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Journal articles on the topic 'Adjoint discret'

Author: Grafiati

Published: 8 February 2025

Last updated: 31 July 2025

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1

Zhao, Shunliu, Matthew G. Russell, Amir Hakami, et al. "A multiphase CMAQ version 5.0 adjoint." Geoscientific Model Development 13, no. 7 (2020): 2925–44. http://dx.doi.org/10.5194/gmd-13-2925-2020.

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Abstract. We present the development of a multiphase adjoint for the Community Multiscale Air Quality (CMAQ) model, a widely used chemical transport model. The adjoint model provides location- and time-specific gradients that can be used in various applications such as backward sensitivity analysis, source attribution, optimal pollution control, data assimilation, and inverse modeling. The science processes of the CMAQ model include gas-phase chemistry, aerosol dynamics and thermodynamics, cloud chemistry and dynamics, diffusion, and advection. Discrete adjoints are implemented for all the sci

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2

Ni, Angxiu. "Backpropagation in hyperbolic chaos via adjoint shadowing." Nonlinearity 37, no. 3 (2024): 035009. http://dx.doi.org/10.1088/1361-6544/ad1aed.

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Abstract To generalise the backpropagation method to both discrete-time and continuous-time hyperbolic chaos, we introduce the adjoint shadowing operator S acting on covector fields. We show that S can be equivalently defined as: S is the adjoint of the linear shadowing operator S; S is given by a ‘split then propagate’ expansion formula; S ( ω ) is the only bounded inhomogeneous adjoint solution of ω. By (a), S adjointly expresses the shadowing contribution, a significant part of the linear response, where the linear response is the derivative of the long-time statistics with respect to syste

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Capps, S. L., D. K. Henze, A. Hakami, A. G. Russell, and A. Nenes. "ANISORROPIA: the adjoint of the aerosol thermodynamic model ISORROPIA." Atmospheric Chemistry and Physics Discussions 11, no. 8 (2011): 23469–511. http://dx.doi.org/10.5194/acpd-11-23469-2011.

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Abstract. 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

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4

Hekmat, Mohamad Hamed, and Masoud Mirzaei. "Development of Discrete Adjoint Approach Based on the Lattice Boltzmann Method." Advances in Mechanical Engineering 6 (January 1, 2014): 230854. http://dx.doi.org/10.1155/2014/230854.

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The purpose of this research is to present a general procedure with low implementation cost to develop the discrete adjoint approach for solving optimization problems based on the LB method. Initially, the macroscopic and microscopic discrete adjoint equations and the cost function gradient vector are derived mathematically, in detail, using the discrete LB equation. Meanwhile, for an elementary case, the analytical evaluation of the macroscopic and microscopic adjoint variables and the cost function gradients are presented. The investigation of the derivation procedure shows that the simplici

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Larour, Eric, Jean Utke, Anton Bovin, Mathieu Morlighem, and Gilberto Perez. "An approach to computing discrete adjoints for MPI-parallelized models applied to Ice Sheet System Model 4.11." Geoscientific Model Development 9, no. 11 (2016): 3907–18. http://dx.doi.org/10.5194/gmd-9-3907-2016.

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Abstract. Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar, gravity, and altimetry observations mainly). However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient ice-flow models. Here, we look at the computation of adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model (ISSM), written in C++ and designed for parallel execution w

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Wu, Hangkong, Xuanlong Da, Dingxi Wang, and Xiuquan Huang. "Multi-Row Turbomachinery Aerodynamic Design Optimization by an Efficient and Accurate Discrete Adjoint Solver." Aerospace 10, no. 2 (2023): 106. http://dx.doi.org/10.3390/aerospace10020106.

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This paper proposes an approach that combines manual differentiation (MD) and automatic differentiation (AD) to develop an efficient and accurate multi-row discrete adjoint solver. In this approach, the structures of adjoint codes generated using an AD tool are first analyzed. Then, the AD-generated codes are manually adjusted to reduce memory and CPU time consumption. This manual adjustment is performed by replacing the automatically generated low-efficient differentiated codes with manually developed ones. To demonstrate the effectiveness of the proposed approach, the single-stage transonic

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Towara, Markus, Michel Schanen, and Uwe Naumann. "MPI-Parallel Discrete Adjoint OpenFOAM." Procedia Computer Science 51 (2015): 19–28. http://dx.doi.org/10.1016/j.procs.2015.05.181.

