In this work we construct multigrid preconditioners to accelerate the solution process of a linear-quadratic optimal control problem constrained by the Stokes system. The first order optimality conditions of the control problem form a linear system (the KKT system) connecting the state, adjoint, and control variables. Our approach is to eliminate the state and adjoint variables by essentially s...

The unsteady discrete adjoint equations are utilized to construct objective function gradients for use in geometry optimization in large scale three-dimensional unsteady ow problems. An existing massively parallel unstructured Reynolds-averaged Navier-Stokes equations solver forms the basis for the framework used to solve both the primal and dual (adjoint) problems. The framework is also capabl...

A synthesis of results of the recently introduced paradigm of multi-adjoint logic programming is presented. These results range from a proof theory together with some (quasi)completeness results to general termination results, and from the neural-like implementation of its fix-point semantics to the more general biresiduated multi-adjoint logic programming and its relationship with other approa...

[1] As the incidence of groundwater contamination continues to grow, a number of inverse modeling methods have been developed to address forensic groundwater problems. In this work the geostatistical approach to inverse modeling is extended to allow for the recovery of the antecedent distribution of a contaminant at a given point back in time, which is critical to the assessment of historical e...

The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydratation of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, fo...

The rst half of this paper derives the adjoint equations for inviscid and viscous compressible ow, with the emphasis being on the correct formulation of the adjoint boundary conditions and restrictions on the permissible choice of operators in the linearised functional. It is also shown that the boundary conditions for the adjoint problem can be simpliied through the use of a linearised perturb...

In order to decrease the fluid drag on an underwater robot manipulator, an optimal trajectory method based on the variational method is presented. By introducing the adjoint variables, which are Lagrange multipliers, we formulate a Lagrange function under certain constraints related to the target angle, target angular velocity, and dynamic equation of the robot manipulator. The state equation (...

Numerical methods for design sensitivity analysis of multibody dynamics are presented. An analysis of the index-3 adjoint differential-algebraic equations is conducted and stability of the integration of the adjoint differential-algebraic equations in the backward direction is proven. Stabilized index-1 formulations are presented and convergence of backward differentiation formulas is shown for...

The use of adjoint error estimation techniques is described for a model problem that is a simplified version of an EHL line contact. Quantities of interest, such as friction, may be dependent upon the accuracy of the solution in some parts of the domain more than in others. The use of an inexpensive extra solve to calculate an adjoint solution is described for estimating the intergrid error in ...