss the numerical computation of sensitivities via the adjoint approach in optimization problems governed by differential equations. We focus on the adjoint problem in its weak form. We show how one can avoid some of the problems with the adjoint approach, such as deriving suitable boundary conditions for the adjoint equation. We discuss the convergence of numerical approximations of the costate computed via the weak form of the adjoint problem and show the significance for the discrete adjoint problem.
NASA Astrophysics Data System (ADS)
Tan, Z.; Zhuang, Q.; Henze, D. K.; Frankenberg, C.; Dlugokencky, E. J.; Sweeney, C.; Turner, A. J.
2015-12-01
Understanding CH4 emissions from wetlands and lakes are critical for the estimation of Arctic carbon balance under fast warming climatic conditions. To date, our knowledge about these two CH4 sources is almost solely built on the upscaling of discontinuous measurements in limited areas to the whole region. Many studies indicated that, the controls of CH4 emissions from wetlands and lakes including soil moisture, lake morphology and substrate content and quality are notoriously heterogeneous, thus the accuracy of those simple estimates could be questionable. Here we apply a high spatial resolution atmospheric inverse model (nested-grid GEOS-Chem Adjoint) over the Arctic by integrating SCIAMACHY and NOAA/ESRL CH4 measurements to constrain the CH4 emissions estimated with process-based wetland and lake biogeochemical models. Our modeling experiments using different wetland CH4 emission schemes and satellite and surface measurements show that the total amount of CH4 emitted from the Arctic wetlands is well constrained, but the spatial distribution of CH4 emissions is sensitive to priors. For CH4 emissions from lakes, our high-resolution inversion shows that the models overestimate CH4 emissions in Alaskan costal lowlands and East Siberian lowlands. Our study also indicates that the precision and coverage of measurements need to be improved to achieve more accurate high-resolution estimates.
Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.
2010-01-01
Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.
Adjoint-Based Design of Rotors using the Navier-Stokes Equations in a Noninertial Reference Frame
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.
2009-01-01
Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated using comparisons with a complex-variable technique, and a number of single- and multi-point optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.
Adjoint active surfaces for localization and imaging.
Cook, Daniel A; Mueller, Martin Fritz; Fedele, Francesco; Yezzi, Anthony J
2015-01-01
This paper addresses the problem of localizing and segmenting regions embedded within a surrounding medium by characterizing their boundaries, as opposed to imaging the entirety of the volume. Active surfaces are used to directly reconstruct the shape of the region of interest. We describe the procedure for finding the optimal surface, which is computed iteratively via gradient descent that exploits the sensitivity of an error minimization functional to changes of the active surface. In doing so, we introduce the adjoint model to compute the sensitivity, and in this respect, the method shares common ground with several other disciplines, such as optimal control. Finally, we illustrate the proposed active surface technique in the framework of wave propagation governed by the scalar Helmholtz equation. Potential applications include electromagnetics, acoustics, geophysics, nondestructive testing, and medical imaging. PMID:25438311
Adjoint tomography of the southern California crust.
Tape, Carl; Liu, Qinya; Maggi, Alessia; Tromp, Jeroen
2009-08-21
Using an inversion strategy based on adjoint methods, we developed a three-dimensional seismological model of the southern California crust. The resulting model involved 16 tomographic iterations, which required 6800 wavefield simulations and a total of 0.8 million central processing unit hours. The new crustal model reveals strong heterogeneity, including local changes of +/-30% with respect to the initial three-dimensional model provided by the Southern California Earthquake Center. The model illuminates shallow features such as sedimentary basins and compositional contrasts across faults. It also reveals crustal features at depth that aid in the tectonic reconstruction of southern California, such as subduction-captured oceanic crustal fragments. The new model enables more realistic and accurate assessments of seismic hazard. PMID:19696349
The Θ-KMS adjoint and time reversed quantum Markov semigroups
NASA Astrophysics Data System (ADS)
Bolaños-Servin, Jorge R.; Quezada, Roberto
2015-08-01
We introduce the notion of Θ-KMS adjoint of a quantum Markov semigroup, which is identified with the time reversed semigroup. The break of Θ-KMS symmetry, or Θ-standard quantum detailed balance in the sense of Fagnola-Umanità,11 is measured by means of the von Neumann relative entropy of states associated with the semigroup and its Θ-KMS adjoint.
Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle
Peplow, Douglas E.; Mosher, Scott W; Evans, Thomas M
2012-08-01
For challenging radiation transport problems, hybrid methods combine the accuracy of Monte Carlo methods with the global information present in deterministic methods. One of the most successful hybrid methods is CADIS Consistent Adjoint Driven Importance Sampling. This method uses a deterministic adjoint solution to construct a biased source distribution and consistent weight windows to optimize a specific tally in a Monte Carlo calculation. The method has been implemented into transport codes using just the spatial and energy information from the deterministic adjoint and has been used in many applications to compute tallies with much higher figures-of-merit than analog calculations. CADIS also outperforms user-supplied importance values, which usually take long periods of user time to develop. This work extends CADIS to develop weight windows that are a function of the position, energy, and direction of the Monte Carlo particle. Two types of consistent source biasing are presented: one method that biases the source in space and energy while preserving the original directional distribution and one method that biases the source in space, energy, and direction. Seven simple example problems are presented which compare the use of the standard space/energy CADIS with the new space/energy/angle treatments.
GPU-accelerated adjoint algorithmic differentiation
NASA Astrophysics Data System (ADS)
Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe
2016-03-01
Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the "tape". Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography.
GPU-Accelerated Adjoint Algorithmic Differentiation
Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe
2015-01-01
Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the “tape”. Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography
A comparison of adjoint and data-centric verification techniques.
Wildey, Timothy Michael; Cyr, Eric Christopher; Shadid, John Nicolas; Pawlowski, Roger Patrick; Smith, Thomas Michael
2013-03-01
This document summarizes the results from a level 3 milestone study within the CASL VUQ effort. We compare the adjoint-based a posteriori error estimation approach with a recent variant of a data-centric verification technique. We provide a brief overview of each technique and then we discuss their relative advantages and disadvantages. We use Drekar::CFD to produce numerical results for steady-state Navier Stokes and SARANS approximations. 3
A Generalized Adjoint Approach for Quantifying Reflector Assembly Discontinuity Factor Uncertainties
Yankov, Artem; Collins, Benjamin; Jessee, Matthew Anderson; Downar, Thomas
2012-01-01
Sensitivity-based uncertainty analysis of assembly discontinuity factors (ADFs) can be readily performed using adjoint methods for infinite lattice models. However, there is currently no adjoint-based methodology to obtain uncertainties for ADFs along an interface between a fuel and reflector region. To accommodate leakage effects in a reflector region, a 1D approximation is usually made in order to obtain the homogeneous interface flux required to calculate the ADF. Within this 1D framework an adjoint-based method is proposed that is capable of efficiently calculating ADF uncertainties. In the proposed method the sandwich rule is utilized to relate the covariance of the input parameters of 1D diffusion theory in the reflector region to the covariance of the interface ADFs. The input parameters covariance matrix can be readily obtained using sampling-based codes such as XSUSA or adjoint-based codes such as TSUNAMI. The sensitivity matrix is constructed using a fixed-source adjoint approach for inputs characterizing the reflector region. An analytic approach is then used to determine the sensitivity of the ADFs to fuel parameters using the neutron balance equation. A stochastic approach is used to validate the proposed adjoint-based method.
NASA Astrophysics Data System (ADS)
Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey
2015-04-01
The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each
Accurate adjoint design sensitivities for nano metal optics.
Hansen, Paul; Hesselink, Lambertus
2015-09-01
We present a method for obtaining accurate numerical design sensitivities for metal-optical nanostructures. Adjoint design sensitivity analysis, long used in fluid mechanics and mechanical engineering for both optimization and structural analysis, is beginning to be used for nano-optics design, but it fails for sharp-cornered metal structures because the numerical error in electromagnetic simulations of metal structures is highest at sharp corners. These locations feature strong field enhancement and contribute strongly to design sensitivities. By using high-accuracy FEM calculations and rounding sharp features to a finite radius of curvature we obtain highly-accurate design sensitivities for 3D metal devices. To provide a bridge to the existing literature on adjoint methods in other fields, we derive the sensitivity equations for Maxwell's equations in the PDE framework widely used in fluid mechanics. PMID:26368483
Application of Adjoint Methodology in Various Aspects of Sonic Boom Design
NASA Technical Reports Server (NTRS)
Rallabhandi, Sriram K.
2014-01-01
One of the advances in computational design has been the development of adjoint methods allowing efficient calculation of sensitivities in gradient-based shape optimization. This paper discusses two new applications of adjoint methodology that have been developed to aid in sonic boom mitigation exercises. In the first, equivalent area targets are generated using adjoint sensitivities of selected boom metrics. These targets may then be used to drive the vehicle shape during optimization. The second application is the computation of adjoint sensitivities of boom metrics on the ground with respect to parameters such as flight conditions, propagation sampling rate, and selected inputs to the propagation algorithms. These sensitivities enable the designer to make more informed selections of flight conditions at which the chosen cost functionals are less sensitive.
On improving storm surge forecasting using an adjoint optimal technique
NASA Astrophysics Data System (ADS)
Li, Yineng; Peng, Shiqiu; Yan, Jing; Xie, Lian
2013-12-01
A three-dimensional ocean model and its adjoint model are used to simultaneously optimize the initial conditions (IC) and the wind stress drag coefficient (Cd) for improving storm surge forecasting. To demonstrate the effect of this proposed method, a number of identical twin experiments (ITEs) with a prescription of different error sources and two real data assimilation experiments are performed. Results from both the idealized and real data assimilation experiments show that adjusting IC and Cd simultaneously can achieve much more improvements in storm surge forecasting than adjusting IC or Cd only. A diagnosis on the dynamical balance indicates that adjusting IC only may introduce unrealistic oscillations out of the assimilation window, which can be suppressed by the adjustment of the wind stress when simultaneously adjusting IC and Cd. Therefore, it is recommended to simultaneously adjust IC and Cd to improve storm surge forecasting using an adjoint technique.
Adjoint-Based Sensitivity Maps for the Nearshore
NASA Astrophysics Data System (ADS)
Orzech, Mark; Veeramony, Jay; Ngodock, Hans
2013-04-01
The wave model SWAN (Booij et al., 1999) solves the spectral action balance equation to produce nearshore wave forecasts and climatologies. It is widely used by the coastal modeling community and is part of a variety of coupled ocean-wave-atmosphere model systems. A variational data assimilation system (Orzech et al., 2013) has recently been developed for SWAN and is presently being transitioned to operational use by the U.S. Naval Oceanographic Office. This system is built around a numerical adjoint to the fully nonlinear, nonstationary SWAN code. When provided with measured or artificial "observed" spectral wave data at a location of interest on a given nearshore bathymetry, the adjoint can compute the degree to which spectral energy levels at other locations are correlated with - or "sensitive" to - variations in the observed spectrum. Adjoint output may be used to construct a sensitivity map for the entire domain, tracking correlations of spectral energy throughout the grid. When access is denied to the actual locations of interest, sensitivity maps can be used to determine optimal alternate locations for data collection by identifying regions of greatest sensitivity in the mapped domain. The present study investigates the properties of adjoint-generated sensitivity maps for nearshore wave spectra. The adjoint and forward SWAN models are first used in an idealized test case at Duck, NC, USA, to demonstrate the system's effectiveness at optimizing forecasts of shallow water wave spectra for an inaccessible surf-zone location. Then a series of simulations is conducted for a variety of different initializing conditions, to examine the effects of seasonal changes in wave climate, errors in bathymetry, and variations in size and shape of the inaccessible region of interest. Model skill is quantified using two methods: (1) a more traditional correlation of observed and modeled spectral statistics such as significant wave height, and (2) a recently developed RMS
Constructing parent Hamiltonians for SU(N) ALKT states - a diagrammatic method
NASA Astrophysics Data System (ADS)
Roy, Abhishek; Quella, Thomas
Over the last decade, there has been increasing experimental interest in alkaline cold atom systems which exhibit SU (N) symmmetry. Theoretical work has shown that a one-dimensional SU (N) chain can have N - 1 symmetric protected states distinguished by fractionalized boundary spins. We introduce a new method for constructing SU (N) invariant Hamiltonians for Haldane phases in one dimension. Working at the AKLT point where the ground state is known exactly, we show a universal form of the Hamiltonian for any appropriate choice of physical and boundary spins. We apply our method to the case where the physical spin is in the adjoint representation and obtain a general expression for the Hamiltonian as well the Transfer Matrix for any N. Finally we comment on the relevance of our results to the generalized Haldane conjecture.
FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations
NASA Astrophysics Data System (ADS)
Ibragimov, N. H.; Torrisi, M.; Tracinà, R.
2010-11-01
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.
Wronskian Method for Bound States
ERIC Educational Resources Information Center
Fernandez, Francisco M.
2011-01-01
We propose a simple and straightforward method based on Wronskians for the calculation of bound-state energies and wavefunctions of one-dimensional quantum-mechanical problems. We explicitly discuss the asymptotic behaviour of the wavefunction and show that the allowed energies make the divergent part vanish. As illustrative examples we consider…
Adjoint-Based Uncertainty Quantification with MCNP
Seifried, Jeffrey E.
2011-09-01
This work serves to quantify the instantaneous uncertainties in neutron transport simulations born from nuclear data and statistical counting uncertainties. Perturbation and adjoint theories are used to derive implicit sensitivity expressions. These expressions are transformed into forms that are convenient for construction with MCNP6, creating the ability to perform adjoint-based uncertainty quantification with MCNP6. These new tools are exercised on the depleted-uranium hybrid LIFE blanket, quantifying its sensitivities and uncertainties to important figures of merit. Overall, these uncertainty estimates are small (< 2%). Having quantified the sensitivities and uncertainties, physical understanding of the system is gained and some confidence in the simulation is acquired.