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8

Niwa, Yosuke, Hirofumi Tomita, Masaki Satoh, et al. "A 4D-Var inversion system based on the icosahedral grid model (NICAM-TM 4D-Var v1.0) – Part 1: Offline forward and adjoint transport models." Geoscientific Model Development 10, no. 3 (2017): 1157–74. http://dx.doi.org/10.5194/gmd-10-1157-2017.

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Abstract. A four-dimensional variational (4D-Var) method is a popular algorithm for inverting atmospheric greenhouse gas (GHG) measurements. In order to meet the computationally intense 4D-Var iterative calculation, offline forward and adjoint transport models are developed based on the Nonhydrostatic ICosahedral Atmospheric Model (NICAM). By introducing flexibility into the temporal resolution of the input meteorological data, the forward model developed in this study is not only computationally efficient, it is also found to nearly match the transport performance of the online model. In a tr

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Agarwal, Ravi P., Safi S. Rabie та Samir H. Saker. "On Discrete Weighted Lorentz Spaces and Equivalent Relations between Discrete ℓp-Classes". Fractal and Fractional 7, № 3 (2023): 261. http://dx.doi.org/10.3390/fractalfract7030261.

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In this paper, we study some relations between different weights in the classes Bp,Bp*,Mp and Mp* that characterize the boundedness of the Hardy operator and the adjoint Hardy operator. We also prove that these classes generate the same weighted Lorentz space Λp. These results will be proven by using the properties of classes Bp,Bp*,Mp and Mp*, including the self-improving properties and also the properties of the generalized Hardy operator Hp, the adjoint operator Sq and some fundamental relations between them connecting their composition to their sum.

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Cao, Junying, Zhongqing Wang, and Ziqiang Wang. "A Uniform Accuracy High-Order Finite Difference and FEM for Optimal Problem Governed by Time-Fractional Diffusion Equation." Fractal and Fractional 6, no. 9 (2022): 475. http://dx.doi.org/10.3390/fractalfract6090475.

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In this paper, the time fractional diffusion equations optimal control problem is solved by 3−α order with uniform accuracy scheme in time and finite element method (FEM) in space. For the state and adjoint state equation, the piecewise linear polynomials are used to make the space variables discrete, and obtain the semidiscrete scheme of the state and adjoint state. The priori error estimates for the semidiscrete scheme for state and adjoint state equation are established. Furthermore, the 3−α order uniform accuracy scheme is used to make the time variable discrete in the semidiscrete scheme

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11

Szenicer, Alexandre, Kuangdai Leng, and Tarje Nissen-Meyer. "A complexity-driven framework for waveform tomography with discrete adjoints." Geophysical Journal International 223, no. 2 (2020): 1247–64. http://dx.doi.org/10.1093/gji/ggaa349.

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Summary We develop a new approach for computing Fréchet sensitivity kernels in full waveform inversion by using the discrete adjoint approach in addition to the widely used continuous adjoint approach for seismic waveform inversion. This method is particularly well suited for the forward solver AxiSEM3D, a combination of the spectral-element method (SEM) and a Fourier pseudo-spectral method, which allows for a sparse azimuthal wavefield parametrization adaptive to wavefield complexity, leading to lower computational costs and better frequency scaling than conventional 3-D solvers. We implement

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12

ATAKISHIYEV, N. M., and A. U. KLIMYK. "DISCRETE COORDINATE REALIZATIONS OF THE q-OSCILLATOR WHEN q>1." Modern Physics Letters A 21, no. 29 (2006): 2205–16. http://dx.doi.org/10.1142/s0217732306021578.

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We elaborate on the Macfarlane–Biedenharn q-oscillator when q>1. In this case the position operator Q = a†+a and the momentum operator P = i(a†-a) are symmetric, but not self-adjoint. For this reason, one cannot specify spectra of Q and P. Since these operators have one-parameter families of self-adjoint extensions with different spectra, the common definition of such q-oscillator is not complete. We derive an action of Q and P (as well as of the related Hamiltonian) upon functions given on the corresponding coordinate spaces, on which Q and P are self-adjoint operators. To each self-adjoin

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13

Mader, Charles A., Joaquim R. R. A. Martins, Juan J. Alonso, and Edwin van der Weide. "ADjoint: An Approach for the Rapid Development of Discrete Adjoint Solvers." AIAA Journal 46, no. 4 (2008): 863–73. http://dx.doi.org/10.2514/1.29123.

