Adjoint Differential Operators Research Articles

New Theory of Hybrid-Upwind Technique and Discrete Del Operator for Finite-Element Method

In this paper, we present a new hybrid-streamline-upwind finite-element method, which is based on the finite analytic method developed in the field of the finite difference method. In order to obtain an optimal shape function, we introduce an adjoint differential operator to the differential operator for a steady advection-diffusion equation. The shape functions which satisfy these differential operators are mutually dual. One of them interpolates accurately the functions appearing in convection-dominated flows, the other becomes a hybrid-streamline-upwind weighting function. Furthermore, we define a discrete del operator for the reduction of memory storage in the computer. As a result, we achieve simplicity of formulation and high-speed calculation of the finite-element method.

New Hybrid-Streamline-Upwind Finite-Element Method in Dual Space. (Fundamental Theory and DiscreteDel Operator).

In this paper, we present a new hybrid-streamline-upwind finite-element method, which is based on the finite analytic method developed in the field of the finite difference analysis. In order to obtain an optimal shape function, we introduce an adjoint differential operator to the differential operator for a steady advection-diffusion equation. The shape functions which satisfy these differential operators are mutually dual. One of them accurately interpolates the functions appearing in convection-dominated flows, and the other becomes a hybrid-streamline-upwind weight function. Furthermore, we define a discrete del operator for the reduction of memory storage in computers. As a result, we achieve simplicity of formulation and high-speed calculation in the finite-element method.

New Hybrid-Streamline-Upwind Finite-Element Method in a Dual Space. 1st Report. Fundamental Theory and Discrete Del Operator.

In this paper, we present a new hybrid-streamline-upwind finite-element method, which is based on the finite analytic method developed in the field of the finite difference method. In order to obtain an optimal shape function, we introduce an adjoint differential operator to the differential operator for a steady advection-diffusion equation. The shape functions which satisfy these differential operators are mutually dual. One of them interpolates accurately the functions appearing in convection-dominated flows, the other becomes a hybrid-streamline-upwind weight function. Furthermore, we define a discrete del operator for the reduction of memory storage in the computer. As a result, we achieve simplicity of formulation and high-speed calculation of the finite-element method.

THERMOELASTICITY OF ANISOTROPIC CYLINDRICAL SHELLS

The quasistatic thertnoelastic equations for radially monoclinic cylindrical shells are solved in closed form for arbitrary temperature distributions and boundary conditions. In addition to both mechanical and thermal material anisotropy, the effects of shear deformation are admitted in the governing shell field equations. The solution to the governing thermomechanical noncanonical field equations is obtained through the use of integral transformations employed in conjunction with the application of adjoint differential operators. To illustrate the substantial effects of mechanical and thermal material anisotropy, the results of several numerical experiments are studied in detail.

Thermoelasticity of Cylindrically Anisotropic Generally Laminated Cylinders

The effects of cylindrically curvilinear mechanical and thermal material anisotropy on the stationary thermoelastic fields of generally laminated cylinders are studied. To model the stated problem, each individual ply of the cylinder is considered to be composed of both mechanically and thermally cylindrically anisotropic media whose governing fields satisfy the 3-D elasticity and conduction equations. Based on finite and infinite Fourier integral transforms together with the use of complex adjoint differential operators and complex power series expansions, a nonhomogeneous pseudo-stiffness procedure is used to develop the general solution form for the stated problem. Through the use of the model and its solution, several numerical experiments are presented which emphasize the significant effects of cylindrical material anisotropy on the governing fields of several different types of laminate configuration.

On solutions to multiply-connected nonself-adjoint systems subject to deterministic and nondeterministic excitations

The Sturm-Liouville-Vodicka-Tittle procedure is extended to handle deterministic and nondeterministic nonconservative phenomena modelled by multiply connected nonself adjoint differential operators. This generalization is facilitated by employing the properties of adjoint differential operators to develop a piecewise weighted bi-orthogonality principle. Employing the inherent generality of the bi-orthogonality principle, an integral transform procedure is established which can handle multiply connected nonself adjoint differential operators subject to deterministic as well as homogeneous and nonhomogeneous nondeterministic initial, external and interdomain conditions. Due to the inherent scope of the procedure, in addition to the mean, both the variance and covariance of the governing field variables are obtained. Furthermore, generalizations to all the higher order statistical moments can be developed as required.

Semi‐analytical finite element procedure for conduction in anisotropic axisymmetric solids

AbstractThrough the use of complex series representations and the properties of adjoint differential operators, a semi‐analytical finite element procedure is developed which can analyse the steady state and transient temperature fields of thermally anisotropic axisymmetric bodies with complete circumferential properties. Due to its generality, the procedure can handle arbitrary laminate construction with possible meridional and radial variations in locally or globally thermally anisotropic materials. In this respect, the procedure developed herein supercedes the classical semi‐analytical treatment which is limited to specially orthotropic materials. Furthermore, in contrast with the classical procedure, the present treatment reveals several important effects of material anisotropy which are entirely missed by the specially orthotropic assumption.

Operators commuting with translation by one part II differential operators with periodic coefficients in Lp(−∞, ∞)

An extension of the theory of differential equations and linear operators, both of which have many applications to engineering and mathematical physics. This memorandum studies representation of operators used to employ perturbation techniques. These techniques were heretofore applicable only to operators with compact resolvents and to nonself adjoint differential operators with periodic coefficients on . Conditions are given on the coefficients of these operators that ensure that they be spectral (completely reducible) even though they have continuous spectrum.