Application of adjoint operators to neural learning
NASA Technical Reports Server (NTRS)
Barhen, J.; Toomarian, N.; Gulati, S.
1990-01-01
A technique for the efficient analytical computation of such parameters of the neural architecture as synaptic weights and neural gain is presented as a single solution of a set of adjoint equations. The learning model discussed concentrates on the adiabatic approximation only. A problem of interest is represented by a system of N coupled equations, and then adjoint operators are introduced. A neural network is formalized as an adaptive dynamical system whose temporal evolution is governed by a set of coupled nonlinear differential equations. An approach based on the minimization of a constrained neuromorphic energylike function is applied, and the complete learning dynamics are obtained as a result of the calculations.
Uematsu, Mikio; Kurosawa, Masahiko
2005-01-01
A generalised and convenient skyshine dose analysis method has been developed based on forward-adjoint folding technique. In the method, the air penetration data were prepared by performing an adjoint DOT3.5 calculation with cylindrical air-over-ground geometry having an adjoint point source (importance of unit flux to dose rate at detection point) in the centre. The accuracy of the present method was certified by comparing with DOT3.5 forward calculation. The adjoint flux data can be used as generalised radiation skyshine data for all sorts of nuclear facilities. Moreover, the present method supplies plenty of energy-angular dependent contribution flux data, which will be useful for detailed shielding design of facilities. PMID:16604693
A self-adjoint decomposition of the radial momentum operator
NASA Astrophysics Data System (ADS)
Liu, Q. H.; Xiao, S. F.
2015-12-01
With acceptance of the Dirac's observation that the canonical quantization entails using Cartesian coordinates, we examine the operator erPr rather than Pr itself and demonstrate that there is a decomposition of erPr into a difference of two self-adjoint but noncommutative operators, in which one is the total momentum and another is the transverse one. This study renders the operator Pr indirectly measurable and physically meaningful, offering an explanation of why the mean value of Pr over a quantum mechanical state makes sense and supporting Dirac's claim that Pr "is real and is the true momentum conjugate to r".
NASA Astrophysics Data System (ADS)
Kavvadias, I. S.; Papoutsis-Kiachagias, E. M.; Dimitrakopoulos, G.; Giannakoglou, K. C.
2015-11-01
In this article, the gradient of aerodynamic objective functions with respect to design variables, in problems governed by the incompressible Navier-Stokes equations coupled with the k-ω SST turbulence model, is computed using the continuous adjoint method, for the first time. Shape optimization problems for minimizing drag, in external aerodynamics (flows around isolated airfoils), or viscous losses in internal aerodynamics (duct flows) are considered. Sensitivity derivatives computed with the proposed adjoint method are compared to those computed with finite differences or a continuous adjoint variant based on the frequently used assumption of frozen turbulence; the latter proves the need for differentiating the turbulence model. Geometries produced by optimization runs performed with sensitivities computed by the proposed method and the 'frozen turbulence' assumption are also compared to quantify the gain from formulating and solving the adjoint to the turbulence model equations.
Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions
NASA Technical Reports Server (NTRS)
Akgun, Mehmet A.; Haftka, Raphael T.
2000-01-01
The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local
Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Park, Michael A.
2006-01-01
An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.
Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Park, Michael A.
2005-01-01
An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.
Examining Tropical Cyclone - Kelvin Wave Interactions using Adjoint Diagnostics
NASA Astrophysics Data System (ADS)
Reynolds, C. A.; Doyle, J. D.; Hong, X.
2015-12-01
Adjoint-based tools can provide valuable insight into the mechanisms that influence the evolution and predictability of atmospheric phenomena, as they allow for the efficient and rigorous computation of forecast sensitivity to changes in the initial state. We apply adjoint-based tools from the non-hydrostatic Coupled Atmosphere/Ocean Mesoscale Prediction System (COAMPS) to explore the initial-state sensitivity and interactions between a tropical cyclone and atmospheric equatorial waves associated with the Madden Julian Oscillation (MJO) in the Indian Ocean during the DYNAMO field campaign. The development of Tropical Cyclone 5 (TC05) coincided with the passage of an equatorial Kelvin wave and westerly wind burst associated with an MJO that developed in the Indian Ocean in late November 2011, but it was unclear if and how one affected the other. COAMPS 24-h and 36-h adjoint sensitivities are analyzed for both TC05 and the equatorial waves to understand how the evolution of each system is sensitive to the other. The sensitivity of equatorial westerlies in the western Indian Ocean on 23 November shares characteristics with the classic Gill (1980) Rossby and Kelvin wave response to symmetric heating about the equator, including symmetric cyclonic circulations to the north and south of the westerlies, and enhanced heating in the area of convergence between the equatorial westerlies and easterlies. In addition, there is sensitivity in the Bay of Bengal associated with the cyclonic circulation that eventually develops into TC05. At the same time, the developing TC05 system shows strongest sensitivity to local wind and heating perturbations, but sensitivity to the equatorial westerlies is also clear. On 24 November, when the Kelvin wave is immediately south of the developing tropical cyclone, both phenomena are sensitive to each other. On 25 November TC05 no longer shows sensitivity to the Kelvin wave, while the Kelvin Wave still exhibits some weak sensitivity to TC05. In
Adjoint tomography of the Middle East
NASA Astrophysics Data System (ADS)
Peter, D. B.; Savage, B.; Rodgers, A. J.; Tromp, J.
2010-12-01
Improvements in nuclear explosion monitoring require refined seismic models of the target region. In our study, we focus on the Middle East, spanning a region from Turkey to the west and West India to the east. This area represents a complex geologic and tectonic setting with sparse seismic data coverage. This has lead to diverging interpretations of crustal and underlying upper-mantle structure by different research groups, complicating seismic monitoring of the Middle East at regional distances. We evaluated an initial 3D seismic model of this region by computing full waveforms for several regional earthquakes by a spectral-element method. We measure traveltime and multitaper phase shifts between observed broadband data and synthetic seismograms for distinct seismic phases within selected time windows using a recently developed automated measurement algorithm. Based on the remaining misfits, we setup an iterative inversion procedure for a fully numerical 3D seismic tomography approach. In order to improve the initial 3D seismic model, the sensitivity to seismic structure of the traveltime and multitaper phase measurements for all available seismic network recordings is computed. As this represents a computationally very intensive task, we take advantage of a fully numerical adjoint approach by using the efficient software package SPECFEM3D_GLOBE on a dedicated cluster. We show examples of such sensitivity kernels for different seismic events and use them in a steepest descent approach to update the 3D seismic model, starting at longer periods between 60 s and up to 200 s and moving towards shorter periods of 11 s. We highlight various improvements in the initial seismic structure during the iterations in order to better fit regional seismic waveforms in the Middle East.
Adjoint tomography of the Middle East
NASA Astrophysics Data System (ADS)
Peter, D. B.; Savage, B.; Rodgers, A.; Morency, C.; Tromp, J.
2011-12-01
Improvements in nuclear explosion monitoring require refined seismic models of the target region. In our study, we focus on the Middle East, spanning a region from Turkey to the west and West India to the east. This area represents a complex geologic and tectonic setting with sparse seismic data coverage. This has lead to diverging interpretations of crustal and underlying upper-mantle structure by different research groups, complicating seismic monitoring of the Middle East at regional distances. We evaluated an initial 3D seismic model of this region by computing full waveforms for several regional earthquakes based on a spectral-element method. We measure traveltime and multitaper phase differences between observed broadband data and synthetic seismograms for distinct seismic phases within selected time windows using a recently developed automated measurement algorithm. Based on the remaining misfits, we setup an iterative inversion procedure for a fully numerical 3D seismic tomography approach. In order to improve the initial 3D seismic model, sensitivity to seismic structures of traveltime and multitaper phase measurements for all available seismic network recordings is computed. As this represents a computationally very intensive task, we take advantage of a fully numerical adjoint approach by using the efficient software package SPECFEM3D_GLOBE on a dedicated cluster. We show examples of such sensitivity kernels for different seismic events. All these `event kernels' are then summed, smoothed and further used in a preconditioned conjugate-gradient approach. Thus we iteratively update the 3D seismic model, starting at longer periods between 60~s and up to 150~s and moving towards shorter periods of 11~s. We highlight various improvements in the initial seismic structure during the iterations in order to better fit regional seismic waveforms in the Middle East.
Fully automatic adjoints: a robust and efficient mechanism for generating adjoint ocean models
NASA Astrophysics Data System (ADS)
Ham, D. A.; Farrell, P. E.; Funke, S. W.; Rognes, M. E.
2012-04-01
The problem of generating and maintaining adjoint models is sufficiently difficult that typically only the most advanced and well-resourced community ocean models achieve it. There are two current technologies which each suffer from their own limitations. Algorithmic differentiation, also called automatic differentiation, is employed by models such as the MITGCM [2] and the Alfred Wegener Institute model FESOM [3]. This technique is very difficult to apply to existing code, and requires a major initial investment to prepare the code for automatic adjoint generation. AD tools may also have difficulty with code employing modern software constructs such as derived data types. An alternative is to formulate the adjoint differential equation and to discretise this separately. This approach, known as the continuous adjoint and employed in ROMS [4], has the disadvantage that two different model code bases must be maintained and manually kept synchronised as the model develops. The discretisation of the continuous adjoint is not automatically consistent with that of the forward model, producing an additional source of error. The alternative presented here is to formulate the flow model in the high level language UFL (Unified Form Language) and to automatically generate the model using the software of the FEniCS project. In this approach it is the high level code specification which is differentiated, a task very similar to the formulation of the continuous adjoint [5]. However since the forward and adjoint models are generated automatically, the difficulty of maintaining them vanishes and the software engineering process is therefore robust. The scheduling and execution of the adjoint model, including the application of an appropriate checkpointing strategy is managed by libadjoint [1]. In contrast to the conventional algorithmic differentiation description of a model as a series of primitive mathematical operations, libadjoint employs a new abstraction of the simulation
Adjoint sensitivity studies of loop current and eddy shedding in the Gulf of Mexico
NASA Astrophysics Data System (ADS)
Gopalakrishnan, Ganesh; Cornuelle, Bruce D.; Hoteit, Ibrahim
2013-07-01
Adjoint model sensitivity analyses were applied for the loop current (LC) and its eddy shedding in the Gulf of Mexico (GoM) using the MIT general circulation model (MITgcm). The circulation in the GoM is mainly driven by the energetic LC and subsequent LC eddy separation. In order to understand which ocean regions and features control the evolution of the LC, including anticyclonic warm-core eddy shedding in the GoM, forward and adjoint sensitivities with respect to previous model state and atmospheric forcing were computed using the MITgcm and its adjoint. Since the validity of the adjoint model sensitivities depends on the capability of the forward model to simulate the real LC system and the eddy shedding processes, a 5 year (2004-2008) forward model simulation was performed for the GoM using realistic atmospheric forcing, initial, and boundary conditions. This forward model simulation was compared to satellite measurements of sea-surface height (SSH) and sea-surface temperature (SST), and observed transport variability. Despite realistic mean state, standard deviations, and LC eddy shedding period, the simulated LC extension shows less variability and more regularity than the observations. However, the model is suitable for studying the LC system and can be utilized for examining the ocean influences leading to a simple, and hopefully generic LC eddy separation in the GoM. The adjoint sensitivities of the LC show influences from the Yucatan Channel (YC) flow and Loop Current Frontal Eddy (LCFE) on both LC extension and eddy separation, as suggested by earlier work. Some of the processes that control LC extension after eddy separation differ from those controlling eddy shedding, but include YC through-flow. The sensitivity remains stable for more than 30 days and moves generally upstream, entering the Caribbean Sea. The sensitivities of the LC for SST generally remain closer to the surface and move at speeds consistent with advection by the high-speed core of
Advances in Global Adjoint Tomography -- Massive Data Assimilation
NASA Astrophysics Data System (ADS)
Ruan, Y.; Lei, W.; Bozdag, E.; Lefebvre, M. P.; Smith, J. A.; Krischer, L.; Tromp, J.
2015-12-01
Azimuthal anisotropy and anelasticity are key to understanding a myriad of processes in Earth's interior. Resolving these properties requires accurate simulations of seismic wave propagation in complex 3-D Earth models and an iterative inversion strategy. In the wake of successes in regional studies(e.g., Chen et al., 2007; Tape et al., 2009, 2010; Fichtner et al., 2009, 2010; Chen et al.,2010; Zhu et al., 2012, 2013; Chen et al., 2015), we are employing adjoint tomography based on a spectral-element method (Komatitsch & Tromp 1999, 2002) on a global scale using the supercomputer ''Titan'' at Oak Ridge National Laboratory. After 15 iterations, we have obtained a high-resolution transversely isotropic Earth model (M15) using traveltime data from 253 earthquakes. To obtain higher resolution images of the emerging new features and to prepare the inversion for azimuthal anisotropy and anelasticity, we expanded the original dataset with approximately 4,220 additional global earthquakes (Mw5.5-7.0) --occurring between 1995 and 2014-- and downloaded 300-minute-long time series for all available data archived at the IRIS Data Management Center, ORFEUS, and F-net. Ocean Bottom Seismograph data from the last decade are also included to maximize data coverage. In order to handle the huge dataset and solve the I/O bottleneck in global adjoint tomography, we implemented a python-based parallel data processing workflow based on the newly developed Adaptable Seismic Data Format (ASDF). With the help of the data selection tool MUSTANG developed by IRIS, we cleaned our dataset and assembled event-based ASDF files for parallel processing. We have started Centroid Moment Tensors (CMT) inversions for all 4,220 earthquakes with the latest model M15, and selected high-quality data for measurement. We will statistically investigate each channel using synthetic seismograms calculated in M15 for updated CMTs and identify problematic channels. In addition to data screening, we also modified
Instantons and the 5D U(1) gauge theory with extra adjoint
NASA Astrophysics Data System (ADS)
Poghossian, Rubik; Samsonyan, Marine
2009-07-01
In this paper, we compute the partition function of 5D supersymmetric U(1) gauge theory with extra adjoint matter in general Ω background. It is well known that such partition functions encode very rich topological information. We show in particular that unlike the case with no extra matter, the partition function with extra adjoint at some special values of the parameters directly reproduces the generating function for the Poincare polynomial of the moduli space of instantons. We compare our results with those recently obtained by Iqbal et al (Refined topological vertex, cylindric partitions and the U(1) adjoint theory, arXiv:0803.2260), who used the so-called refined topological vertex method.