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14

Hekmat, Mohamad Hamed, and Masoud Mirzaei. "Continuous and Discrete Adjoint Approach Based on Lattice Boltzmann Method in Aerodynamic Optimization Part I: Mathematical Derivation of Adjoint Lattice Boltzmann Equations." Advances in Applied Mathematics and Mechanics 6, no. 5 (2014): 570–89. http://dx.doi.org/10.4208/aamm.2013.m226.

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AbstractThe significance of flow optimization utilizing the lattice Boltzmann (LB) method becomes obvious regarding its advantages as a novel flow field solution method compared to the other conventional computational fluid dynamics techniques. These unique characteristics of the LB method form the main idea of its application to optimization problems. In this research, for the first time, both continuous and discrete adjoint equations were extracted based on the LB method using a general procedure with low implementation cost. The proposed approach could be performed similarly for any optimiz

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15

Giles, Michael B., Mihai C. Duta, Jens-Dominik Muller, and Niles A. Pierce. "Algorithm Developments for Discrete Adjoint Methods." AIAA Journal 41, no. 2 (2003): 198–205. http://dx.doi.org/10.2514/2.1961.

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16

Towara, M., and U. Naumann. "A Discrete Adjoint Model for OpenFOAM." Procedia Computer Science 18 (2013): 429–38. http://dx.doi.org/10.1016/j.procs.2013.05.206.

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17

Xu, Shenren, David Radford, Marcus Meyer, and Jens-Dominik Müller. "Stabilisation of discrete steady adjoint solvers." Journal of Computational Physics 299 (October 2015): 175–95. http://dx.doi.org/10.1016/j.jcp.2015.06.036.

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18

BERTOLAZZI, ENRICO. "DISCRETE CONSERVATION AND DISCRETE MAXIMUM PRINCIPLE FOR ELLIPTIC PDEs." Mathematical Models and Methods in Applied Sciences 08, no. 04 (1998): 685–711. http://dx.doi.org/10.1142/s0218202598000317.

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A class of finite volume numerical schemes for the solution of self-adjoint elliptic equations is described. The main feature of the schemes is that numerical solutions share both discrete conservation and discrete strong maximum principle without restriction on the differential operator or on the volume elements.

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19

Esquível, Manuel L., Nadezhda P. Krasii, and Philippe L. Didier. "On a Schrödinger Equation in the Complex Space Variable." AppliedMath 4, no. 4 (2024): 1555–87. https://doi.org/10.3390/appliedmath4040083.

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We study a separable Hilbert space of smooth curves taking values in the Segal–Bergmann space of analytic functions in the complex plane, and two of its subspaces that are the domains of unbounded non self-adjoint linear partial differential operators of the first and second order. We show how to build a Hilbert basis for this space. We study these first- and second-order partial derivation non-self-adjoint operators defined on this space, showing that these operators are defined on dense subspaces of the initial space of smooth curves; we determine their respective adjoints, compute their res

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20

Ren, Guojing, and Huaqing Sun. "J-Self-Adjoint Extensions for a Class of Discrete Linear Hamiltonian Systems." Abstract and Applied Analysis 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/904976.

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This paper is concerned with formallyJ-self-adjoint discrete linear Hamiltonian systems on finite or infinite intervals. The minimal and maximal subspaces are characterized, and the defect indices of the minimal subspaces are discussed. All theJ-self-adjoint subspace extensions of the minimal subspace are completely characterized in terms of the square summable solutions and boundary conditions. As a consequence, characterizations of all theJ-self-adjoint subspace extensions are given in the limit point and limit circle cases.

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21

Elham, Ali, and Michel J. L. van Tooren. "Discrete adjoint aerodynamic shape optimization using symbolic analysis with OpenFEMflow." Structural and Multidisciplinary Optimization 63, no. 5 (2021): 2531–51. http://dx.doi.org/10.1007/s00158-020-02799-7.

