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The steady state drift-diffusion model (DDM) of organic solar cells that considers the surface recombination processes for majority and minority carriers, as well as their thermionic emission on both electrodes, is presented in this paper. When the full Robin boundary conditions (BCs) and the popular finite difference method with Schaffeter-Gummel discretization (FDSG) were applied, significant instabilities were observed when surface recombination velocities (SRVs) for majority carriers on one or both electrodes were reduced. To analyze this problem and perceive the independent impacts of electron and hole contact processes, the model was simplified by assuming a constant electric field in the device and by solving the electron and hole continuity equations separately. The stability of numerical DDM solutions obtained by the FDSG and Discontinuous Galerkin (DG) methods for three different types of BCs (Dirichlet and two mixed BCs) was examined. The DG method showed a better stability when majority carriers SRVs were reduced. The current density versus voltage (J-V) characteristic calculated by the DDM with Dirichlet BCs using the DG method was compared to the measured ITO/PEDOT:PSS/P3HT:PCBM/Al solar cell J-V curve for the model validation.

This paper deals with blow-up and global solutions for a porous medium equation under Robin boundary conditions. By constructing auxiliary functions and using modified differential inequality techniques, we establish conditions to ensure that the solution blows up in some finite time or remains global. Moreover, an upper and a lower bound for blow-up time are derived. Finally, an example is given to illustrate the applications of obtained results.

This paper presents an approach for the efficient numerical implementation of backstepping observers for a one dimensional reaction-diffusion-system with Robin boundary conditions. The associated observer gains are interpreted as unbounded operators. Approximating these observer gains together with the system equations the implementation of the observers as well as the whole design process can be considerably simplified. It is shown that for a complete modal observer approximation further simplifications are possible and that the observer can be finally realized without computing the backstepping-kernel.

The present analysis is concerned with the determination of the magnetic field distribution and eddy current loss in a heavy ferromagnetic core by linear theory. An analytical method is used to solve a simple one dimensional rectangular coordinate diffusion equation governing the H field using Robin boundary condition which is the combination of Dirichlet and Neumann boundary condition. For linear analysis, different choices of Permeability are chosen to compute eddy current loss and the results are compared with the experimental value.

A surface wave, propagating from infinity along a semi-infinite part, interacts with the impedance boundary of a 2D polygonal domain and gives rise to the reflected surface wave on this side and to the transmitted surface wave outgoing to infinity along the second semi-infinite side of the domain. The circular outgoing wave also propagates at infinity. It is shown that the classical solution of the problem is unique. By use of some known extension of the Sommerfeld–Malyuzhinets technique the problem at hand is reduced to functional Malyuzhinets equations and then to a system of integral equations of the second kind with the integral operator depending on a characteristic parameter. The integral equations are carefully studied. From the Sommerfeld integral representation of the solution the far field asymptotics is developed.

A combination of a domain decomposition algorithm and a finite element method for the efficient three dimensional simulation of electro-quasistatic multi-scale problems is presented and applied to the simulation of the dielectric properties of biological cell suspensions. In this scheme, cells and membranes are discretized by meshes fitted to their geometrical scales. The simulation can be carried out for all considered cells in parallel. The data exchange between the particular meshes relies on Robin boundary conditions assuring the conservation of fluxes according to Maxwell's equations. Efficient algorithms are provided for data exchange between the meshes. From simulation results, biologically relevant quantities, such as the transmembrane potential, are computed.

We investigate different criteria for locating sensors for the state estimation in a controlled thermal fluid modeled by the Boussinesq equations. This paper focuses on the linearized Boussinesq equation. We combine optimal sensor location with observer design to obtain a sensor placement. One way to locate sensors is to minimize the covariance of the estimation error. Another way is based on the geometric structure of the feedback functional gain. The controllers are finite dimensional and act on a portion of the boundary through Neumann/Robin boundary conditions. Dirichlet boundary conditions are imposed on the rest of the boundary. A lower order observer is constructed by using the LQG balanced truncation for the linearized controlled system. Computer simulations are presented to compare the effectiveness of different sensor locations.

Controllability properties of the thermoelastic plate with a curved middle surface are studied. By virtue of the Riemannian geometry approach and the multiplier technique, we show that one can simultaneously control the displacement of the plate exactly and the temperature approximately, provided with three controls exerted through the free boundary conditions of the plate equation and the Robin boundary condition of the heat equation, respectively.

In this paper, we consider the control problem of the complex Ginzburg-Landau equation with Neumann boundary control (input) and Dirichlet boundary observation (output). We show that the input-output map is continuous for this nonlinear equation.

