Coupled Boundary Conditions Research Articles

3-D Parallel Simulations of Streamer Discharges in Air Considering Photoionization

We perform the 3-D parallel simulations of the streamer discharges in air using the minimal fluid model considering the photoionization. The SP 3 photoionization model, which consists of a series of elliptic equations with coupled boundary conditions, is solved using an alternating iteration method, which separates the coupled elliptic equations into independent equations; during each alternating iteration, a geometric multigrid-preconditioned flexible generalized minimal residual method (FGMRES) solver is used to efficiently solve the elliptic equation in the photoionization model. It is numerically shown that the proposed photoionization solver typically converges to a relative residual of 10 −6 with two to four alternating iterations and has a very good parallel efficiency. The interaction of two double-headed streamers is studied considering the photoionization, using 1000 CPU cores and more than 2 billion mesh cells.

Blow-up Rate Estimates and Blow-up Set for a System of Two Heat Equations with Coupled Nonlinear Neumann Boundary Conditions

This paper deals with the blow-up properties of positive solutions to a parabolic system of two heat equations, defined on a ball in associated with coupled Neumann boundary conditions of exponential type. The upper bounds of blow-up rate estimates are derived. Moreover, it is proved that the blow-up in this problem can only occur on the boundary.

Spectrum of a Class of Difference Operators with Indefinite Weights

In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign-changing weight has lasted a long time. The number of eigenvalues and the number of sign changes of the corresponding eigenfunctions of discrete equations under different boundary conditions are mainly studied. For the discrete Sturm-Liouville problems, similar conclusions about the properties of eigenvalues and the number of sign changes of the corresponding eigenfunctions are obtained under different boundary conditions, such as periodic boundary conditions, antiperiodic boundary conditions and separated boundary conditions etc. The purpose of this paper is to extend the similar conclusion to the coupled boundary conditions, which is of great significance to the perfection of the theory of the discrete Sturm-Liouville problems. We came to the following conclusions: first, the eigenvalues of the problem are real and single, the number of the positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. Second, under some conditions, we obtain the sign change of the eigenfunction corresponding to the j-th positive/negative eigenvalue.

Eigenvalues of discrete Sturm-Liouville problems with sign-changing weight and coupled boundary conditions

Eigenvalues of discrete Sturm-Liouville problems with sign-changing weight and coupled boundary conditions

A macroscopic traffic flow model with finite buffers on networks: well-posedness by means of Hamilton–Jacobi equations

We introduce a model dealing with conservation laws on networks and coupled boundary conditions at the junctions. In particular, we introduce buffers of fixed arbitrary size and time dependent split ratios at the junctions , which represent how traffic is routed through the network, while guaranteeing spill-back phenomena at nodes. Having defined the dynamics at the level of conservation laws, we lift it up to the Hamilton-Jacobi (H-J) formulation and write boundary datum of incoming and outgoing junctions as functions of the queue sizes and vice-versa. The Hamilton-Jacobi formulation provides the necessary regularity estimates to derive a fixed-point problem in a proper Banach space setting, which is used to prove well-posedness of the model. Finally, we detail how to apply our framework to a non-trivial road network, with several intersections and finite-length links.

Nonlocal boundary value problems with BV-type data

In this paper we present some existence and uniqueness results for solutions of second order boundary value problems, which are functions of bounded variation along with their derivatives. To this end, we apply fixed point theorems to an equivalent nonlinear perturbed Hammerstein integral equation. Here we consider non- standard boundary conditions like coupled boundary conditions, uncoupled boundary conditions, or integral-type boundary conditions. We also prove an abstract result concerning the spectral radii of some general classes of operators which applies to all boundary value problems mentioned above. The abstract results are throughout illustrated by a large number of examples.

Dynamic Effect Research of Cable-Lead-In Rod on Towed System

This paper aims to research the cable-lead-in rod effect on a towed system through mathematical modeling and numerical simulations. The rod dynamics, as a key part of this study, is modeled using the combination of cable node governing equations and kinematic constraint conditions. As the first attempt to analyze such a problem, the rod is simply treated as an elastic cable segment so as to be incorporated into the dynamics of the cable, and a set of algorithm is then proposed based on the kinematic constraint conditions to fully describe its motions. Meanwhile, the cable and the underwater vehicle are modeled by the traditional lumped mass method and the 6 degree-of-freedom maneuverability equations for submarines respectively; the coupling boundary conditions besides the rod dynamics are also given to form the whole system’s model. Several numerical cases are performed to investigate the rod effect on the system in different maneuver situations. Some meaningful conclusions are drawn through comparative analysis.