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AbstractThe combination of gradient-based optimization with the adjoint method for sensitivity analysis is a very powerful and popular approach for aerodynamic shape optimization. However, differentiating CFD codes is a time consuming and sometimes a challenging task. Although there are a few open-source adjoint CFD codes available, due to the complexity of the code, they might not be very suitable to be used for educational purposes. An adjoint CFD code is developed to support students for learning adjoint aerodynamic shape optimization as well as developing differentiated CFD codes. To achie

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22

Darwish, A. A. "A boundary value problem with a discontinuous coefficient and containing a spectral parameter in the boundary condition." International Journal of Mathematics and Mathematical Sciences 18, no. 1 (1995): 133–40. http://dx.doi.org/10.1155/s0161171295000172.

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A singular non-self-adjoint boundary value problem is considered. This problem has a discontinuous coefficient with a spectral parameter in the boundary condition. Some solutions of the eigenvalue equation are given. The discrete spectrum is studied and the resolvent is obtained. Formulation of the adjoint problem is deduced and hence the continuous spectrum of the considered problem is given. Furthermore, the spectrum of the adjoint problem is investigated.

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23

Yang, L., and J. Yang. "Gradient-based aerodynamic shape optimization using a discrete adjoint approach on a graphics processing unit." Journal of Physics: Conference Series 2784, no. 1 (2024): 012008. http://dx.doi.org/10.1088/1742-6596/2784/1/012008.

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Abstract This paper presents a gradient-based aerodynamic shape optimization framework that utilizes a Graphics Processing Unit (GPU) for solving both flow and adjoint equations. It is built based on a GPU-accelerated flow solver that has been developed previously. Hence, the focus of this work is on how to solve the adjoint equations on the GPU and subsequently compute the gradients. The adjoint equations are right-preconditioned by a block Incomplete Lower Upper (ILU) preconditioner and solved by a restarted Generalized Minimum Residual (GMRES) method. The exact residual Jacobian matrix in t

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24

Sandilya, Ruchi, and Sarvesh Kumar. "Convergence Analysis of Discontinuous Finite Volume Methods for Elliptic Optimal Control Problems." International Journal of Computational Methods 13, no. 02 (2016): 1640012. http://dx.doi.org/10.1142/s0219876216400120.

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In this paper, we discuss the convergence analysis of discontinuous finite volume methods applied to distribute the optimal control problems governed by a class of second-order linear elliptic equations. In order to approximate the control, two different methodologies are adopted: one is the method of variational discretization and second is piecewise constant discretization technique. For variational discretization method, optimal order of convergence in the [Formula: see text]-norm for state, adjoint state and control variables is derived. Moreover, optimal order of convergence in discrete [

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Belikov, D. A., S. Maksyutov, A. Yaremchuk, et al. "Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric transport model (A-GELCA v1.0): development and validation." Geoscientific Model Development Discussions 8, no. 7 (2015): 5983–6019. http://dx.doi.org/10.5194/gmdd-8-5983-2015.

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Abstract. We present the development of the Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian plume diffusion model (LPDM). The tangent and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com), with additio

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Damm, Kyle A., Rowan J. Gollan, Peter A. Jacobs, et al. "Discrete Adjoint Optimization of a Hypersonic Inlet." AIAA Journal 58, no. 6 (2020): 2621–34. http://dx.doi.org/10.2514/1.j058913.

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Kulkarni, Mandar D., David M. Cross, and Robert A. Canfield. "Discrete Adjoint Formulation for Continuum Sensitivity Analysis." AIAA Journal 54, no. 2 (2016): 758–66. http://dx.doi.org/10.2514/1.j053827.

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Popa, Ioan-Lucian, Traian Ceaușu, Larisa Elena Biriș, Tongxing Li, and Akbar Zada. "GENERALIZED EXPONENTIALLY STABLE LINEAR TIME-VARYING DISCRETE BEHAVIORS." Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application 12, no. 1-2 (2020): 256–73. http://dx.doi.org/10.56082/annalsarscimath.2020.1-2.256.