Method of weighted residuals is used for developing of the boundary integral representation for a solenoidal vector field. It is shown that the solenoidal vector in an arbitrary point of domain can be expressed through its values and curls of the different order on the boundary domain. Boundary integral representation for the linear Beltrami vector fields are obtained. The boundary integral equations of the second kind for the solving of the boundary value problems of the second kind are received. It is marked that the given integral equations allow the effective numerical solving. Shown that in the case boundary value problem of the first kind solution can be obtained by quadratures. Showing the relationship between Beltrami vector fields and the solutions of the first boundary value problem for the Helmholtz equation.

An inverse coefficient problem for a stationary semilinear equation is considered and consists in finding the coefficients, which are included both in the equation and in the third type boundary condition, using additional information about the solution of the boundary value problem. The mentioned coefficients depend nonlinearly on both spacial variables and on the solution of the boundary value problem.

In the paper, boundary integral equations are derived for the problem of an isotropic homogeneous elastic half-plane with a cavity of an arbitrary configuration. The initially straight-line boundary is assumed to be fixed under a given displacement while the cut surface is subjected to a certain load. A concentrated force is also applied at an inner point of the half-plane. Using the complex variable representation and the method of superposition, the problem is reduced to Fredholm integral equations of the first kind for the boundary of the notch.

We consider a Dirichlet boundary value problem for a system of elliptic equations of special type in domains with inclusions. The use of Green's function technique leads to boundary integral equations with unknown functions only on the surface of the inclusion. The direct and indirect approaches of the boundary integral equation method are discussed. A modified boundary elements method is obtained and a series of numerical experiments is conducted.

In this paper, the author discuss oscillation of nonzero solutions for a class of impulsive parabolic system. Several oscillation criteria are obtained under Dirichlet boundary condition by using the Green formula and Jensen inequality.

This paper presents 4-point 1-step block method (4LBVP) to solve the linear 2nd order boundary value problem (BVP) with Dirichlet boundary condition. 4LBVP will solve the linear 2nd order BVP with Dirichlet boundary condition directly without the need to reduce it first into the system of 1st order equations. 4LBVP will produce several numerical solutions simultaneously in one step. The formulation of the 4LBVP will be based on the Lagrange interpolating polynomial. 4LBVP will be used together with the linear shooting technique to produce the numerical solutions. Comparison with other methods will be given to show the advantages of this method.

Transparent boundary conditions for the hierarchies of parabolic equations where the solution of n-th equation is used as an input term for n+1-th equation are derived. The existence, uniqueness, and well-posedness of the initial boundary value problem for the system of coupled parabolic equations with the derived boundary conditions is established. Such coupled systems of parabolic equations can be used to approximate the solution of the Helmholtz equation. The derived transparent boundary conditions may be therefore used for the simulation of wave propagation in unbounded media.

In this paper, we consider the quasilinear parabolic-elliptic repulsion chemotaxis system with logistic source under homogeneous Neumann boundary condition in a smooth bounded domain. It is proved that the classical solutions to the corresponding initial boundary value problem are uniformly bounded in time.

We propose a new way for computation of local wave number or instantaneous frequency, which is used in adaptive artificial boundary conditions using for nonlinear 1D Schrodinger equation. Computer simulation results, obtained by using of this method, are compared with corresponding results obtained by solving this equation with zero-value boundary condition for enough bigger size of domain and demonstrated the efficiency of proposed method.

Skewon-axion medium is a bi-anisotropic medium defined by 16 free parameters out of 36. A plane wave in such a medium is not restricted by a dispersion equation. Applying plane-wave equations in four-dimensional formalism, it is shown that an interface of a skewon-axion medium can be defined to produce a boundary condition which generalizes the DB and soft-and-hard boundary conditions to SHDB conditions. The SHDB boundary is self-dual, invariant in any three-parameter duality transformation.

We present verified computational solutions of a one-dimensional nonlinear Poisson equation with Neumann boundary condition. This equation is derived from the Keller-Segel system known as chemotactic model by steady state, and its solution curve possesses a turning point. Using the idea of the shooting method for the boundary value problems, we transform this equation into two integral equations corresponding to the initial value problems, and use Nakao's method with local uniqueness to enclose the solutions and a bordering algorithm to treat a turning point. We describe numerical verification conditions and give some numerical results.