Adjoint-based sensitivity analysis for reactor safety applications
Parks, C.V.
1986-08-01
The application and usefulness of an adjoint-based methodology for performing sensitivity analysis on reactor safety computer codes is investigated. The adjoint-based methodology, referred to as differential sensitivity theory (DST), provides first-order derivatives of the calculated quantities of interest (responses) with respect to the input parameters. The basic theoretical development of DST is presented along with the needed general extensions for consideration of model discontinuities and a variety of useful response definitions. A simple analytic problem is used to highlight the general DST procedures. finally, DST procedures presented in this work are applied to two highly nonlinear reactor accident analysis codes: (1) FASTGAS, a relatively small code for analysis of a loss-of-decay-heat-removal accident in a gas-cooled fast reactor, and (2) an existing code called VENUS-II which has been employed for analyzing the core disassembly phase of a hypothetical fast reactor accident. The two codes are different both in terms of complexity and in terms of the facets of DST which can be illustrated. Sensitivity results from the adjoint codes ADJGAS and VENUS-ADJ are verified with direct recalcualtions using perturbed input parameters. The effectiveness of the DST results for parameter ranking, prediction of response changes, and uncertainty analysis are illustrated. The conclusion drawn from this study is that DST is a viable, cost-effective methodology for accurate sensitivity analysis. In addition, a useful sensitivity tool for use in the fast reactor safety area has been developed in VENUS-ADJ. Future work needs to concentrate on combining the accurate first-order derivatives/results from DST with existing methods (based solely on direct recalculations) for higher-order response surfaces.
Adjoint optimization of natural convection problems: differentially heated cavity
NASA Astrophysics Data System (ADS)
Saglietti, Clio; Schlatter, Philipp; Monokrousos, Antonios; Henningson, Dan S.
2016-06-01
Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr=0.15{-}7 ) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors' knowledge, this behavior is illustrated here
NEMOTAM: tangent and adjoint models for the ocean modelling platform NEMO
NASA Astrophysics Data System (ADS)
Vidard, A.; Bouttier, P.-A.; Vigilant, F.
2014-10-01
The tangent linear and adjoint model (TAM) are efficient tools to analyse and to control dynamical systems such as NEMO. They can be involved in a large range of applications such as sensitivity analysis, parameter estimation or the computation of characteristics vectors. TAM is also required by the 4-D-VAR algorithm which is one of the major method in Data Assimilation. This paper describes the development and the validation of the Tangent linear and Adjoint Model for the NEMO ocean modelling platform (NEMOTAM). The diagnostic tools that are available alongside NEMOTAM are detailed and discussed and several applications are also presented.
Dual of QCD with one adjoint fermion
Mojaza, Matin; Nardecchia, Marco; Pica, Claudio; Sannino, Francesco
2011-03-15
We construct the magnetic dual of QCD with one adjoint Weyl fermion. The dual is a consistent solution of the 't Hooft anomaly matching conditions, allows for flavor decoupling, and remarkably constitutes the first nonsupersymmetric dual valid for any number of colors. The dual allows to bound the anomalous dimension of the Dirac fermion mass operator to be less than one in the conformal window.
NASA Astrophysics Data System (ADS)
Ito, Shin-Ichi; Nagao, Hiromichi; Yamanaka, Akinori; Tsukada, Yuhki; Koyama, Toshiyuki; Inoue, Junya
Phase field (PF) method, which phenomenologically describes dynamics of microstructure evolutions during solidification and phase transformation, has progressed in the fields of hydromechanics and materials engineering. How to determine, based on observation data, an initial state and model parameters involved in a PF model is one of important issues since previous estimation methods require too much computational cost. We propose data assimilation (DA), which enables us to estimate the parameters and states by integrating the PF model and observation data on the basis of the Bayesian statistics. The adjoint method implemented on DA not only finds an optimum solution by maximizing a posterior distribution but also evaluates the uncertainty in the estimations by utilizing the second order information of the posterior distribution. We carried out an estimation test using synthetic data generated by the two-dimensional Kobayashi's PF model. The proposed method is confirmed to reproduce the true initial state and model parameters we assume in advance, and simultaneously estimate their uncertainties due to quality and quantity of the data. This result indicates that the proposed method is capable of suggesting the experimental design to achieve the required accuracy.
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
NASA Astrophysics Data System (ADS)
Al-Hashimi, M. H.; Salman, M.; Shalaby, A.; Wiese, U.-J.
2013-10-01
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.
Limitations of Adjoint-Based Optimization for Separated Flows
NASA Astrophysics Data System (ADS)
Otero, J. Javier; Sharma, Ati; Sandberg, Richard
2015-11-01
Cabin noise is generated by the transmission of turbulent pressure fluctuations through a vibrating panel and can lead to fatigue. In the present study, we model this problem by using DNS to simulate the flow separating off a backward facing step and interacting with a plate downstream of the step. An adjoint formulation of the full compressible Navier-Stokes equations with varying viscosity is used to calculate the optimal control required to minimize the fluid-structure-acoustic interaction with the plate. To achieve noise reduction, a cost function in wavenumber space is chosen to minimize the excitation of the lower structural modes of the structure. To ensure the validity of time-averaged cost functions, it is essential that the time horizon is long enough to be a representative sample of the statistical behaviour of the flow field. The results from the current study show how this scenario is not always feasible for separated flows, because the chaotic behaviour of turbulence surpasses the ability of adjoint-based methods to compute time-dependent sensitivities of the flow.
Nievaart, V. A.; Legrady, D.; Moss, R. L.; Kloosterman, J. L.; Hagen, T. H. J. J. van der; Dam, H. van
2007-04-15
This paper deals with the application of the adjoint transport theory in order to optimize Monte Carlo based radiotherapy treatment planning. The technique is applied to Boron Neutron Capture Therapy where most often mixed beams of neutrons and gammas are involved. In normal forward Monte Carlo simulations the particles start at a source and lose energy as they travel towards the region of interest, i.e., the designated point of detection. Conversely, with adjoint Monte Carlo simulations, the so-called adjoint particles start at the region of interest and gain energy as they travel towards the source where they are detected. In this respect, the particles travel backwards and the real source and real detector become the adjoint detector and adjoint source, respectively. At the adjoint detector, an adjoint function is obtained with which numerically the same result, e.g., dose or flux in the tumor, can be derived as with forward Monte Carlo. In many cases, the adjoint method is more efficient and by that is much quicker when, for example, the response in the tumor or organ at risk for many locations and orientations of the treatment beam around the patient is required. However, a problem occurs when the treatment beam is mono-directional as the probability of detecting adjoint Monte Carlo particles traversing the beam exit (detector plane in adjoint mode) in the negative direction of the incident beam is zero. This problem is addressed here and solved first with the use of next event estimators and second with the application of a Legendre expansion technique of the angular adjoint function. In the first approach, adjoint particles are tracked deterministically through a tube to a (adjoint) point detector far away from the geometric model. The adjoint particles will traverse the disk shaped entrance of this tube (the beam exit in the actual geometry) perpendicularly. This method is slow whenever many events are involved that are not contributing to the point
Generalized uncertainty principle and self-adjoint operators
Balasubramanian, Venkat; Das, Saurya; Vagenas, Elias C.
2015-09-15
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.
Coupling of Monte Carlo adjoint leakages with three-dimensional discrete ordinates forward fluences
Slater, C.O.; Lillie, R.A.; Johnson, J.O.; Simpson, D.B.
1998-04-01
A computer code, DRC3, has been developed for coupling Monte Carlo adjoint leakages with three-dimensional discrete ordinates forward fluences in order to solve a special category of geometrically-complex deep penetration shielding problems. The code extends the capabilities of earlier methods that coupled Monte Carlo adjoint leakages with two-dimensional discrete ordinates forward fluences. The problems involve the calculation of fluences and responses in a perturbation to an otherwise simple two- or three-dimensional radiation field. In general, the perturbation complicates the geometry such that it cannot be modeled exactly using any of the discrete ordinates geometry options and thus a direct discrete ordinates solution is not possible. Also, the calculation of radiation transport from the source to the perturbation involves deep penetration. One approach to solving such problems is to perform the calculations in three steps: (1) a forward discrete ordinates calculation, (2) a localized adjoint Monte Carlo calculation, and (3) a coupling of forward fluences from the first calculation with adjoint leakages from the second calculation to obtain the response of interest (fluence, dose, etc.). A description of this approach is presented along with results from test problems used to verify the method. The test problems that were selected could also be solved directly by the discrete ordinates method. The good agreement between the DRC3 results and the direct-solution results verify the correctness of DRC3.
NASA Astrophysics Data System (ADS)
Smith, J. A.; Peter, D. B.; Tromp, J.; Komatitsch, D.; Lefebvre, M. P.
2015-12-01
We present both SPECFEM3D_Cartesian and SPECFEM3D_GLOBE open-source codes, representing high-performance numerical wave solvers simulating seismic wave propagation for local-, regional-, and global-scale application. These codes are suitable for both forward propagation in complex media and tomographic imaging. Both solvers compute highly accurate seismic wave fields using the continuous Galerkin spectral-element method on unstructured meshes. Lateral variations in compressional- and shear-wave speeds, density, as well as 3D attenuation Q models, topography and fluid-solid coupling are all readily included in both codes. For global simulations, effects due to rotation, ellipticity, the oceans, 3D crustal models, and self-gravitation are additionally included. Both packages provide forward and adjoint functionality suitable for adjoint tomography on high-performance computing architectures. We highlight the most recent release of the global version which includes improved performance, simultaneous MPI runs, OpenCL and CUDA support via an automatic source-to-source transformation library (BOAST), parallel I/O readers and writers for databases using ADIOS and seismograms using the recently developed Adaptable Seismic Data Format (ASDF) with built-in provenance. This makes our spectral-element solvers current state-of-the-art, open-source community codes for high-performance seismic wave propagation on arbitrarily complex 3D models. Together with these solvers, we provide full-waveform inversion tools to image the Earth's interior at unprecedented resolution.
Estimation of ex-core detector responses by adjoint Monte Carlo
Hoogenboom, J. E.
