In this paper has been studied the wave equation in some non-classic cases. In the  rst case boundary conditions are non-local and non-periodic. At that case the associated spectral problem is a self-adjoint problem and consequently the eigenvalues are real. But the second case the associated spectral problem is non-self-adjoint and consequently the eigenvalues are complex numbers,in which two ...

We study practical strategies for estimating numerical errors in scalar outputs calculated from unsteady simulations of convection-dominated flows, including those governed by the compressible Navier–Stokes equations. The discretization is a discontinuous Galerkin finite element method in space and time on static spatial meshes. Time-integral quantities are considered for scalar outputs and the...

A modified version of the truncated-Newton algorithm of Nash ([24], 125], [29]) is presented differing from it only in the use of an exact Hessian vector product for carrying out the large-scale unconstrained optimization required in variational data assimilation. The exact Hessian vector product is obtained by solving an optimal control problem of distributed parameters. (i.e. the system under...

Adjoint methods are widely used in various areas of computational science to efficiently obtain sensitivities of functionals which result from the solution of partial differential equations (PDEs). In addition, adjoint methods have been used in other settings including error estimation, uncertainty quantification and inverse problem formulations. When deriving the adjoint equations, there are t...

In this paper, an adjoint-based error estimation and mesh adaptation framework is developed for the compressible inviscid flows. The algorithm employs the Finite Calculus (FIC) scheme for the numerical solution of the flow and discrete adjoint equations in the context of the Galerkin finite element method (FEM) on triangular grids. The FIC scheme treats the instabilities normally generated in t...

The design of adaptive observations strategies must account for the particular properties of the data assimilation method. A new adjoint sensitivity approach to the targeted observations problem is proposed in the context of fourdimensional variational data assimilation (4D-Var). The method is based on a periodic update of the adjoint sensitivity field that takes into account the interaction be...

The focus of CFD applications has shifted to aerodynamic design. This shift has been mainly motivated by the availability of high performance computing platforms and by the development of new and efficient analysis and design algorithms. In particular automatic design procedures, which use CFD combined with gradient-based optimization techniques, have had a significant impact on the design proc...

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 inte...