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This paper presents a new approach to formulating exponential behaviors like stability/instability for the linear time-varying systems and for the adjoint one. The classical concept of uniform exponential stability is generalized. Using this generalized concepts, some results extending existing uniform exponential stability conditions for linear time-varying systems are derived. As special cases for these results, some conditions are derived for the adjoint system. A characterization of the generalized concepts in terms of Lyapunov sequences is also given. Also, an example is included to furth

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Evans, K. Franklin. "SHDOMPPDA: A Radiative Transfer Model for Cloudy Sky Data Assimilation." Journal of the Atmospheric Sciences 64, no. 11 (2007): 3854–64. http://dx.doi.org/10.1175/2006jas2047.1.

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Abstract The spherical harmonics discrete ordinate method for plane-parallel data assimilation (SHDOMPPDA) model is an unpolarized plane-parallel radiative transfer forward model, with corresponding tangent linear and adjoint models, suitable for use in assimilating cloudy sky visible and infrared radiances. It is derived from the spherical harmonics discrete ordinate method plane-parallel (SHDOMPP, also described in this article) version of the spherical harmonics discrete ordinate method (SHDOM) model for three-dimensional atmospheric radiative transfer. The inputs to the SHDOMPPDA forward m

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Henze, D. K., and J. H. Seinfeld. "Development of the adjoint of GEOS-Chem." Atmospheric Chemistry and Physics Discussions 6, no. 5 (2006): 10591–648. http://dx.doi.org/10.5194/acpd-6-10591-2006.

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Abstract. We present the adjoint of the global chemical transport model GEOS-Chem, focusing on the chemical and thermodynamic relationships between sulfate – ammonium – nitrate aerosols and their gas-phase precursors. The adjoint model is constructed from a combination of manually and automatically derived discrete adjoint algorithms and numerical solutions to continuous adjoint equations. Explicit inclusion of the processes that govern secondary formation of inorganic aerosol is shown to afford efficient calculation of model sensitivities such as the dependence of sulfate and nitrate aerosol

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Henze, D. K., A. Hakami, and J. H. Seinfeld. "Development of the adjoint of GEOS-Chem." Atmospheric Chemistry and Physics 7, no. 9 (2007): 2413–33. http://dx.doi.org/10.5194/acp-7-2413-2007.

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Abstract. We present the adjoint of the global chemical transport model GEOS-Chem, focusing on the chemical and thermodynamic relationships between sulfate – ammonium – nitrate aerosols and their gas-phase precursors. The adjoint model is constructed from a combination of manually and automatically derived discrete adjoint algorithms and numerical solutions to continuous adjoint equations. Explicit inclusion of the processes that govern secondary formation of inorganic aerosol is shown to afford efficient calculation of model sensitivities such as the dependence of sulfate and nitrate aerosol

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Encinas, A. M., and M. J. Jiménez. "Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients." Open Mathematics 16, no. 1 (2018): 75–82. http://dx.doi.org/10.1515/math-2018-0007.

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AbstractIn this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.

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Zhao, Jia, Guoliang Shi та Jun Yan. "Discreteness of spectrum for Schrödinger operators with δʹ-type conditions on infinite regular trees". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, № 5 (2017): 1091–117. http://dx.doi.org/10.1017/s030821051600041x.

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This paper deals with the spectral properties of self-adjoint Schrödinger operators with δʹ-type conditions on infinite regular trees. Firstly, we discuss the semi-boundedness and self-adjointness of this kind of Schrödinger operator. Secondly, by using the form approach, we give the necessary and sufficient condition that ensures that the spectra of the self-adjoint Schrödinger operators with δʹ-type conditions are discrete.

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Faure, Christèle, and Isabelle Charpentier. "Comparing Global Strategies for Coding Adjoints." Scientific Programming 9, no. 1 (2001): 1–10. http://dx.doi.org/10.1155/2001/485915.

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From a computational point of view, sensitivity analysis, calibration of a model, or variational data assimilation may be tackled after the differentiation of the numerical code representing the model into an adjoint code. This paper presents and compares methodologies to generate discrete adjoint codes. These methods can be implemented when hand writing adjoint codes, or within Automatic Differentiation (AD) tools. AD has been successfully applied to industrial codes that were large and general enough to fully validate this new technology. We compare these methodologies in terms of execution

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Vitale, Salvatore, Tim A. Albring, Matteo Pini, Nicolas R. Gauger, and Piero Colonna. "Fully turbulent discrete adjoint solver for non-ideal compressible flow applications." Journal of the Global Power and Propulsion Society 1 (November 22, 2017): Z1FVOI. http://dx.doi.org/10.22261/jgpps.z1fvoi.