2006-07-01
Ex-core detector responses can be efficiently calculated by combining an adjoint Monte Carlo calculation with the converged source distribution of a forward Monte Carlo calculation. As the fission source distribution from a Monte Carlo calculation is given only as a collection of discrete space positions, the coupling requires a point flux estimator for each collision in the adjoint calculation. To avoid the infinite variance problems of the point flux estimator, a next-event finite-variance point flux estimator has been applied, witch is an energy dependent form for heterogeneous media of a finite-variance estimator known from the literature. To test the effects of this combined adjoint-forward calculation a simple geometry of a homogeneous core with a reflector was adopted with a small detector in the reflector. To demonstrate the potential of the method the continuous-energy adjoint Monte Carlo technique with anisotropic scattering was implemented with energy dependent absorption and fission cross sections and constant scattering cross section. A gain in efficiency over a completely forward calculation of the detector response was obtained, which is strongly dependent on the specific system and especially the size and position of the ex-core detector and the energy range considered. Further improvements are possible. The method works without problems for small detectors, even for a point detector and a small or even zero energy range. (authors)
Development of CO2 inversion system based on the adjoint of the global coupled transport model
NASA Astrophysics Data System (ADS)
Belikov, Dmitry; Maksyutov, Shamil; Chevallier, Frederic; Kaminski, Thomas; Ganshin, Alexander; Blessing, Simon
2014-05-01
We present the development of an inverse modeling system employing an adjoint of the global coupled transport model consisting of the National Institute for Environmental Studies (NIES) Eulerian transport model (TM) and the Lagrangian plume diffusion model (LPDM) FLEXPART. NIES TM is a three-dimensional atmospheric transport model, which solves the continuity equation for a number of atmospheric tracers on a grid spanning the entire globe. Spatial discretization is based on a reduced latitude-longitude grid and a hybrid sigma-isentropic coordinate in the vertical. NIES TM uses a horizontal resolution of 2.5°×2.5°. However, to resolve synoptic-scale tracer distributions and to have the ability to optimize fluxes at resolutions of 0.5° and higher we coupled NIES TM with the Lagrangian model FLEXPART. The Lagrangian component of the forward and adjoint models uses precalculated responses of the observed concentration to the surface fluxes and 3-D concentrations field simulated with the FLEXPART model. NIES TM and FLEXPART are driven by JRA-25/JCDAS reanalysis dataset. Construction of the adjoint of the Lagrangian part is less complicated, as LPDMs calculate the sensitivity of measurements to the surrounding emissions field by tracking a large number of "particles" backwards in time. Developing of the adjoint to Eulerian part was performed with automatic differentiation tool the Transformation of Algorithms in Fortran (TAF) software (http://www.FastOpt.com). This method leads to the discrete adjoint of NIES TM. The main advantage of the discrete adjoint is that the resulting gradients of the numerical cost function are exact, even for nonlinear algorithms. The overall advantages of our method are that: 1. No code modification of Lagrangian model is required, making it applicable to combination of global NIES TM and any Lagrangian model; 2. Once run, the Lagrangian output can be applied to any chemically neutral gas; 3. High-resolution results can be obtained over
NASA Astrophysics Data System (ADS)
Heimbach, Patick; Menemenlis, Dimitris; Losch, Martin; Campin, Jean-Michel; Hill, Chris
The adjoint of an ocean general circulation model is at the heart of the ocean state estimation system of the Estimating the Circulation and Climate of the Ocean (ECCO) project. As part of an ongoing effort to extend ECCO to a coupled ocean/sea-ice estimation system, a dynamic and thermodynamic sea-ice model has been developed for the Massachusetts Institute of Technology general circulation model (MITgcm). One key requirement is the ability to generate, by means of automatic differentiation (AD), tangent linear (TLM) and adjoint (ADM) model code for the coupled MITgcm ocean/sea-ice system. This second part of a two-part paper describes aspects of the adjoint model. The adjoint ocean and sea-ice model is used to calculate transient sensitivities of solid (ice and snow) freshwater export through Lancaster Sound in the Canadian Arctic Archipelago (CAA). The adjoint state provides a complementary view of the dynamics. In particular, the transient, multi-year sensitivity patterns reflect dominant pathways and propagation timescales through the CAA as resolved by the model, thus shedding light on causal relationships, in the model, across the Archipelago. The computational cost of inferring such causal relationships from forward model diagnostics alone would be prohibitive. The role of the exact model trajectory around which the adjoint is calculated (and therefore of the exactness of the adjoint) is exposed through calculations using free-slip vs no-slip lateral boundary conditions. Effective ice thickness, sea surface temperature, and precipitation sensitivities, are discussed in detail as examples of the coupled sea-ice/ocean and atmospheric forcing control space. To test the reliability of the adjoint, finite-difference perturbation experiments were performed for each of these elements and the cost perturbations were compared to those "predicted" by the adjoint. Overall, remarkable qualitative and quantitative agreement is found. In particular, the adjoint correctly
Using adjoint-based optimization to study wing flexibility in flapping flight
NASA Astrophysics Data System (ADS)
Wei, Mingjun; Xu, Min; Dong, Haibo
2014-11-01
In the study of flapping-wing flight of birds and insects, it is important to understand the impact of wing flexibility/deformation on aerodynamic performance. However, the large control space from the complexity of wing deformation and kinematics makes usual parametric study very difficult or sometimes impossible. Since the adjoint-based approach for sensitivity study and optimization strategy is a process with its cost independent of the number of input parameters, it becomes an attractive approach in our study. Traditionally, adjoint equation and sensitivity are derived in a fluid domain with fixed solid boundaries. Moving boundary is only allowed when its motion is not part of control effort. Otherwise, the derivation becomes either problematic or too complex to be feasible. Using non-cylindrical calculus to deal with boundary deformation solves this problem in a very simple and still mathematically rigorous manner. Thus, it allows to apply adjoint-based optimization in the study of flapping wing flexibility. We applied the ``improved'' adjoint-based method to study the flexibility of both two-dimensional and three-dimensional flapping wings, where the flapping trajectory and deformation are described by either model functions or real data from the flight of dragonflies. Supported by AFOSR.
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
Al-Hashimi, M.H.; Salman, M.; Shalaby, A.; Wiese, U.-J.
2013-10-15
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.
NASA Technical Reports Server (NTRS)
Ustinov, Eugene A.; Sunseri, Richard F.
2005-01-01
An approach is presented to the inversion of gravity fields based on evaluation of partials of observables with respect to gravity harmonics using the solution of adjoint problem of orbital dynamics of the spacecraft. Corresponding adjoint operator is derived directly from the linear operator of the linearized forward problem of orbital dynamics. The resulting adjoint problem is similar to the forward problem and can be solved by the same methods. For given highest degree N of gravity harmonics desired, this method involves integration of N adjoint solutions as compared to integration of N2 partials of the forward solution with respect to gravity harmonics in the conventional approach. Thus, for higher resolution gravity models, this approach becomes increasingly more effective in terms of computer resources as compared to the approach based on the solution of the forward problem of orbital dynamics.
Adjoint-based optimal control of an airfoil in gusting flows
NASA Astrophysics Data System (ADS)
Choi, Jeesoon; Colonius, Tim; California Institute of Technology Team
2015-11-01
In this study, we apply optimal control to an airfoil in gusting flow to investigate the possibility of extracting energy. The gradients of an objective function are obtained via the adjoint method and used to minimize the cost. The immersed boundary projection method is used for our forward solver, and the relevant adjoint equations are derived by the discrete-then-differentiate approach. Translational gusts are generated by a body force in the computational domain upstream to the body, and the method finds the optimal angles of the airfoil that exploits the greatest amount of energy. The influence of a vortex traversing an airfoil is also investigated and optimized to reduce the fluctuating lift.
Self-adjointness and conservation laws of difference equations
NASA Astrophysics Data System (ADS)
Peng, Linyu
2015-06-01
A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.
Adjoint tomography of crust and upper-mantle structure beneath Continental China
NASA Astrophysics Data System (ADS)
Chen, M.; Niu, F.; Liu, Q.; Tromp, J.
2013-12-01
Four years of regional earthquake recordings from 1,869 seismic stations are used for high-resolution and high-fidelity seismic imaging of the crust and upper-mantle structure beneath Continental China. This unprecedented high-density dataset is comprised of seismograms recorded by the China Earthquake Administration Array (CEArray), NorthEast China Extended SeiSmic Array (NECESSArray), INDEPTH-IV Array, F-net and other global and regional seismic networks, and involves 1,326,384 frequency-dependent phase measurements. Adjoint tomography is applied to this unprecedented dataset, aiming to resolve detailed 3D maps of compressional and shear wavespeeds, and radial anisotropy. Contrary to traditional ray-theory based tomography, adjoint tomography takes into account full 3D wave propagation effects and off-ray-path sensitivity. In our implementation, it utilizes a spectral-element method for precise wave propagation simulations. The tomographic method starts with a 3D initial model that combines smooth radially anisotropic mantle model S362ANI and 3D crustal model Crust2.0. Traveltime and amplitude misfits are minimized iteratively based on a conjugate gradient method, harnessing 3D finite-frequency kernels computed for each updated 3D model. After 17 iterations, our inversion reveals strong correlations of 3D wavespeed heterogeneities in the crust and upper mantle with surface tectonic units, such as the Himalaya Block, the Tibetan Plateau, the Tarim Basin, the Ordos Block, and the South China Block. Narrow slab features emerge from the smooth initial model above the transition zone beneath the Japan, Ryukyu, Philippine, Izu-Bonin, Mariana and Andaman arcs. 3D wavespeed variations appear comparable to or much sharper than in high-frequency P-and S-wave models from previous studies. Moreover our results include new information, such as 3D variations of radial anisotropy and the Vp/Vs ratio, which are expected to shed new light to the composition, thermal state, flow
Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Kleb, William L.
2005-01-01
A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Kleb, William L.
2005-01-01
A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.
Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization
NASA Technical Reports Server (NTRS)
Green, Lawrence; Carle, Alan; Fagan, Mike
1999-01-01
Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop
Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation
NASA Astrophysics Data System (ADS)
Yaşar, Emrullah; San, Sait; Özkan, Yeşim Sağlam
2016-01-01
In this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.
Universal Racah matrices and adjoint knot polynomials: Arborescent knots
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.
2016-04-01
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.
Unsteady adjoint of a gas turbine inlet guide vane
NASA Astrophysics Data System (ADS)
Talnikar, Chaitanya; Wang, Qiqi
2015-11-01
Unsteady fluid flow simulations like large eddy simulation have been shown to be crucial in accurately predicting heat transfer in turbomachinery applications like transonic flow over an inlet guide vane. To compute sensitivities of aerothermal objectives for a vane with respect to design parameters an unsteady adjoint is required. In this talk we present unsteady adjoint solutions for a vane from VKI using pressure loss and heat transfer over the vane surface as the objectives. The boundary layer on the suction side near the trailing edge of the vane is turbulent and this poses a challenge for an adjoint solver. The chaotic dynamics cause the adjoint solution to diverge exponentially to infinity from that region when simulated backwards in time. The prospect of adding artificial viscosity to the adjoint equations to dampen the adjoint fields is investigated. Results for the vane from simulations performed on the Titan supercomputer will be shown and the effect of the additional viscosity on the accuracy of the sensitivities will be discussed.
Neural network training by integration of adjoint systems of equations forward in time
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)
1992-01-01
A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically, it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved, but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. The trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.
Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)
1999-01-01
A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.
Seismic wave-speed structure beneath the metropolitan area of Japan based on adjoint tomography
NASA Astrophysics Data System (ADS)
Miyoshi, T.; Obayashi, M.; Tono, Y.; Tsuboi, S.
2015-12-01
We have obtained a three-dimensional (3D) model of seismic wave-speed structure beneath the metropolitan area of Japan. We applied the spectral-element method (e.g. Komatitsch and Tromp 1999) and adjoint method (Liu and Tromp 2006) to the broadband seismograms in order to infer the 3D model. We used the travel-time tomography result (Matsubara and Obara 2011) as an initial 3D model and used broadband waveforms recorded at the NIED F-net stations. We selected 147 earthquakes with magnitude of larger than 4.5 from the F-net earthquake catalog and used their bandpass filtered seismograms between 5 and 20 second with a high S/N ratio. The 3D model used for the forward and adjoint simulations is represented as a region of approximately 500 by 450 km in horizontal and 120 km in depth. Minimum period of theoretical waveforms was 4.35 second. For the adjoint inversion, we picked up the windows of the body waves from the observed and theoretical seismograms. We used SPECFEM3D_Cartesian code (e.g. Peter et al. 2011) for the forward and adjoint simulations, and their simulations were implemented by K-computer in RIKEN. Each iteration required about 0.1 million CPU hours at least. The model parameters of Vp and Vs were updated by using the steepest descent method. We obtained the fourth iterative model (M04), which reproduced observed waveforms better than the initial model. The shear wave-speed of M04 was significantly smaller than the initial model at any depth. The model of compressional wave-speed was not improved by inversion because of small alpha kernel values. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We thank to the NIED for providing seismological data.
NASA Astrophysics Data System (ADS)
Zhao, Xiao-Feng; Huang, Si-Xun; Du, Hua-Dong
2011-02-01
This paper puts forward possibilities of refractive index profile retrieval using field measurements at an array of radio receivers in terms of variational adjoint approach. The derivation of the adjoint model begins with the parabolic wave equation for a smooth, perfectly conducting surface and horizontal polarization conditions. To deal with the ill-posed difficulties of the inversion, the regularization ideas are introduced into the establishment of the cost function. Based on steepest descent iterations, the optimal value of refractivity could be retrieved quickly at each point over height. Numerical experiments demonstrate that the method works well for low-distance signals, while it is not accurate enough for long-distance propagations. Through curve fitting processing, however, giving a good initial refractivity profile could generally improve the inversions.
Adjoint equations and analysis of complex systems: Application to virus infection modelling
NASA Astrophysics Data System (ADS)
Marchuk, G. I.; Shutyaev, V.; Bocharov, G.
2005-12-01
Recent development of applied mathematics is characterized by ever increasing attempts to apply the modelling and computational approaches across various areas of the life sciences. The need for a rigorous analysis of the complex system dynamics in immunology has been recognized since more than three decades ago. The aim of the present paper is to draw attention to the method of adjoint equations. The methodology enables to obtain information about physical processes and examine the sensitivity of complex dynamical systems. This provides a basis for a better understanding of the causal relationships between the immune system's performance and its parameters and helps to improve the experimental design in the solution of applied problems. We show how the adjoint equations can be used to explain the changes in hepatitis B virus infection dynamics between individual patients.
Towards efficient backward-in-time adjoint computations using data compression techniques
Cyr, E. C.; Shadid, J. N.; Wildey, T.
2014-12-16
In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for themore » difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintaining reasonable accuracy in the error-estimates.« less
Towards efficient backward-in-time adjoint computations using data compression techniques
Cyr, E. C.; Shadid, J. N.; Wildey, T.
2014-12-16
In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for the difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintaining reasonable accuracy in the error-estimates.
Baryogenesis via leptogenesis in adjoint SU(5)
Blanchet, Steve; Fileviez Perez, Pavel E-mail: fileviez@physics.wisc.edu
2008-08-15
The possibility of explaining the baryon asymmetry in the Universe through the leptogenesis mechanism in the context of adjoint SU(5) is investigated. In this model neutrino masses are generated through the type I and type III seesaw mechanisms, and the field responsible for the type III seesaw, called {rho}{sub 3}, generates the B-L asymmetry needed to satisfy the observed value of the baryon asymmetry in the Universe. We find that the CP asymmetry originates only from the vertex correction, since the self-energy contribution is not present. When neutrino masses have a normal hierarchy, successful leptogenesis is possible for 10{sup 11} GeV{approx}
A variational level set method for the topology optimization of steady-state Navier Stokes flow
NASA Astrophysics Data System (ADS)
Zhou, Shiwei; Li, Qing
2008-12-01
The smoothness of topological interfaces often largely affects the fluid optimization and sometimes makes the density-based approaches, though well established in structural designs, inadequate. This paper presents a level-set method for topology optimization of steady-state Navier-Stokes flow subject to a specific fluid volume constraint. The solid-fluid interface is implicitly characterized by a zero-level contour of a higher-order scalar level set function and can be naturally transformed to other configurations as its host moves. A variational form of the cost function is constructed based upon the adjoint variable and Lagrangian multiplier techniques. To satisfy the volume constraint effectively, the Lagrangian multiplier derived from the first-order approximation of the cost function is amended by the bisection algorithm. The procedure allows evolving initial design to an optimal shape and/or topology by solving the Hamilton-Jacobi equation. Two classes of benchmarking examples are presented in this paper: (1) periodic microstructural material design for the maximum permeability; and (2) topology optimization of flow channels for minimizing energy dissipation. A number of 2D and 3D examples well demonstrated the feasibility and advantage of the level-set method in solving fluid-solid shape and topology optimization problems.
