
TAMC
 Referenced in 72 articles
[sw07198]
 with respect to control variables. Generation of adjoint code may be seen as the special ... function is a scalar. The described method for adjoint code generation is based ... generation of adjoint code represents a distinct advantage. An implementation of the method, described...

torchdiffeq
 Referenced in 59 articles
[sw35082]
 solvers is supported using the adjoint method. For usage of ODE solvers in deep learning...

CVODES
 Referenced in 35 articles
[sw04946]
 with sensitivity analysis capabilities (both forward and adjoint modes). CVODES is a superset of CVODE ... also available for CVODES. Both integration methods (AdamsMoulton and BDF) and the corresponding nonlinear ... iteration methods, as well as all linear solver and preconditioner modules are available ... chain rule of differentiation. The adjoint sensitivity analysis (ASA) method is more practical than...

Nek5000
 Referenced in 143 articles
[sw08064]
 adjoint eigenmodes. The large eigenvalue problems are solved using matrixfree methods adopting the time...

Adjoint
 Referenced in 11 articles
[sw08877]
 compute total derivatives using an adjoint method. The resulting linear discrete adjoint system is then ... cost of increased memory requirements for the adjoint solver. Derivatives of drag and lift coefficients ... cost and ease of implementation of the method are shown...

HSL_MI20
 Referenced in 56 articles
[sw07246]
 most effective iterative methods for the solution of large, sparse linear systems obtained from ... discretization of secondorder scalar elliptic selfadjoint partial differential equations. It can also ... used as a preconditioner for Krylov subspace methods. In this communication, we report...

FDFD
 Referenced in 10 articles
[sw01172]
 easily parallelized. Finally, an adjoint field method of data inversion, developed in parallel for solving ... both forward and adjoint fields. Results obtained from this inversion method for highcontrast media...

amodMC
 Referenced in 6 articles
[sw06614]
 Adjoint mode computation of subgradients for McCormick relaxations In [{it A. Mitsos}, {it B. Chachuat ... method similar to Algorithmic Differentiation (AD) is presented which allows the propagation of, in general ... this article an adjoint method for the computation of subgradients for McCormick relaxations is presented ... branchandbound method. The superiority of adjoint over tangentlinear mode is illustrated...

DiffEqFlux
 Referenced in 7 articles
[sw27559]
 conclude by discussing the various adjoint methods used for backpropogation of the differential equation solvers...

JiffyTune
 Referenced in 6 articles
[sw11681]
 procedure. In addition to traditional adjoint and direct methods ... technique called the adjoint Lagrangian method, which computes all the gradients necessary for one iteration ... optimization in a single adjoint analysis. This paper describes the algorithms and the environment...

DAFoam
 Referenced in 3 articles
[sw41098]
 Multidisciplinary Design Optimization with OpenFOAM. The adjoint method is an efficient approach for computing derivatives ... variables. Despite this advantage, implementing the adjoint method for a partialdifferentialequationbased primal ... proposed to rapidly implement the discrete adjoint method for any steadystate OpenFOAM primal solver ... illustrated. Using this strategy, the adjoint method is implemented for eight primal solvers, five turbulence...

Algorithm 922
 Referenced in 38 articles
[sw12858]
 Algorithm 922: A mixed finite element method for Helmholtz transmission eigenvalues. Transmission eigenvalue problem ... scattering. Since the problem is nonselfadjoint, the computation of transmission eigenvalues needs special ... transmission eigenvalue problem, a mixed finite element method is applied. The method has two major...

NEWOPT/AIMS
 Referenced in 7 articles
[sw02967]
 systems the software is augmented by additional methods for sensitivity analysis and scalar optimization ... provided by the efficient semianalytical adjoint variable method, automatic differentiation or finite differences...

DASPKADJOINT
 Referenced in 4 articles
[sw12821]
 difierentialalgebraic equations (DAEs) by the adjoint method, is introduced and described. Several critical issues...

KPP
 Referenced in 11 articles
[sw10179]
 Forward, tangent linear, and adjoint RungeKutta methods in KPP2.2. This paper presents ... Hessian. A set of integration methods was added to the comprehensive suite of stiff numerical ... well as the continuous and discrete adjoint models of the chemical system to do sensitivity...

AESOP
 Referenced in 3 articles
[sw02849]
 obtain the best computational efficiency, the adjoint method is applied on the complete mapping, from ... numerical platform AESOP integrates the flow and adjoint flow solver, mesh deformation schemes, algorithms ... examples of applications are presented. The method of shape parameterization using Radial Basis Functions...

FATODE
 Referenced in 9 articles
[sw11044]
 ordinary differential equations with direct and adjoint sensitivity analysis capabilities. The paper describes the capabilities ... this package. Fatode implements four families of methods: explicit RungeKutta for nonstiff problems, fully ... methods by simply providing their coefficients. For each family the forward, adjoint, and tangent linear ... forward and adjoint sensitivity analysis capabilities in the context of RungeKutta methods. A wide...

SLEIGN2
 Referenced in 41 articles
[sw01230]
 code is based on the ideas and methods of the original SLEIGN code ... eigenfunctions of regular and singular selfadjoint SturmLiouville problems, with both separated and coupled...

TRICE
 Referenced in 46 articles
[sw05197]
 linearized state equation and the adjoint equation. They are well suited for large scale problems ... bound constraints by using an affine scaling method proposed, for a different class of problems...

pFOSM
 Referenced in 1 article
[sw27927]
 aerodynamic robust design based on continuous adjoint and matrixvector products. This article proposes ... novel robust design tool based on the method of moments (MoM), demonstrated in problems governed ... variables are computed using the continuous adjoint method. Using a firstorder MoM to compute ... vector products instead, using a combination of adjoint and direct differentiation. This makes the cost...