Some singular third‐order boundary value problems

In this paper, we consider some singular formally symmetric (self‐adjoint) boundary value problems generated by a singular third‐order differential expression and separated and coupled boundary conditions. In particular, we consider that the minimal symmetric operator generated by the third‐order differential expression has the deficiency indices (3,3). We investigate same spectral properties related with these problems, and we introduce a method to find the resolvent operator.

Successive iteration technique for singular nonlinear system with four-point boundary conditions

In this paper, the existence of at least one positive solution of the system of singular differential equations with four-point coupled boundary conditions is discussed. A constructive monotonic iterative technique on the equivalent completely continuous nonlinear operator is used to establish the result. This method produces an approximate solution in the form of series which is very helpful in developing a numerical scheme for the positive solution of the system. It is demonstrated through the examples.

Forced acoustic analysis and energy distribution for a theoretical model of coupled rooms with a transparent opening

This study presents a forced acoustic analysis and investigation of the energy distribution of a theoretical model of coupled rooms with a transparent coupling aperture. The energy principle is employed in combination with a 3D modified Fourier cosine series approach to formulate the theoretical model. The sound pressures inside individual subrooms are expanded as 3D Fourier cosine series supplemented with auxiliary functions, which are introduced to ensure the uniform convergence of the solution over the entire solution domain. Both the energy transmission through the coupling interface and the work done by the external load are considered as the external work in the energy expressions for the coupled system. The theoretical results are verified using the experimental results obtained for the room with a transparent opening. The influences of the coupling aperture and boundary conditions on the acoustic behaviors and energy distribution inside the coupled room system are investigated, including: opening positions, opening size, and impedance boundaries.

Fully Nonlinear Analysis of the Interaction between Water and Free Floating Ship

Based on the theory of velocity potential function, the fully nonlinear interaction between water and free floating simplified ship is studied through numerical model of fluid-solid coupling of ship-lift. The nonlinear numerical analysis of the coupling model of the water and the simplified ship body with different sizes, in which the boundary conditions included the free water surface boundary condition, the non-moving boundary condition and the water-solid coupling boundary condition. The numerical results show that the size change of the floating body affected the dynamic mechanical characteristics of the fluid-solid interaction of ship lift system, and affected the stress response of the floating simplified ship body.

Existence theory for a system of coupled multi‐term fractional differential equations with integral multi‐strip coupled boundary conditions

In this paper, we study a new boundary value problem of coupled nonlinear multi‐term fractional differential equations supplemented with integral multi‐strip coupled boundary conditions. The modern tools of fractional analysis are applied to derive the existence and uniqueness results for the given problem. We emphasize that our results are new and enrich the literature on the topic.

A fast preconditioned iterative method for the electromagnetic scattering by multiple cavities with high wave numbers

We study the problem of electromagnetic scattering by multiple open cavities embedded in an infinite ground plane with high wave numbers. The problem can be described by a series of Helmholtz equations with coupled boundary conditions. We develop a sixth-order finite difference scheme to discretize the coupled Helmholtz equations. By Gaussian elimination in the vertical direction and Fourier transform in the horizontal direction, we can reduce the multiple cavity scattering problem to an aperture linear system. However, in the situation of high wave numbers, the condition number of the coefficient matrix of the reduced linear system is especially large and the system tends to be ill-conditioned. The convergence histories of most iterative methods become oscillating which consume considerable computations and memory spaces. In order to overcome the difficulty caused by high wave numbers, we develop an efficient preconditioned iterative method based on the Krylov subspace, which greatly improves the eigenvalue distributions and reduces the number of iterations. Numerical experiments show the validity and efficiency of the proposed sixth-order fast preconditioned algorithm for solving the scattering by multiple cavities with high wave numbers.