Automatic verification methods for finite state systems
Sifakis, J. )
1990-01-01
This volume contains the proceedings of a workshop devoted to the verification of finite state systems. The workshop focused on the development and use of methods, tools and theories for automatic verification of finite state systems. The goal at the workshop was to compare verification methods and tools to assist the applications designer. The papers review verification techniques for finite state systems and evaluate their relative advantages. The techniques considered cover various specification formalisms such as process algebras, automata and logics. Most of the papers focus on exploitation of existing results in three application areas: hardware design, communication protocols and real-time systems.
Big Data Challenges in Global Seismic 'Adjoint Tomography' (Invited)
NASA Astrophysics Data System (ADS)
Tromp, J.; Bozdag, E.; Krischer, L.; Lefebvre, M.; Lei, W.; Smith, J.
2013-12-01
The challenge of imaging Earth's interior on a global scale is closely linked to the challenge of handling large data sets. The related iterative workflow involves five distinct phases, namely, 1) data gathering and culling, 2) synthetic seismogram calculations, 3) pre-processing (time-series analysis and time-window selection), 4) data assimilation and adjoint calculations, 5) post-processing (pre-conditioning, regularization, model update). In order to implement this workflow on modern high-performance computing systems, a new seismic data format is being developed. The Adaptable Seismic Data Format (ASDF) is designed to replace currently used data formats with a more flexible format that allows for fast parallel I/O. The metadata is divided into abstract categories, such as "source" and "receiver", along with provenance information for complete reproducibility. The structure of ASDF is designed keeping in mind three distinct applications: earthquake seismology, seismic interferometry, and exploration seismology. Existing time-series analysis tool kits, such as SAC and ObsPy, can be easily interfaced with ASDF so that seismologists can use robust, previously developed software packages. ASDF accommodates an automated, efficient workflow for global adjoint tomography. Manually managing the large number of simulations associated with the workflow can rapidly become a burden, especially with increasing numbers of earthquakes and stations. Therefore, it is of importance to investigate the possibility of automating the entire workflow. Scientific Workflow Management Software (SWfMS) allows users to execute workflows almost routinely. SWfMS provides additional advantages. In particular, it is possible to group independent simulations in a single job to fit the available computational resources. They also give a basic level of fault resilience as the workflow can be resumed at the correct state preceding a failure. Some of the best candidates for our particular workflow
Conformal versus confining scenario in SU(2) with adjoint fermions
Del Debbio, L.; Pica, C.; Lucini, B.; Patella, A.; Rago, A.
2009-10-01
The masses of the lowest-lying states in the meson and in the gluonic sector of an SU(2) gauge theory with two Dirac flavors in the adjoint representation are measured on the lattice at a fixed value of the lattice coupling {beta}=4/g{sub 0}{sup 2}=2.25 for values of the bare fermion mass m{sub 0} that span a range between the quenched regime and the massless limit, and for various lattice volumes. Even for light constituent fermions the lightest glueballs are found to be lighter than the lightest mesons. Moreover, the string tension between two static fundamental sources strongly depends on the mass of the dynamical fermions and becomes of the order of the inverse squared lattice linear size before the chiral limit is reached. The implications of these findings for the phase of the theory in the massless limit are discussed and a strategy for discriminating between the (near-)conformal and the confining scenario is outlined.
Strong Adjoint Sensitivities in Tropical Eddy-Permitting Variational Data Assimilation
NASA Astrophysics Data System (ADS)
Cornuelle, B.; Hoteit, I.; Koehl, A.; Stammer, D.
2007-05-01
A variational data assimilation system has been implemented for the tropical Pacific Ocean for an eddy-permitting regional implementation of the MIT general circulation model (MITgcm). The model uses realistic topography with parameterizations for the surface boundary layer (KPP) and open boundaries at the south and north, as well as in the Indonesian throughflow. The adjoint method is used to adjust the model to observations in the tropical Pacific region using control parameters which include initial temperature and salinity, temperature, salinity and horizontal velocities at the open boundaries, and twice-daily surface fluxes of momentum, heat and freshwater. The model is constrained with most of the available datasets in the tropical Pacific, including climatologies, TAO, ARGO, XBT, and satellite SST and SSH data. The forward model runs exhibit strongly growing flow instabilities in the regions of high kinetic energy and low planetary potential vorticity gradient. The growth of these perturbations is limited by nonlinearities once they reach finite size, meaning that the high linear growth rates do not apply for long time periods. This poses a technical problem for adjoint-based assimilation, which depends on the linearized sensitivities to adjust the controls. Relative to the forward model runs, increased viscosity and diffusivity terms are used in the adjoint model runs to avoid large sensitivities related to the flow instabilities present in the high-resolution model. This talk will discuss some of the technical aspects and show results for 1 year assimilation period.
Global adjoint tomography: Perspectives, initial results and future directions
NASA Astrophysics Data System (ADS)
Bozdag, Ebru; Zhu, Hejun; Peter, Daniel; Tromp, Jeroen
2013-04-01
Adjoint methods provide an efficient way for incorporating the full nonlinearity of wave propagation and 3D Fréchet kernels in iterative seismic inversions. Our goal is to take adjoint tomography forward to image the entire planet using the opportunities offered by advances in numerical wave propagation solvers and high-performance computing. Using an iterative pre-conditioned conjugate gradient scheme, we initially set the aim to obtain a global crustal and mantle model with confined transverse isotropy in the upper mantle. Our strategy is to invert crustal and mantle structure together to avoid any bias introduced into upper-mantle images due to "crustal corrections", which are commonly used in classical tomography. We have started with 255 global CMT events (5.8 ≤ Mw ≤ 7) and used GSN stations as well as some local networks such as USArray, European stations, etc. We have demonstrated the feasibility of global scale inversions by performing two iterations based on numerical simulations accurate down to ~27 s. To simplify the problem, we primarily focus on elastic structure, and therefore our measurements are based on multitaper traveltime differences between observed and synthetic seismograms. We compute 3D sensitivity kernels for the selected events combining long-period surface waves (initially T > 60 s), where it is easier to handle nonlinearities due to the crust, with shorter-period body waves (initially T > 27 s), which are more sensitive to deeper parts of the mantle. 3D simulations dramatically increase the usable amount of data so that, with the current earthquake-station setup, we perform each iteration with more than two million measurements. Our initial results are promising to improve images from the upper mantle all the way down to the core-mantle boundary. Recent improvements in our 3D solvers (e.g., a GPU version) and access to high-performance computational centers (e.g., ORNL's Cray XK7 "Titan" system) now enable us to perform iterations
Determining scaling laws from geodynamic simulations using adjoint gradients.
NASA Astrophysics Data System (ADS)
Reuber, Georg; Kaus, Boris; Popov, Anton
2016-04-01
Whereas significant progress has been made in modelling of lithospheric and crustal scale processes in recent years, it often remains a challenge to understand which of the many model parameters is of key importance for a particular simulation. Determining this is usually done by manually changing the model input parameters and performing new simulations. For a few cases, such as for crustal-scale folding instabilities (with viscous rheologies, e.g. [1]) or for Rayleigh-Taylor instabilities, one can use existing scaling laws to obtain such insights. Yet, for a more general case, it is not straightforward to do this (apart from running many simulations). Here, we test a different approach which computes gradients of the model parameters using adjoint based methods, which has the advantage that we can test the influence of an independent number of parameters on the system by computing and analysing the covariance matrix and the gradient of the parameter space. This method might give us the chance to get insights on which parameters affect for example subduction processes and how strong the system depends on their influence. [1] Fernandez, N., & Kaus, B. J. (2014). Fold interaction and wavelength selection in 3D models of multilayer detachment folding. Tectonophysics, 632, 199-217.
Receptivity in parallel flows: An adjoint approach
NASA Technical Reports Server (NTRS)
Hill, D. Christopher
1993-01-01
Linear receptivity studies in parallel flows are aimed at understanding how external forcing couples to the natural unstable motions which a flow can support. The vibrating ribbon problem models the original Schubauer and Skramstad boundary layer experiment and represents the classic boundary layer receptivity problem. The process by which disturbances are initiated in convectively-unstable jets and shear layers has also received attention. Gaster was the first to handle the boundary layer analysis with the recognition that spatial modes, rather than temporal modes, were relevant when studying convectively-unstable flows that are driven by a time-harmonic source. The amplitude of the least stable spatial mode, far downstream of the source, is related to the source strength by a coupling coefficient. The determination of this coefficient is at the heart of this type of linear receptivity study. The first objective of the present study was to determine whether the various wave number derivative factors, appearing in the coupling coefficients for linear receptivity problems, could be reexpressed in a simpler form involving adjoint eigensolutions. Secondly, it was hoped that the general nature of this simplification could be shown; indeed, a rather elegant characterization of the receptivity properties of spatial instabilities does emerge. The analysis is quite distinct from the usual Fourier-inversion procedures, although a detailed knowledge of the spectrum of the Orr-Sommerfeld equation is still required. Since the cylinder wake analysis proved very useful in addressing control considerations, the final objective was to provide a foundation upon which boundary layer control theory may be developed.
A Posteriori Analysis for Hydrodynamic Simulations Using Adjoint Methodologies
Woodward, C S; Estep, D; Sandelin, J; Wang, H
2009-02-26
This report contains results of analysis done during an FY08 feasibility study investigating the use of adjoint methodologies for a posteriori error estimation for hydrodynamics simulations. We developed an approach to adjoint analysis for these systems through use of modified equations and viscosity solutions. Targeting first the 1D Burgers equation, we include a verification of the adjoint operator for the modified equation for the Lax-Friedrichs scheme, then derivations of an a posteriori error analysis for a finite difference scheme and a discontinuous Galerkin scheme applied to this problem. We include some numerical results showing the use of the error estimate. Lastly, we develop a computable a posteriori error estimate for the MAC scheme applied to stationary Navier-Stokes.
Learning a trajectory using adjoint functions and teacher forcing
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad B.; Barhen, Jacob
1992-01-01
A new methodology for faster supervised temporal learning in nonlinear neural networks is presented which builds upon the concept of adjoint operators to allow fast computation of the gradients of an error functional with respect to all parameters of the neural architecture, and exploits the concept of teacher forcing to incorporate information on the desired output into the activation dynamics. The importance of the initial or final time conditions for the adjoint equations is discussed. A new algorithm is presented in which the adjoint equations are solved simultaneously (i.e., forward in time) with the activation dynamics of the neural network. We also indicate how teacher forcing can be modulated in time as learning proceeds. The results obtained show that the learning time is reduced by one to two orders of magnitude with respect to previously published results, while trajectory tracking is significantly improved. The proposed methodology makes hardware implementation of temporal learning attractive for real-time applications.
A method of enciphering quantum states
NASA Astrophysics Data System (ADS)
Azuma, Hiroo; Ban, Masashi
2001-04-01
In this paper, we propose a method of enciphering quantum states of two-state systems (qubits) for sending them in secrecy without entangled qubits shared by two legitimate users (Alice and Bob). This method has the following two properties. First, even if an eavesdropper (Eve) steals qubits, she can extract information from them with only a certain probability at most. Second, Alice and Bob can confirm that the qubits are transmitted between them correctly by measuring a signature. If Eve measures m qubits one by one from n enciphered qubits and sends alternative ones (the intercept/resend attack), the probability that Alice and Bob do not notice Eve's action is equal to (3/4)m or less. Passwords for decryption and the signature are given by classical binary strings and they are disclosed through a public channel. Enciphering classical information by this method is equivalent to the one-time pad method with distributing a classical key (random binary string) by the BB84 protocol. If Eve takes away qubits, Alice and Bob lose the original quantum information. If we apply our method to a state in iteration, Eve's success probability decreases exponentially. We cannot examine security against the case that Eve makes an attack using entanglement. This remains to be solved in the future.
Diffusion Acceleration Schemes for Self-Adjoint Angular Flux Formulation with a Void Treatment
Yaqi Wang; Hongbin Zhang; Richard C. Martineau
2014-02-01
A Galerkin weak form for the monoenergetic neutron transport equation with a continuous finite element method and discrete ordinate method is developed based on self-adjoint angular flux formulation. This weak form is modified for treating void regions. A consistent diffusion scheme is developed with projection. Correction terms of the diffusion scheme are derived to reproduce the transport scalar flux. A source iteration that decouples the solution of all directions with both linear and nonlinear diffusion accelerations is developed and demonstrated. One-dimensional Fourier analysis is conducted to demonstrate the stability of the linear and nonlinear diffusion accelerations. Numerical results of these schemes are presented.
NASA Technical Reports Server (NTRS)
Reuther, James; Jameson, Antony; Alonso, Juan Jose; Rimlinger, Mark J.; Saunders, David
1997-01-01
An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat
ANISORROPIA: the adjoint of the aerosol thermodynamic model ISORROPIA
NASA Astrophysics Data System (ADS)
Capps, S. L.; Henze, D. K.; Hakami, A.; Russell, A. G.; Nenes, A.
