Many applications of various self-adjoint differential equations, whose solutions are complex, are produced Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011 . In this work we propose a method for the solving some self-adjoint equations with variable change in problem, and then we obtain a analytical solutions. Because this solution, an exact analytical solution can be provided to us, we benefi...

This paper presents an adjoint method for the optimum shape design of unsteady three-dimensional viscous flows. The goal is to develop a set of discrete unsteady adjoint equations and the corresponding boundary condition for the non-linear frequency domain method. First, this paper presents the complete formulation of the time dependent optimal design problem. Second, we present the non-linear ...

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...

6 Data assimilation obtains improved estimates of the state of a physical system by com7 bining imperfect model results with sparse and noisy observations of reality. In the four 8 dimensional variational (4D-Var) framework data assimilation is formulated as an opti9 mization problem, which is solved using gradient based optimization methods.The 4D10 Var gradient is obtained by forcing the adjo...

In this paper we derive a posteriori error estimates for linear functionals of the solution to an elliptic problem discretized using a multiscale nonoverlapping domain decomposition method. The error estimates are based on the solution of an appropriately defined adjoint problem. We present a general framework that allows us to consider both primal and mixed formulations of the forward and adjo...

We study spectral properties of a nonself-adjoint problem for (2n) th order operator differentiation with nonlocal conditions representing multipoint perturbations the Birkhoff strongly regular self-adjoint conditions. establish sufficient under which system eigenfunctions is complete and, certain additional assumptions, forms Riesz basis. construct set transformation operators, each element ma...

This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral equation is derived by reformulating the conformal mapping as an adjoint Riemann-Hilbert problem. From the adjoint Riemann-Hilbert problem, we derive a bound...