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Abstract Non-Ideal Compressible Fluid-Dynamics (NICFD) has recently been established as a sector of fluid mechanics dealing with the flows of dense vapors, supercritical fluids, and two-phase fluids, whose properties significantly depart from those of the ideal gas. The flow through an Organic Rankine Cycle (ORC) turbine is an exemplary application, as stators often operate in the supersonic and transonic regime, and are affected by NICFD effects. Other applications are turbomachinery using supercritical CO2 as working fluid or other fluids typical of the oil and gas industry, and components o

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Blower, Gordon, and Andrew McCafferty. "Discrete Tracy–Widom operators." Proceedings of the Edinburgh Mathematical Society 52, no. 3 (2009): 545–59. http://dx.doi.org/10.1017/s001309150700140x.

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AbstractIntegrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. We consider discrete Tracy–Widom operators and give sufficient conditions for a discrete integrable operator to be the square of a Hankel matrix. Examples include the discrete Bessel kernel and kernels arising from the almost Mathieu equation and the Fourier transform of Mathieu's equation.

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Fleischli, Benno, Luca Mangani, Armando Del Rio, and Ernesto Casartelli. "A discrete adjoint method for pressure-based algorithms." Computers & Fluids 227 (September 2021): 105037. http://dx.doi.org/10.1016/j.compfluid.2021.105037.

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Biava, Massimo, Mark Woodgate, and George N. Barakos. "Fully Implicit Discrete-Adjoint Methods for Rotorcraft Applications." AIAA Journal 54, no. 2 (2016): 735–49. http://dx.doi.org/10.2514/1.j054006.

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Ren, Guojing, and Yuming Shi. "Self-adjoint extensions for discrete linear Hamiltonian systems." Linear Algebra and its Applications 454 (August 2014): 1–48. http://dx.doi.org/10.1016/j.laa.2014.04.016.

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Jones, Dominic, Jens-Dominik Müller, and Faidon Christakopoulos. "Preparation and assembly of discrete adjoint CFD codes." Computers & Fluids 46, no. 1 (2011): 282–86. http://dx.doi.org/10.1016/j.compfluid.2011.01.042.

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Milatovic, Ognjen, and Françoise Truc. "Self-Adjoint Extensions of Discrete Magnetic Schrödinger Operators." Annales Henri Poincaré 15, no. 5 (2013): 917–36. http://dx.doi.org/10.1007/s00023-013-0261-9.

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Luo, Songting, Shingyu Leung, and Jianliang Qian. "An Adjoint State Method for Numerical Approximation of Continuous Traffic Congestion Equilibria." Communications in Computational Physics 10, no. 5 (2011): 1113–31. http://dx.doi.org/10.4208/cicp.020210.311210a.

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AbstractThe equilibrium metric for minimizing a continuous congested traffic model is the solution of a variational problem involving geodesic distances. The continuous equilibrium metric and its associated variational problem are closely related to the classical discrete Wardrop’s equilibrium. We propose an adjoint state method to numerically approximate continuous traffic congestion equilibria through the continuous formulation. The method formally derives an adjoint state equation to compute the gradient descent direction so as to minimize a nonlinear functional involving the equilibrium me

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Ancourt, Kevin, Jacques Peter, and Olivier Atinault. "Adjoint and Direct Characteristic Equations for Two-Dimensional Compressible Euler Flows." Aerospace 10, no. 9 (2023): 797. http://dx.doi.org/10.3390/aerospace10090797.

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The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D steady-state Euler equations and the first goal of this paper is to present a linear algebra analysis that greatly simplifies the discussion of the number of independent characteristic equations satisfied along a family of characteristic curves. This method may be applied for both the direct and the adjoint problem. Our second goal is to directly derive in conservative variables the characteristic equat

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Okello, Boaz, Fredrick Nyamwala, and David Ambogo. "Spectral theory of commutative higher order difference operators with unbounded coefficients." Annals of Mathematics and Computer Science 26 (January 5, 2025): 1–27. https://doi.org/10.56947/amcs.v26.415.