2011-08-01
We present the development of ANISORROPIA, the discrete adjoint of the ISORROPIA thermodynamic equilibrium model that treats the Na+-SO42--HSO4--NH4+-NO3--Cl--H2O aerosol system, and we demonstrate its sensitivity analysis capabilities. ANISORROPIA calculates sensitivities of an inorganic species in aerosol or gas phase with respect to the total concentrations of each species present with only a two-fold increase in computational time over the forward model execution. Due to the highly nonlinear and discontinuous solution surface of ISORROPIA, evaluation of the adjoint required a new, complex-variable version of the the model, which determines first-order sensitivities with machine precision and avoids cancellation errors arising from finite difference calculations. The adjoint is verified over an atmospherically relevant range of concentrations, temperature, and relative humidity. We apply ANISORROPIA to recent field campaign results from Atlanta, GA, USA, and Mexico City, Mexico, to characterize the inorganic aerosol sensitivities of these distinct urban air masses. The variability in the relationship between PM2.5 mass and precursor concentrations shown has important implications for air quality and climate. ANISORROPIA enables efficient elucidation of aerosol concentration dependence on aerosol precursor emissions in the context of atmospheric chemical transport model adjoints.
Assimilating Remote Ammonia Observations with a Refined Aerosol Thermodynamics Adjoint"
Ammonia emissions parameters in North America can be refined in order to improve the evaluation of modeled concentrations against observations. Here, we seek to do so by developing and applying the GEOS-Chem adjoint nested over North America to conductassimilation of observations...
Adjoint-Operator Learning For A Neural Network
NASA Technical Reports Server (NTRS)
Barhen, Jacob; Toomarian, Nikzad
1993-01-01
Electronic neural networks made to synthesize initially unknown mathematical models of time-dependent phenomena or to learn temporally evolving patterns by use of algorithms based on adjoint operators. Algorithms less complicated, involve less computation and solve learning equations forward in time possibly simultaneously with equations of evolution of neural network, thereby both increasing computational efficiency and making real-time applications possible.
Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation
NASA Technical Reports Server (NTRS)
Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David
1996-01-01
This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.
NASA Astrophysics Data System (ADS)
Zheng, Xiangyang; Mayerle, Roberto; Xing, Qianguo; Fernández Jaramillo, José Manuel
2016-08-01
In this paper, a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method is applied to an existing storm surge model of the German North Sea. To avoid the need of an adjoint model, an ensemble-like method to explicitly represent the linear tangent equation is adopted. Results of twin experiments have shown that the method is able to recover the contaminated low dimension model parameters to their true values. The data assimilation scheme was applied to a severe storm surge event which occurred in the North Sea in December 5, 2013. By adjusting wind drag coefficient, the predictive ability of the model increased significantly. Preliminary experiments have shown that an increase in the predictive ability is attained by narrowing the data assimilation time window.
NASA Astrophysics Data System (ADS)
Zheng, Xiangyang; Mayerle, Roberto; Xing, Qianguo; Fernández Jaramillo, José Manuel
2016-06-01
In this paper, a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method is applied to an existing storm surge model of the German North Sea. To avoid the need of an adjoint model, an ensemble-like method to explicitly represent the linear tangent equation is adopted. Results of twin experiments have shown that the method is able to recover the contaminated low dimension model parameters to their true values. The data assimilation scheme was applied to a severe storm surge event which occurred in the North Sea in December 5, 2013. By adjusting wind drag coefficient, the predictive ability of the model increased significantly. Preliminary experiments have shown that an increase in the predictive ability is attained by narrowing the data assimilation time window.
Solid oxide fuel cell simulation and design optimization with numerical adjoint techniques
NASA Astrophysics Data System (ADS)
Elliott, Louie C.
This dissertation reports on the application of numerical optimization techniques as applied to fuel cell simulation and design. Due to the "multi-physics" inherent in a fuel cell, which results in a highly coupled and non-linear behavior, an experimental program to analyze and improve the performance of fuel cells is extremely difficult. This program applies new optimization techniques with computational methods from the field of aerospace engineering to the fuel cell design problem. After an overview of fuel cell history, importance, and classification, a mathematical model of solid oxide fuel cells (SOFC) is presented. The governing equations are discretized and solved with computational fluid dynamics (CFD) techniques including unstructured meshes, non-linear solution methods, numerical derivatives with complex variables, and sensitivity analysis with adjoint methods. Following the validation of the fuel cell model in 2-D and 3-D, the results of the sensitivity analysis are presented. The sensitivity derivative for a cost function with respect to a design variable is found with three increasingly sophisticated techniques: finite difference, direct differentiation, and adjoint. A design cycle is performed using a simple optimization method to improve the value of the implemented cost function. The results from this program could improve fuel cell performance and lessen the world's dependence on fossil fuels.
Gardner, Adam R; Hayakawa, Carole K; Venugopalan, Vasan
2014-06-01
We present a coupled forward-adjoint Monte Carlo (cFAMC) method to determine the spatially resolved sensitivity distributions produced by optical interrogation of three-dimensional (3-D) tissue volumes. We develop a general computational framework that computes the spatial and angular distributions of the forward-adjoint light fields to provide accurate computations in mesoscopic tissue volumes. We provide full computational details of the cFAMC method and provide results for low- and high-scattering tissues probed using a single pair of optical fibers. We examine the effects of source-detector separation and orientation on the sensitivity distributions and consider how the degree of angular discretization used in the 3-D tissue model impacts the accuracy of the resulting absorption sensitivity profiles. We discuss the value of such computations for optical imaging and the design of optical measurements. PMID:24972356
Gardner, Adam R.; Hayakawa, Carole K.; Venugopalan, Vasan
2014-01-01
Abstract. We present a coupled forward-adjoint Monte Carlo (cFAMC) method to determine the spatially resolved sensitivity distributions produced by optical interrogation of three-dimensional (3-D) tissue volumes. We develop a general computational framework that computes the spatial and angular distributions of the forward-adjoint light fields to provide accurate computations in mesoscopic tissue volumes. We provide full computational details of the cFAMC method and provide results for low- and high-scattering tissues probed using a single pair of optical fibers. We examine the effects of source-detector separation and orientation on the sensitivity distributions and consider how the degree of angular discretization used in the 3-D tissue model impacts the accuracy of the resulting absorption sensitivity profiles. We discuss the value of such computations for optical imaging and the design of optical measurements. PMID:24972356
Mapping Emissions that Contribute to Air Pollution Using Adjoint Sensitivity Analysis
NASA Astrophysics Data System (ADS)
Bastien, L. A. J.; Mcdonald, B. C.; Brown, N. J.; Harley, R.
2014-12-01
The adjoint of the Community Multiscale Air Quality model (CMAQ) is used to map emissions that contribute to air pollution at receptors of interest. Adjoint tools provide an efficient way to calculate the sensitivity of a model response to a large number of model inputs, a task that would require thousands of simulations using a more traditional forward sensitivity approach. Initial applications of this technique, demonstrated here, are to benzene and directly-emitted diesel particulate matter, for which atmospheric reactions are neglected. Emissions of these pollutants are strongly influenced by light-duty gasoline vehicles and heavy-duty diesel trucks, respectively. We study air quality responses in three receptor areas where populations have been identified as especially susceptible to, and adversely affected by air pollution. Population-weighted air basin-wide responses for each pollutant are also evaluated for the entire San Francisco Bay area. High-resolution (1 km horizontal grid) emission inventories have been developed for on-road motor vehicle emission sources, based on observed traffic count data. Emission estimates represent diurnal, day of week, and seasonal variations of on-road vehicle activity, with separate descriptions for gasoline and diesel sources. Emissions that contribute to air pollution at each receptor have been mapped in space and time using the adjoint method. Effects on air quality of both relative (multiplicative) and absolute (additive) perturbations to underlying emission inventories are analyzed. The contributions of local versus upwind sources to air quality in each receptor area are quantified, and weekday/weekend and seasonal variations in the influence of emissions from upwind areas are investigated. The contribution of local sources to the total air pollution burden within the receptor areas increases from about 40% in the summer to about 50% in the winter due to increased atmospheric stagnation. The effectiveness of control
The basis spline method and associated techniques
Bottcher, C.; Strayer, M.R.
1989-01-01
We outline the Basis Spline and Collocation methods for the solution of Partial Differential Equations. Particular attention is paid to the theory of errors, and the handling of non-self-adjoint problems which are generated by the collocation method. We discuss applications to Poisson's equation, the Dirac equation, and the calculation of bound and continuum states of atomic and nuclear systems. 12 refs., 6 figs.
Examination of Observation Impacts derived from OSEs and Adjoint Models
NASA Technical Reports Server (NTRS)
Gelaro, Ronald
2008-01-01
With the adjoint of a data assimilation system, the impact of any or all assimilated observations on measures of forecast skill can be estimated accurately and efficiently. The approach allows aggregation of results in terms of individual data types, channels or locations, all computed simultaneously. In this study, adjoint-based estimates of observation impact are compared with results from standard observing system experiments (OSEs) in the NASA Goddard Earth Observing System Model, Version 5 (GEOS-5) GEOS-5 system. The two approaches are shown to provide unique, but complimentary, information. Used together, they reveal both redundancies and dependencies between observing system impacts as observations are added or removed. Understanding these dependencies poses a major challenge for optimizing the use of the current observational network and defining requirements for future observing systems.
Three-Dimensional Turbulent RANS Adjoint-Based Error Correction
NASA Technical Reports Server (NTRS)
Park, Michael A.
2003-01-01
Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predicting a fine grid functional on a coarser mesh. Such an estimate can be computed by solving the flow equations and the associated adjoint problem for the functional of interest. An adjoint-based error correction procedure is demonstrated for transonic inviscid and subsonic laminar and turbulent flow. A mesh adaptation procedure is formulated to target uncertainty in the corrected functional and terminate when error remaining in the calculation is less than a user-specified error tolerance. This adaptation scheme is shown to yield anisotropic meshes with corrected functionals that are more accurate for a given number of grid points then isotropic adapted and uniformly refined grids.
Seismic Window Selection and Misfit Measurements for Global Adjoint Tomography
NASA Astrophysics Data System (ADS)
Lei, W.; Bozdag, E.; Lefebvre, M.; Podhorszki, N.; Smith, J. A.; Tromp, J.
2013-12-01
Global Adjoint Tomography requires fast parallel processing of large datasets. After obtaing the preprocessed observed and synthetic seismograms, we use the open source software packages FLEXWIN (Maggi et al. 2007) to select time windows and MEASURE_ADJ to make measurements. These measurements define adjoint sources for data assimilation. Previous versions of these tools work on a pair of SAC files---observed and synthetic seismic data for the same component and station, and loop over all seismic records associated with one earthquake. Given the large number of stations and earthquakes, the frequent read and write operations create severe I/O bottlenecks on modern computing platforms. We present new versions of these tools utilizing a new seismic data format, namely the Adaptive Seismic Data Format(ASDF). This new format shows superior scalability for applications on high-performance computers and accommodates various types of data, including earthquake, industry and seismic interferometry datasets. ASDF also provides user-friendly APIs, which can be easily integrated into the adjoint tomography workflow and combined with other data processing tools. In addition to solving the I/O bottleneck, we are making several improvements to these tools. For example, FLEXWIN is tuned to select windows for different types of earthquakes. To capture their distinct features, we categorize earthquakes by their depths and frequency bands. Moreover, instead of only picking phases between the first P arrival and the surface-wave arrivals, our aim is to select and assimilate many other later prominent phases in adjoint tomography. For example, in the body-wave band (17 s - 60 s), we include SKS, sSKS and their multiple, while in the surface-wave band (60 s - 120 s) we incorporate major-arc surface waves.
Adjoint calculations for multiple scattering of Compton and Rayleigh effects
NASA Astrophysics Data System (ADS)
Fernández, J. E.; Sumini, M.
1992-08-01
As is well known, the experimental determination of the Compton profile requires a particular geometry with a scattering angle close to π. That situation involves a narrow multiple-scattering spectrum that overlaps the Compton peak, making it difficult to analyze the different contributions to the profile. We show how the solution of the adjoint problem can help in devising more useful experimental configurations, giving, through its classical "importance" meaning, a formally clear picture of the whole problem.
Forward and adjoint sensitivity computation of chaotic dynamical systems
Wang, Qiqi
2013-02-15
This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor.
Monopole condensation in two-flavor adjoint QCD
Cossu, Guido; D'Elia, Massimo; Di Giacomo, Adriano; Lacagnina, Giuseppe; Pica, Claudio
2008-04-01
In QCD with adjoint fermions, the deconfining transition takes place at a lower temperature than the chiral transition. We study the two transitions by use of the Polyakov loop, the monopole order parameter, and the chiral condensate. The deconfining transition is first order, the chiral is a crossover. The order parameters for confinement are not affected by the chiral transition. We conclude that the degrees of freedom relevant to confinement are different from those describing chiral symmetry.
Adjoint Tomography of Taiwan Region: From Travel-Time Toward Waveform Inversion
NASA Astrophysics Data System (ADS)
Huang, H. H.; Lee, S. J.; Tromp, J.