In this paper we discuss an approximation method for dealing with Dirichlet boundary control of thermal-fluid systems. The physics of displacement ventilation and buoyancy-driven flows are described by the Boussinesq equations. We first develop a computational algorithm for solving the corresponding LQR control problem for the Boussinesq equations with general Robin boundary conditions. This scheme is combined with a finite element method that generalizes Nitsche's perturbation theory for approximating Dirichlet boundary conditions. Using this approach we are able to avoid imposing the “compatibility condition” that is required for Dirichlet boundary control in 3D problems. Numerical examples are presented to illustrate the computational algorithm.

We consider flow past a flat plate with small periodic irregularities for large Reynolds number. This flow has double-deck boundary layer structure. For oscillations in classical boundary layer we obtained the time-dependent Rayleigh-type equation with some boundary condition. We prove the existence and uniqueness of the stationary solution for the obtained problem and also the property of its stability.

The problem of designing and numerically implementing a controller for a fluid flow system at the boundary of the flow domain is complicated by the facts that the basic model is truly nonlinear and the flow is usually highly sensitive to boundary conditions. High sensitivity to small changes in the boundary such as wall roughness or dynamic excitations can trigger transition to undesirable states. One approach to preventing or delaying a transition is to introduce a simple control loop along the boundary to reduce the sensitivity. In this work we demonstrate the aforementioned idea for a system governed by the one dimensional Burgers' equation. In particular, we focus on the initial boundary value problem for a viscous Burgers' equation which is known to be is extremely sensitive with respect to a small perturbation in a Neumann boundary condition. We use this model to illustrate how this sensitivity can generate erroneous numerical solutions and “transitions” to these states. In particular, for a fixed viscosity and certain initial data the numerical solution z(x; t) of Burgers' equation with a Neumann boundary condition z x (0; t) = 0 converges to a (large) solution that satisfies z x (0; t) = −α for a number α > 0 less than machine precision zero. Thus, the solution of the Burgers' equations for this problem exhibits an extreme sensitivity to the boundary perturbation α and this sensitivity can produce unexpected and undesired dynamic behavior. We use a continuous sensitivity equation method to compute these sensitivities and show that the sensitivity can be eliminated by introducing a very simple proportional error boundary feedback mechanism.

A parallel algorithm of non-linear high order boundary condition problem is discussed, and super-cavitation hydrofoil with finite span near free surface is given. by using non-linear initial boundary two dimension condition and three dimension lifting line theories, the numeric results of a flat plate hydrofoil are better than that of Furuya.

In this paper, based on the boundary reduction advanced by Han, we present a new method for solving an exterior Dirichlet problem in the plane. The technique consists in coupling the boundary element with the mixed finite element method. An artifical boundary is introduced separating an interior region from an exterior one. From the theory of the boundary element in the exterior domain we deduce the connection which relates the solution and its normal derivative over the artificial boundary. These results are incorporated into the so-called mixed formulation of the problem in the interior region.

In the paper, the Neumann problem with non-classical boundary conditions not requiring agreement conditions in considered for a pseudoparabolic equation of fourth order. The equivalence of the conditions with classic boundary condition is substantiated in the case if the solution of the stated problem is sought in S.L. Sobolev space W p (2,2) (G).

Various domain decomposition methods (DDM) have been developed as popular divide-and-conquer strategies to solve numerical electromagnetic problems of unprecedented scale. The DDM techniques invariably divide the original large problem into multiple smaller sub-problems, solve each sub-problem separately, and then, re-couple them into a continuous global solution over the entire domain. Key to all DDM approaches is the proper merging of all subdomain solutions. Bi-directional Robin boundary conditions have been popular in connecting non-overlapping individual solutions with remarkable success. However, similar to traditional absorbing boundary conditions, Robin conditions become inadequate when subdomain boundaries are partitioned in a way that dominant modes run parallel to the boundaries. Under these circumstances, spurious fields can occur along the subdomain boundaries that contaminate the accuracy of the entire solution. In this paper, extra constraints in the form of Lagrange multipliers are incorporated to suppress spurious fields in the fully overlapping DDM setup.

Different kinds of boundary conditions (Dirichlet, Neumann, Robin) for time-fractional heat conduction equation are discussed. The fundamental solutions to time-fractional heat conduction equation with the Caputo derivative of the order 0 < α < 2 is considered in a half-plane under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of the values of temperatute and the values of its normal derivative and the physical condition with the prescribed linear combination of the values of temperature and the values of the heat flux at the boundary of the domain.

This paper concerns homogenization for the elliptic operator in L 2 (Π), Π = ℝ × (0,a), defined by the differential expression equation with periodic, Neumann or Dirichlet boundary conditions. All the coefficients are assumed to be periodic of period 1 with respect to the first variable. Sharp-order approximations for the inverse of B λ e in the norms of B(L 2 (Π)) and B(L 2 (Π), H1(Π)) are obtained, with error terms being O(e).