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We have established the necessary and sufficient conditions for any two even higher order symmetric difference maps to generate commuting minimal difference operators. We have done this through construction of appropriate comparison algebras of the self-adjoint operator extensions of the minimal operators generated and application of asymptotic summation. The results show that if the first difference on the coefficients tends to zero whenever the coefficients are allowed to be unbounded and that the difference maps considered have the same order, then they generate minimal operators that commu

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Jun, Deng, Gao Zhenghong, Huang Jiangtao, Zhao Ke, and Xia Lu. "Design method of aircraft boundary characteristics based on upwind adjoint equation." Journal of Applied Artificial Intelligence 1, no. 3 (2024): 192–206. http://dx.doi.org/10.59782/aai.v1i3.324.

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The boundary characteristics of an aircraft determine its safety and flight performance, and have always been the difficulty and focus of aircraft design. This paper aims to improve the accuracy, efficiency and robustness of the adjoint equation solution for complex flow problems by introducing the adjoint equation of the upwind format and different flux limiter processing forms, thereby expanding the application scope of the adjoint optimization method in the design of the boundary characteristics of aircraft. Firstly, the basic principle of discrete adjoint gradient solution is introduced. O

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Wang, Qiming, and Zhaojie Zhou. "SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation." Entropy 23, no. 6 (2021): 723. http://dx.doi.org/10.3390/e23060723.

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In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed based on the first-optimize-then-discretize strategy and SUPG stabilized virtual element approximation of the state equation and adjoint state equation. An a priori error estimate is derived for both the state, adjoint state, and the control. Numerical experiments are carried out to illustrate the theoretical findings.

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Kadchenko, S. I. "NUMERICAL METHOD FOR SOLVING INVERSE SPECTRAL PROBLEMS GENERATED BY PERTURBED SELF-ADJOINT OPERATORS." Vestnik of Samara University. Natural Science Series 19, no. 9.1 (2017): 5–11. http://dx.doi.org/10.18287/2541-7525-2013-19-9.1-5-11.

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A new numerical method for solving inverse spectral problems generated by perturbed self-adjoint operators from their spectral characteristics is developed. The method was tested on the problems for perturbed Sturm - Liouville operator. The results of numerous calculations have shown its computational efficiency. The simple algebraic formulas for finding the eigenvalues of discrete operators was found. At that the calculation of eigenvalues of perturbed self-adjoint operator can start from any number, no matter known the eigenvalues from previous numbers or not.

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Ma, Chuang, Jiangtao Huang, Daochun Li, et al. "Discrete Adjoint Optimization Method for Low-Boom Aircraft Design Using Equivalent Area Distribution." Aerospace 11, no. 7 (2024): 545. http://dx.doi.org/10.3390/aerospace11070545.

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This paper introduces a low-boom aircraft optimization design method guided by equivalent area distribution, which effectively improves the intuitiveness and refinement of inverse design. A gradient optimization method based on discrete adjoint equations is proposed to achieve the fast solution of the gradient information of target equivalent area distribution relative to design variables and to drive the aerodynamic shape update to the optimal solution. An optimization experiment is carried out based on a self-developed supersonic civil aircraft configuration with engines. The results show th

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BIRIŞ, LARISA ELENA, TRAIAN CEAUŞU, IOAN-LUCIAN POPA, and "NICOLAE MARIAN" SEIMEANU. ""Lyapunov Conditions for One-Sided Discrete-Time Random Dynamical Systems"." Carpathian Journal of Mathematics 38, no. 3 (2022): 777–88. http://dx.doi.org/10.37193/cjm.2022.03.21.

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"This paper considers nonuniform exponential stability and nonuniform exponential instability concepts for one-sided discrete-time random dynamical systems. These concepts are generalizations from the deterministic case. Using this, characterizations in terms of Lyapunov functions respectively Lyapunov norms are presented. Also, an approach in terms of considered concepts for the inverse and adjoint random discrete- time systems is derived."

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Kholkin, Aleksandr Mikhailovich. "Resolvent for Non-Self-Adjoint Differential Operator with Block-Triangular Operator Potential." Abstract and Applied Analysis 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/2964817.

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A resolvent for a non-self-adjoint differential operator with a block-triangular operator potential, increasing at infinity, is constructed. Sufficient conditions under which the spectrum is real and discrete are obtained.

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