2014-12-01
The complicated tectonic environment such as Taiwan region can modulate the seismic waveform severely and hamper the discrimination and the utilization of later phases. Restricted to the use of only first arrivals of P- and S-wave, the travel-time tomographic models of Taiwan can simulate the seismic waveform barely to a frequency of 0.2 Hz to date. While it has been sufficient for long-period studies, e.g. source inversion, this frequency band is still far from the applications to the community and high-resolution studies. To achieve a higher-frequency simulation, more data and the considerations of off-path and finite-frequency effects are necessary. Based on the spectral-element and the adjoint method recently developed, we prepared 94 MW 3.5-6.0 earthquakes with well-defined location and focal mechanism solutions from Real-Time Moment Tensor Monitoring System (RMT), and preformed an iterative gradient-based inversion employing waveform modeling and finite-frequency measurements of adjoint method. By which the 3-D sensitivity kernels are taken into account realistically and the full waveform information are naturally sought, without a need of any phase pick. A preliminary model m003 using 10-50 sec data was demonstrated and compared with previous travel-time models. The primary difference appears in the mountainous area, where the previous travel-time model may underestimate the S-wave speed in the upper crust, but overestimates in the lower crust.
NASA Astrophysics Data System (ADS)
Yu, Jia; Ji, Lucheng; Li, Weiwei; Yi, Weilin
2016-06-01
Adjoint method is an important tool for design refinement of multistage compressors. However, the radial static pressure distribution deviates during the optimization procedure and deteriorates the overall performance, producing final designs that are not well suited for realistic engineering applications. In previous development work on multistage turbomachinery blade optimization using adjoint method and thin shear-layer N-S equations, the entropy production is selected as the objective function with given mass flow rate and total pressure ratio as imposed constraints. The radial static pressure distribution at the interfaces between rows is introduced as a new constraint in the present paper. The approach is applied to the redesign of a five-stage axial compressor, and the results obtained with and without the constraint on the radial static pressure distribution at the interfaces between rows are discussed in detail. The results show that the redesign without the radial static pressure distribution constraint (RSPDC) gives an optimal solution that shows deviations on radial static pressure distribution, especially at rotor exit tip region. On the other hand, the redesign with the RSPDC successfully keeps the radial static pressure distribution at the interfaces between rows and make sure that the optimization results are applicable in a practical engineering design.
Coupling of MASH-MORSE Adjoint Leakages with Space- and Time-Dependent Plume Radiation Sources
Slater, C.O.
2001-04-20
In the past, forward-adjoint coupling procedures in air-over-ground geometry have typically involved forward fluences arising from a point source a great distance from a target or vehicle system. Various processing codes were used to create localized forward fluence files that could be used to couple with the MASH-MORSE adjoint leakages. In recent years, radiation plumes that result from reactor accidents or similar incidents have been modeled by others, and the source space and energy distributions as a function of time have been calculated. Additionally, with the point kernel method, they were able to calculate in relatively quick fashion free-field radiation doses for targets moving within the fluence field or for stationary targets within the field, the time dependence for the latter case coming from the changes in position, shape, source strength, and spectra of the plume with time. The work described herein applies the plume source to the MASH-MORSE coupling procedure. The plume source replaces the point source for generating the forward fluences that are folded with MASH-MORSE adjoint leakages. Two types of source calculations are described. The first is a ''rigorous'' calculation using the TORT code and a spatially large air-over-ground geometry. For each time step desired, directional fluences are calculated and are saved over a predetermined region that encompasses a structure within which it is desired to calculate dose rates. Processing codes then create the surface fluences (which may include contributions from radiation sources that deposit on the roof or plateout) that will be coupled with the MASH-MORSE adjoint leakages. Unlike the point kernel calculations of the free-field dose rates, the TORT calculations in practice include the effects of ground scatter on dose rates and directional fluences, although the effects may be underestimated or overestimated because of the use of necessarily coarse mesh and quadrature in order to reduce computational
Spectral monodromy of non-self-adjoint operators
NASA Astrophysics Data System (ADS)
Phan, Quang Sang
2014-01-01
In the present paper, we build a combinatorial invariant, called the "spectral monodromy" from the spectrum of a single (non-self-adjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting self-adjoint h-pseudodifferential operators, given by S. Vu Ngoc ["Quantum monodromy in integrable systems," Commun. Math. Phys. 203(2), 465-479 (1999)]. The first simple case that we treat in this work is a normal operator. In this case, the discrete spectrum can be identified with the joint spectrum of an integrable quantum system. The second more complex case we propose is a small perturbation of a self-adjoint operator with a classical integrability property. We show that the discrete spectrum (in a small band around the real axis) also has a combinatorial monodromy. The main difficulty in this case is that we do not know the description of the spectrum everywhere, but only in a Cantor type set. In addition, we also show that the corresponding monodromy can be identified with the classical monodromy, defined by J. Duistermaat ["On global action-angle coordinates," Commun. Pure Appl. Math. 33(6), 687-706 (1980)].
Adjoint-based sensitivity analysis for reactor-safety applications
Parks, C.V.
1985-01-01
The application and usefulness of an adjoint-based methodology for performing sensitivity analysis on reactor safety computer codes is investigated. The adjoint-based methodology, referred to as differential sensitivity theory (DST), provides first-order derivatives of the calculated quantities of interest (responses) with respect to the input parameters. The basic theoretical development of DST is presented along with the needed general extensions for consideration of model discontinuities and a variety of useful response definitions. A simple analytic problem is used to highlight the general DST procedures. Finally, DST procedures presented in this work are applied to two highly nonlinear reactor accident analysis codes: (1) FASTGAS, a relatively small code for analysis of loss-of-decay-heat-removal accident in a gas-cooled fast reactor, and (2) an existing code called VENUS-II which is typically employed for analyzing the core disassembly phase of a hypothetical fast reactor accident. The two codes are different both in terms of complexity and in terms of the facets of DST which can be illustrated. Sensitivity results from the adjoint codes ADJGAS and VENUS-ADJ are verified with direct recalculations using perturbed input parameters. The effectiveness of the DST results for parameter ranking, prediction of response changes, and uncertainty analysis are illustrated. The conclusion drawn from this study is that DST is a viable, cost-effective methodology for accurate sensitivity analysis.
ANISORROPIA: the adjoint of the aerosol thermodynamic model ISORROPIA
NASA Astrophysics Data System (ADS)
Capps, S. L.; Henze, D. K.; Hakami, A.; Russell, A. G.; Nenes, A.
2012-01-01
We present the development of ANISORROPIA, the discrete adjoint of the ISORROPIA thermodynamic equilibrium model that treats the Na+-SO42-- HSO4--NH4+ -NO3--Cl--H2O aerosol system, and we demonstrate its sensitivity analysis capabilities. ANISORROPIA calculates sensitivities of an inorganic species in aerosol or gas phase with respect to the total concentrations of each species present with less than a two-fold increase in computational time over the concentration calculations. Due to the highly nonlinear and discontinuous solution surface of ISORROPIA, evaluation of the adjoint required a new, complex-variable version of the model, which determines first-order sensitivities with machine precision and avoids cancellation errors arising from finite difference calculations. The adjoint is verified over an atmospherically relevant range of concentrations, temperature, and relative humidity. We apply ANISORROPIA to recent field campaign results from Atlanta, GA, USA, and Mexico City, Mexico, to characterize the inorganic aerosol sensitivities of these distinct urban air masses. The variability in the relationship between fine mode inorganic aerosol mass and precursor concentrations shown has important implications for air quality and climate.
Self-adjoint time operators and invariant subspaces
NASA Astrophysics Data System (ADS)
Gómez, Fernando
2008-02-01
The question of existence of self-adjoint time operators for unitary evolutions in classical and quantum mechanics is revisited on the basis of Halmos-Helson theory of invariant subspaces, Sz.-Nagy-Foiaş dilation theory and Misra-Prigogine-Courbage theory of irreversibility. It is shown that the existence of self-adjoint time operators is equivalent to the intertwining property of the evolution plus the existence of simply invariant subspaces or rigid operator-valued functions for its Sz.-Nagy-Foiaş functional model. Similar equivalent conditions are given in terms of intrinsic randomness in the context of statistical mechanics. The rest of the contents are mainly a unifying review of the subject scattered throughout an unconnected literature. A well-known extensive set of equivalent conditions is derived from the above results; such conditions are written in terms of Schrrdinger couples, the Weyl commutation relation, incoming and outgoing subspaces, innovation processes, Lax-Phillips scattering, translation and spectral representations, and spectral properties. Also the natural procedure dealing with symmetric time operators in standard quantum mechanics involving their self-adjoint extensions is illustrated by considering the quantum Aharonov-Bohm time-of-arrival operator.
Unsteady Adjoint Approach for Design Optimization of Flapping Airfoils
NASA Technical Reports Server (NTRS)
Lee, Byung Joon; Liou, Meng-Sing
2012-01-01
This paper describes the work for optimizing the propulsive efficiency of flapping airfoils, i.e., improving the thrust under constraining aerodynamic work during the flapping flights by changing their shape and trajectory of motion with the unsteady discrete adjoint approach. For unsteady problems, it is essential to properly resolving time scales of motion under consideration and it must be compatible with the objective sought after. We include both the instantaneous and time-averaged (periodic) formulations in this study. For the design optimization with shape parameters or motion parameters, the time-averaged objective function is found to be more useful, while the instantaneous one is more suitable for flow control. The instantaneous objective function is operationally straightforward. On the other hand, the time-averaged objective function requires additional steps in the adjoint approach; the unsteady discrete adjoint equations for a periodic flow must be reformulated and the corresponding system of equations solved iteratively. We compare the design results from shape and trajectory optimizations and investigate the physical relevance of design variables to the flapping motion at on- and off-design conditions.
Spectral monodromy of non-self-adjoint operators
Phan, Quang Sang
2014-01-15
In the present paper, we build a combinatorial invariant, called the “spectral monodromy” from the spectrum of a single (non-self-adjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting self-adjoint h-pseudodifferential operators, given by S. Vu Ngoc [“Quantum monodromy in integrable systems,” Commun. Math. Phys. 203(2), 465–479 (1999)]. The first simple case that we treat in this work is a normal operator. In this case, the discrete spectrum can be identified with the joint spectrum of an integrable quantum system. The second more complex case we propose is a small perturbation of a self-adjoint operator with a classical integrability property. We show that the discrete spectrum (in a small band around the real axis) also has a combinatorial monodromy. The main difficulty in this case is that we do not know the description of the spectrum everywhere, but only in a Cantor type set. In addition, we also show that the corresponding monodromy can be identified with the classical monodromy, defined by J. Duistermaat [“On global action-angle coordinates,” Commun. Pure Appl. Math. 33(6), 687–706 (1980)].
On a Time-Space Operator (and other Non-Self-Adjoint Operators) for Observables in QM and QFT
NASA Astrophysics Data System (ADS)
Recami, Erasmo; Zamboni-Rached, Michel; Licata, Ignazio
The aim of this paper is to show the possible significance, and usefulness, of various non-self-adjoint operators for suitable Observables in non-relativistic and relativistic quantum mechanics (QM), and in quantum electrodynamics. More specifically, this work deals with: (i) the Hermitian (but not self-adjoint) Time operator in non-relativistic QM and in quantum electrodynamics; (ii) idem, the introduction of Time and Space operators; and (iii) the problem of the four-position and four-momentum operators, each one with its Hermitian and anti-Hermitian parts, for relativistic spin-zero particles. Afterwards, other physical applications of non-self-adjoint (and even non-Hermitian) operators are briefly discussed. We mention how non-Hermitian operators can indeed be used in physics [as it was done, elsewhere, for describing Unstable States]; and some considerations are added on the cases of the nuclear optical potential, of quantum dissipation, and in particular of an approach to the measurement problem in QM in terms of a chronon. This paper is largely based on work developed, along the years, in collaboration with V.S. Olkhovsky, and, in smaller parts, with P. Smrz, with R.H.A. Farias, and with S.P. Maydanyuk.
NASA Astrophysics Data System (ADS)
Holdaway, D.; Coy, L.
2015-12-01
In September 2002 a major sudden stratospheric warming (SSW) occurred in the southern hemisphere. Although numerous SSWs have been observed in the northern hemisphere, this remains the only recorded major SSW in the southern hemisphere. Much debate has focused on this unique event and the causes, even resulting in a special issue of the Journal of Atmospheric Science. In this work we use the adjoint of NASA's Goddard Earth Observing System version 5 (GEOS-5) to investigate sensitivity to initial conditions during the onset of the 2002 SSW. The adjoint model provides a framework for propagating gradients with respect to the model state backwards in time. As such it is used to reveal aspects of the model initial conditions that have the biggest impact on the temperature in the stratosphere during the warming. The adjoint model reveals a large sensitivity over the southern Atlantic ocean and in the troposphere. This reinforces previous studies that attributed the SSW to a blocking ridge in this region. By converting sensitivity to perturbations it is shown that relatively small localized tropospheric perturbations to winds and temperature can be transported to the stratosphere and have a large impact on the SSW.
NASA Astrophysics Data System (ADS)
Holdaway, D. R.; Errico, R.