Investigation on dynamic performances of a set of composite laminated plate system under the influences of boundary and coupling conditions

• The MRRM method is adopted to analyze the combination of composite laminated plate system. • A simple first-order shear deformation plate theory (S-FSDPT) is proposed. • The dynamic performance of the composite laminated plate system is discussed. • Parametric studies of the structural parameters are carried out. The method of reverberation-ray matrix (MRRM) is adopted to analyze the dynamic performance including the free vibration and power-low transfer characteristics of the combination of composite laminated plate system with arbitrary boundary and coupling boundary conditions. The classical plate theory (CPT) and a simple order shear deformation plate theory (S-FSDPT) are adopted. The artificial virtual boundary condition technology is taken to achieve arbitrary boundary conditions. At the coupling edges of the system, the generalized forces and displacements in local coordinates are transformed into the global coordinate of each component according to the coordinate transformation relationship. By using the artificial virtual coupling technology, the support springs at the coupling boundary are evenly arranged in the generalized displacement direction under the global coordinates. By changing each spring stiffness value to satisfy the generalized equilibrium relationship and the generalized displacement coordination conditions, thereby arbitrary coupling conditions of the coupled plate system are achieved. Through the numerical calculation of the common “L” type, “T” type and “ □ ” type coupled plate structure, the superior calculation performance of the method is proved, and it is not limited by the number of coupling plates and the coupling angle. On this basis, the effects of material parameters and coupling parameters on power flow and its transfer efficiency are discussed separately.

Multi-objective optimization for the best possible thermal, electrical and overall energy performance of a novel perforated-type regenerative evaporative humidifier

A perforated-type regenerative type evaporative humidifier is presented which has an innovative flow configuration. Such a flow configuration prevents the moist air from achieving quick saturation, and as a result, it maximizes the humidification capacity. A control volume formulation based mathematical model is developed which is simulated using nested numerical techniques having coupled boundary conditions. The system performance is gauged by three objective functions, namely humidification capacity, total electrical energy consumption, and efficiency factor. A detailed sensitivity analysis is carried out to report the system performance with respect to outdoor air conditions, geometric parameters, and operating conditions. Afterwards, an optimization study is conducted for 11 different climatic zones all around the world. An optimized humidification capacity of ∼32 gwater vapor/min, energy consumption of 2.1 kW, and an efficiency factor of ∼40% is reported for the proposed configuration for dry climatic zone which is 64%, 11%, and 26% more than a direct-contact evaporative humidifier respectively. It is also found that the optimal ranges for channel length, channel width, channel height, and water temperature, are 900–1000 mm, 55–60 cm, 7–8 mm, and 60–70 °C, respectively.

Coupled system of fractional differential equations with impulsive and nonlocal coupled boundary conditions

In this paper, we study existence and uniqueness of solutions for a coupled system of fractional differential equations of Caputo-type subject to nonlocal coupled and impulsive boundary conditions. The results are based on contraction principle and a generalized form of Krasnoselskii’s fixed point theorem (Avramescu and Vladimirescu in Fixed Point Theory 4(1), 3–13, 2003). An example is presented to illustrate the applicability of results.

Singular boundary method for 3D time-harmonic electromagnetic scattering problems

A frequency domain singular boundary method is presented for solving 3D time-harmonic electromagnetic scattering problem from perfect electric conductors. To avoid solving the coupled partial differential equations with fundamental solutions involving hypersingular terms, we decompose the governing equation into a system of independent Helmholtz equations with mutually coupled boundary conditions. Then the singular boundary method employs the fundamental solutions of the Helmholtz equations to approximate the scattered electric field variables. To desingularize the source singularity in the fundamental solutions, the origin intensity factors are introduced. In the novel formulation, only the origin intensity factors for fundamental solutions of 3D Helmholtz equations and its derivatives need to be considered which have been derived in the paper. Several numerical examples involving various perfectly conducting obstacles are carried out to demonstrate the validity and accuracy of the present method.

Positive solutions for a class of fractional difference systems with coupled boundary conditions

In this paper we use the fixed point index and nonnegative matrices to study the existence of positive solutions for a class of fractional difference systems with coupled boundary conditions.

Fractional order differential systems involving right Caputo and left Riemann\u2013Liouville fractional derivatives with nonlocal coupled conditions

In this paper, we introduce and study a new kind of coupled fractional differential system involving right Caputo and left Riemann–Liouville fractional derivatives, supplemented with nonlocal three-point coupled boundary conditions. Existence and uniqueness results for the given problem are derived with the aid of modern techniques of functional analysis. An example illustrating the existence of a unique solution is presented.

A System of Coupled Multi-Term Fractional Differential Equations with Three-Point Coupled Boundary Conditions

Abstract This paper studies the existence and uniqueness of solutions for a new boundary value problem of coupled nonlinear multi-term fractional differential equations supplemented with three-point coupled boundary conditions. We make use of Banach’s contraction principle and Leray-Schauder’s alternative to derive the desired results, which are well illustrated with examples. We emphasize that the obtained results are new and make a significant contribution to the existing literature on the topic.