Domestic and overseas investigation showed that boundary element method was widely used in seepage flow, but it was mostly used in well bore pressure curve feature research of different reservoir types. Its use in unsteady production prediction has not been reported. Based on unsteady pressure dynamic problems research by boundary element method, the calculating method used to predict unsteady production by boundary element method is provided for the first time after adjusting the boundary integral equation. For checking prediction results, the homogeneous reservoir production with closed boundary or stable boundary was predicted, the small error with analytical solution showed that the production predicting method is accurate.

Optimal boundary control problems for linear parabolic-hyperbolic systems with the Neumann boundary conditions involving integral time delays are considered. Sufficient conditions for the existence of a unique solution for such parabolic-hyperbolic systems are proved. Necessary and sufficient conditions of optimality are derived for the Neumann problem. The problem of determining of the optimal control is discussed.

This paper investigates a fourth-order boundary value problem with integral boundary conditions. The existence of iterative solutions is obtained via the lower and upper solutions method.

In this paper, nonlinear three-point boundary value problems for a class of third order nonlinear differential equations is studied by means of differential inequality theories and upper and lower solutions. Based on the given results of second order boundary value problem, and under suit upper and lower solution, iteration sequences were constructed, and existence and unique of solutions of nonlinear boundary value problems of second order nonlinear Volterra type integro-differential equation were obtained by means of applying the Arzela-Ascoli theorem and Lebesque control convergence theorem and disproof method. Finally, the existence and uniqueness of solution for three-point nonlinear boundary value problems were established. The result showed that is seems new to apply these technique to solving other boundary value problems.

Singular perturbation of Volterra type integro-differential equation for linear boundary value problems by means of differential inequality theories was studied. Based on the results of second order linear boundary value problems, the upper and lower solutions method of Volterra type integro-differential equation for nonlinear boundary value problems was established. Specific upper and lower solutions were constructed existence and uniformly valid estimate of solutions for linear boundary value problems of a Volterra type integro-differential equation under suitable condition were obtained. The results showed that seems new to apply these kinds of Volterra type integro-differential equation for linear boundary value problems.

This paper proposes a new hybrid algorithm, which is referred to as FETI-DP-BI, to solve antenna array radiation and scattering problems in electromagnetic simulation. Our mathematical treatment is based on the combination of the dual-primal finite element tearing and interconnecting (FETI-DP) and boundary integral (BI) methods. Decomposed interior FE domains are glued together by the Robin transmission condition (TC) using two Lagrange multipliers, while they communicate with the exterior BI region through the Dirichlet-Neumann or Robin boundary condition (BC). Such a hybridization exhibits an excellent numerical scalability and accuracy, especially when equipped with preconditioners based on absorbing boundary condition (ABC).

Model with small parameter and Robin boundary condition is considered. This is a multi-scale problem. The presence of small parameter leads to boundary layer phenomena. In order to discrete robin boundary condition and improve the order of uniform convergence, first transition point, which is very small, is introduced firstly. The domain is divided into the inner boundary layer region and the outside boundary layer region according to second transition point secondly. The new method is proved to be stable and high order uniformly convergent with respect to small parameter finally.

In this paper the equation with periodical condition and small parameter is considered. The equation will lose boundary condition and lead to large oscillation in boundary layer. The properties of the equation is studied firstly. The analytical solution is decomposed into the smooth component and the singular component. The asymptotic solution is proposed secondly. The asymptotic solution is used to solve the equation outside the boundary layer. Based on Shishkin-type mesh, fitted mesh method is presented for boundary layer thirdly. Error estimation of our method is studied finally.

The boundary stabilization problem of a one-dimensional unstable heat conduction system with boundary disturbance is investigated using a sliding-mode approach. This infinite-dimensional system, mathematical modeled by a parabolic partial differential equation (PDE), is powered with a Dirichlet type boundary actuator and only sensing at opposite end. By applying the Volterra integral transformation, a stabilizing boundary control law is obtained to achieve exponential stability in the ideal situation when there are no system uncertainties. The associated Lyapunov function is used for designing an infinite-dimensional sliding manifold, on which the system exhibits the same type of stability and robustness against of bounded exogenous boundary disturbance. By utilizing the similar transformation, an infinite-dimensional sliding-mode observer is proposed to reconstruct the system' states, which is with robustness to boundary disturbance. Moreover, the relative degree of the chosen sliding function with respect to the output-feedback boundary control input is zero. A continuous control law satisfying the reaching condition is obtained by passing a discontinuous (signum) signal through an integrator.