2011-12-01
Inherent in the minimization process in the 4D-Var data assimilation system is the need for the model's adjoint. It is straightforward to obtain the exact adjoint by linearizing the code in a line by line sense; however it only provides an accurate overall representation of the physical processes if the model behaviour is linear. Moist processes in the atmosphere, and thus the models that represent them, are intrinsically highly non-linear and can contain discrete switches. The adjoint that is required in the data assimilation system needs to provide an accurate representation of the physical behaviour for perturbation sizes of the order of the analysis error, so an exact adjoint of the moist physics model is likely to be inaccurate. Instead a non-exact adjoint model, which is accurate for large enough perturbations, must be developed. The constraint on the development is that the simplified adjoint be consistent with the actual trajectory of the model. Previous attempts to include the moist physics in the 4D-Var have emphasized the need for redevelopment of the actual moist scheme to a simpler version. These schemes are designed to be linear in the limit of realistic perturbation size but also capture the essence of the physical behaviour, making the adjoint version of the scheme suitable for use in the 4D-Var. A downside to this approach is that it can result in an over simplification of the physics and represent a larger departure from the true model trajectory than necessary. The adjoint is just the transpose of the tangent linear model, which is the differential of the model operator. This differential of the operator can be constructed from Jacobian matrices. Examining the structures of the Jacobians as perturbations of varying size are added to the state vector can help determine whether the adjoint model - be it of actual or simplified physics - will be suitable for use in the assimilation algorithm. If Jacobian structures change considerably when the
Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes
NASA Astrophysics Data System (ADS)
Peter, Daniel; Komatitsch, Dimitri; Luo, Yang; Martin, Roland; Le Goff, Nicolas; Casarotti, Emanuele; Le Loher, Pieyre; Magnoni, Federica; Liu, Qinya; Blitz, Céline; Nissen-Meyer, Tarje; Basini, Piero; Tromp, Jeroen
2011-08-01
We present forward and adjoint spectral-element simulations of coupled acoustic and (an)elastic seismic wave propagation on fully unstructured hexahedral meshes. Simulations benefit from recent advances in hexahedral meshing, load balancing and software optimization. Meshing may be accomplished using a mesh generation tool kit such as CUBIT, and load balancing is facilitated by graph partitioning based on the SCOTCH library. Coupling between fluid and solid regions is incorporated in a straightforward fashion using domain decomposition. Topography, bathymetry and Moho undulations may be readily included in the mesh, and physical dispersion and attenuation associated with anelasticity are accounted for using a series of standard linear solids. Finite-frequency Fréchet derivatives are calculated using adjoint methods in both fluid and solid domains. The software is benchmarked for a layercake model. We present various examples of fully unstructured meshes, snapshots of wavefields and finite-frequency kernels generated by Version 2.0 'Sesame' of our widely used open source spectral-element package SPECFEM3D.
Global Adjoint Tomography: Combining Big Data with HPC Simulations
NASA Astrophysics Data System (ADS)
Bozdag, E.; Lefebvre, M. P.; Lei, W.; Peter, D. B.; Smith, J. A.; Komatitsch, D.; Tromp, J.
2014-12-01
The steady increase in data quality and the number of global seismographic stations have substantially grown the amount of data available for construction of Earth models. Meanwhile, developments in the theory of wave propagation, numerical methods and HPC systems have enabled unprecedented simulations of seismic wave propagation in realistic 3D Earth models which lead the extraction of more information from data, ultimately culminating in the use of entire three-component seismograms.Our aim is to take adjoint tomography further to image the entire planet which is one of the extreme cases in seismology due to its intense computational requirements and vast amount of high-quality seismic data that can potentially be assimilated in inversions. We have started low resolution (T > 27 s, soon will be > 17 s) global inversions with 253 earthquakes for a transversely isotropic crust and mantle model on Oak Ridge National Laboratory's Cray XK7 "Titan" system. Recent improvements in our 3D solvers, such as the GPU version of the SPECFEM3D_GLOBE package, will allow us perform higher-resolution (T > 9 s) and longer-duration (~180 m) simulations to take the advantage of high-frequency body waves and major-arc surface waves to improve imbalanced ray coverage as a result of uneven distribution of sources and receivers on the globe. Our initial results after 10 iterations already indicate several prominent features reported in high-resolution continental studies, such as major slabs (Hellenic, Japan, Bismarck, Sandwich, etc.) and enhancement in plume structures (the Pacific superplume, the Hawaii hot spot, etc.). Our ultimate goal is to assimilate seismic data from more than 6,000 earthquakes within the magnitude range 5.5 ≤ Mw ≤ 7.0. To take full advantage of this data set on ORNL's computational resources, we need a solid framework for managing big data sets during pre-processing (e.g., data requests and quality checks), gradient calculations, and post-processing (e
NASA Astrophysics Data System (ADS)
Xie, Zhinan; Komatitsch, Dimitri; Martin, Roland; Matzen, René
2014-09-01
In recent years, the application of time-domain adjoint methods to improve large, complex underground tomographic models at the regional scale has led to new challenges for the numerical simulation of forward or adjoint elastic wave propagation problems. An important challenge is to design an efficient infinite-domain truncation method suitable for accurately truncating an infinite domain governed by the second-order elastic wave equation written in displacement and computed based on a finite-element (FE) method. In this paper, we make several steps towards this goal. First, we make the 2-D convolution formulation of the complex-frequency-shifted unsplit-field perfectly matched layer (CFS-UPML) derived in previous work more flexible by providing a new treatment to analytically remove singular parameters in the formulation. We also extend this new formulation to 3-D. Furthermore, we derive the auxiliary differential equation (ADE) form of CFS-UPML, which allows for extension to higher order time schemes and is easier to implement. Secondly, we rigorously derive the CFS-UPML formulation for time-domain adjoint elastic wave problems, which to our knowledge has never been done before. Thirdly, in the case of classical low-order FE methods, we show numerically that we achieve long-time stability for both forward and adjoint problems both for the convolution and the ADE formulations. In the case of higher order Legendre spectral-element methods, we show that weak numerical instabilities can appear in both formulations, in particular if very small mesh elements are present inside the absorbing layer, but we explain how these instabilities can be delayed as much as needed by using a stretching factor to reach numerical stability in practice for applications. Fourthly, in the case of adjoint problems with perfectly matched absorbing layers we introduce a computationally efficient boundary storage strategy by saving information along the interface between the CFS-UPML and
Bastien, Lucas A J; McDonald, Brian C; Brown, Nancy J; Harley, Robert A
2015-06-16
The adjoint of the Community Multiscale Air Quality (CMAQ) model at 1 km horizontal resolution is used to map emissions that contribute to ambient concentrations of benzene and diesel black carbon (BC) in the San Francisco Bay area. Model responses of interest include population-weighted average concentrations for three highly polluted receptor areas and the entire air basin. We consider both summer (July) and winter (December) conditions. We introduce a novel approach to evaluate adjoint sensitivity calculations that complements existing methods. Adjoint sensitivities to emissions are found to be accurate to within a few percent, except at some locations associated with large sensitivities to emissions. Sensitivity of model responses to emissions is larger in winter, reflecting weaker atmospheric transport and mixing. The contribution of sources located within each receptor area to the same receptor's air pollution burden increases from 38-74% in summer to 56-85% in winter. The contribution of local sources is higher for diesel BC (62-85%) than for benzene (38-71%), reflecting the difference in these pollutants' atmospheric lifetimes. Morning (6-9am) and afternoon (4-7 pm) commuting-related emissions dominate region-wide benzene levels in winter (14 and 25% of the total response, respectively). In contrast, afternoon rush hour emissions do not contribute significantly in summer. Similar morning and afternoon peaks in sensitivity to emissions are observed for the BC response; these peaks are shifted toward midday because most diesel truck traffic occurs during off-peak hours. PMID:26001097
Andrade, F.M.; Silva, E.O.; Pereira, M.
2013-12-15
In this work the bound state and scattering problems for a spin- 1/2 particle undergone to an Aharonov–Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a δ-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and S matrix are determined in terms of the self-adjoint extension parameter, which is explicitly determined in terms of the parameters of the problem. The relation between the bound state and zero modes and the failure of helicity conservation in the scattering problem and its relation with the gyromagnetic ratio g are discussed. Also, as an application, we consider the spin- 1/2 Aharonov–Bohm problem in conical space plus a two-dimensional isotropic harmonic oscillator. -- Highlights: •Planar dynamics of a spin- 1/2 neutral particle. •Bound state for Aharonov–Bohm systems. •Aharonov–Bohm scattering. •Helicity nonconservation. •Determination of the self-adjoint extension parameter.
42 CFR 455.452 - Other State screening methods.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 42 Public Health 4 2011-10-01 2011-10-01 false Other State screening methods. 455.452 Section 455....452 Other State screening methods. Nothing in this subpart must restrict the State Medicaid agency from establishing provider screening methods in addition to or more stringent than those required...
42 CFR 455.452 - Other State screening methods.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 42 Public Health 4 2013-10-01 2013-10-01 false Other State screening methods. 455.452 Section 455....452 Other State screening methods. Nothing in this subpart must restrict the State Medicaid agency from establishing provider screening methods in addition to or more stringent than those required...
NASA Technical Reports Server (NTRS)
Andrews, Arlyn; Kawa, Randy; Zhu, Zhengxin; Burris, John; Abshire, Jim
2004-01-01
A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future CO2 levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an 'inverse problem', where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from longterm surface and aircraft monitoring stations with data from intensive field campaigns and with proposed future satellite observations. We have recently developed an adjoint for the GSFC 3-D Parameterized Chemistry and Transport Model (PCTM). Here, we will present results from a PCTM Adjoint study comparing the sampling footprints of tall tower, aircraft and potential future lidar observations of CO2. The vertical resolution and extent of the profiles and the observation frequency will be considered for several sites in North America.
Adjoint-based optimization for understanding and suppressing jet noise
NASA Astrophysics Data System (ADS)
Freund, Jonathan B.
2011-08-01
Advanced simulation tools, particularly large-eddy simulation techniques, are becoming capable of making quality predictions of jet noise for realistic nozzle geometries and at engineering relevant flow conditions. Increasing computer resources will be a key factor in improving these predictions still further. Quality prediction, however, is only a necessary condition for the use of such simulations in design optimization. Predictions do not themselves lead to quieter designs. They must be interpreted or harnessed in some way that leads to design improvements. As yet, such simulations have not yielded any simplifying principals that offer general design guidance. The turbulence mechanisms leading to jet noise remain poorly described in their complexity. In this light, we have implemented and demonstrated an aeroacoustic adjoint-based optimization technique that automatically calculates gradients that point the direction in which to adjust controls in order to improve designs. This is done with only a single flow solutions and a solution of an adjoint system, which is solved at computational cost comparable to that for the flow. Optimization requires iterations, but having the gradient information provided via the adjoint accelerates convergence in a manner that is insensitive to the number of parameters to be optimized. This paper, which follows from a presentation at the 2010 IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction, reviews recent and ongoing efforts by the author and co-workers. It provides a new formulation of the basic approach and demonstrates the approach on a series of model flows, culminating with a preliminary result for a turbulent jet.
Adjoint-Based Methodology for Time-Dependent Optimal Control (AMTOC)
NASA Technical Reports Server (NTRS)
Yamaleev, Nail; Diskin, boris; Nishikawa, Hiroaki
2012-01-01
During the five years of this project, the AMTOC team developed an adjoint-based methodology for design and optimization of complex time-dependent flows, implemented AMTOC in a testbed environment, directly assisted in implementation of this methodology in the state-of-the-art NASA's unstructured CFD code FUN3D, and successfully demonstrated applications of this methodology to large-scale optimization of several supersonic and other aerodynamic systems, such as fighter jet, subsonic aircraft, rotorcraft, high-lift, wind-turbine, and flapping-wing configurations. In the course of this project, the AMTOC team has published 13 refereed journal articles, 21 refereed conference papers, and 2 NIA reports. The AMTOC team presented the results of this research at 36 international and national conferences, meeting and seminars, including International Conference on CFD, and numerous AIAA conferences and meetings. Selected publications that include the major results of the AMTOC project are enclosed in this report.
Spectral Solutions of Self-adjoint Elliptic Problems with Immersed Interfaces
Auchmuty, G.; Kloucek, P.
2011-12-15
This paper describes a spectral representation of solutions of self-adjoint elliptic problems with immersed interfaces. The interface is assumed to be a simple non-self-intersecting closed curve that obeys some weak regularity conditions. The problem is decomposed into two problems, one with zero interface data and the other with zero exterior boundary data. The problem with zero interface data is solved by standard spectral methods. The problem with non-zero interface data is solved by introducing an interface space H{sub {Gamma}}({Omega}) and constructing an orthonormal basis of this space. This basis is constructed using a special class of orthogonal eigenfunctions analogously to the methods used for standard trace spaces by Auchmuty (SIAM J. Math. Anal. 38, 894-915, 2006). Analytical and numerical approximations of these eigenfunctions are described and some simulations are presented.
Supersonic wing and wing-body shape optimization using an adjoint formulation
NASA Technical Reports Server (NTRS)
Reuther, James; Jameson, Antony
1995-01-01
This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design of supersonic configurations. The work represents an extension of our earlier research in which control theory is used to devise a design procedure that significantly reduces the computational cost by employing an adjoint equation. In previous studies it was shown that control theory could be used toeviseransonic design methods for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. The method has also been implemented for both transonic potential flows and transonic flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can treat more general configurations. Here results are presented for three-dimensional design cases subject to supersonic flows governed by the Euler equation.
A Note About HARP's State Trimming Method
NASA Technical Reports Server (NTRS)
Butler, Ricky W.; Hayhurst, Kelly J.; Johnson, Sally C.
1998-01-01
This short note provides some additional insight into how the HARP program works. In some cases, it is possible for HARP to tdm away too many states and obtain an optimistic result. The HARP Version 7.0 manual warns the user that 'Unlike the ALL model, the SAME model can automatically drop failure modes for certain system models. The user is cautioned to insure that no important failure modes are dropped; otherwise, a non-conservative result can be given.' This note provides an example of where this occurs and a pointer to further documentation that gives a means of bounding the error associated with trimming these states.
7 CFR 215.5 - Method of payment to States.
Code of Federal Regulations, 2011 CFR
2011-01-01
... AGRICULTURE CHILD NUTRITION PROGRAMS SPECIAL MILK PROGRAM FOR CHILDREN § 215.5 Method of payment to States. (a... 7 Agriculture 4 2011-01-01 2011-01-01 false Method of payment to States. 215.5 Section 215.5... Authorities and child-care institutions through presentation by designated State officials of a...