We consider a boundary feedback control problem for two coupled first-order hyperbolic partial differential equations with nonlinear coupling of Lotka-Volterra type. We use boundary control action on only one channel and design static and dynamic boundary controllers to drive the state at the end of the spatial domain to the desired constant reference values. The control design is based on a special Lyapunov functional related to an entropy function for Lotka-Volterra systems. The time derivative of the Lyapunov-based energy function can be made strictly negative by an appropriate choice of boundary conditions. We show global in time existence of the classical solutions and (asymptotic) exponential convergence of the state to the desired set point in the (C°) L2-norm. The design is illustrated with simulations.

Parabolic partial differential equation with periodical boundary value condition is considered. The equation also contains small parameter in x direction and different small parameter in t direction. The present of small parameter leads to boundary layer phenomena in both side of x direction and bottom side of t direction. The solution changes rapidly near three boundary layer. Left boundary layer function, right boundary layer function and bottom boundary layer function are derived by introducing three stretched variable and comparing small parameter in equation. The asymptotic solution is approximated by the degenerate solution and three boundary layer functions. Finally, numerical result is also presented in support of the proposed method.

We present a study on tunneling current density and an investigation of the optical gain of GaAs/Al x Ga 1−x As quantum cascade lasers. Current carrying states are obtained by taking into account Robin boundary conditions. Our simulation results show that this approach gives a very good agreement with other calculations using the Tsu-Esaki model and with simulations based on nonequilibrium Green's functions. Furthermore, by incorporating this method into optical gain calculations we establish good agreement with experimental results.

A system with infinite quantity of the boundary integral equations which is equivalent to the Dirichlet problem for some triangular system of elliptical equations and its weak formulation has been considered. A recurrent algorithm for solving such systems has been constructed. It involves finding the components of the solution using the boundary elements method step-by-step. The convergence orders for the collocation and the Galerkin methods have been compared.

In order to solve multi-body elastic contact problem, condensation boundary element method is used in this paper. Taking three bodies elastic contact without friction for example, the theory of elastic contact boundary element method is given, the boundary integral equations and the discrete boundary integral equations are established and the process of condensation solution is illustrated. An example is given to show the effectiveness and high accuracy of boundary element method.

Contact problems widely exist in diverse fields. Many contact problems are induced to boundary values and variational problems. Boundary variational inequality methods have been playing crucial roles in contact problems fields, which induce all the boundary conditions and contact conditions to one variational inequality and make the theoretical analysis very easy. Variational problem is a bridge to solve boundary values by variational inequality. In the paper, a function is derived on the base of the functional of potential energy, and their equivalence between a boundary value problem with obstacles on the boundary and equal variational problem is proved. So the partial differential equation's boundary value with obstacles can be solved by the corresponding variational problem.

There is a relatively complete style of homogeneous function about the boundary condition in the problem of sure resolution of inhomogeneous boundary condition based on the summarizing of mass former experiences and is proved in this article. It can be very easy to work out the homogeneous function in use of the theorem which is proved in this paper.

Method of weighted residual is used for developing of the boundary integral representation for Maxwell's equations. It is shown that the vectors of the electric and magnetic fields in an arbitrary point of domain can be expressed through its values on the boundary. The boundary integral equations of the second kind for the solving of the boundary-valued problems are received. It is marked that the given integral equation allows the effective numerical solving.

This research present an iterative approach that can estimate the boundary condition from the temperature measured at the interior point of the fluid field in the inverse natural convection problems. Based on the proposed method, the undetermined boundary condition is first denoted as the unknown variables in a set of nonlinear equations, which are formulated from the measured temperature and the calculated temperature of the inverse problem. Then, a modified Newton-Raphson method is used to estimate the unknown boundary condition. In the example problem, the close agreement between the exact solutions and the estimated results shows the potential of the proposed model in finding the accurate value of the boundary condition in the inverse natural convection problems.

We are concerned with the existence of positive solutions of general two point boundary value problems for the nonlinear equation xDeltaDelta(t) + lambdaf(t, x(sigma(t))) = 0 without the assumption of f being nonnegative.

Methods of construction of boundary operators for the boundary value problems for the Laplacian in the case of closed surface in R3 by means of double layer potential in the Hilbert space elements of which have a jump through boundary surface were considered in Polishchuk, A. D., 2005. The properties of these operators were investigated. Now we propose such methods and investigate the properties of corresponding operators in the case of tired boundary surface