Showing papers on "Boundary value problem published in 1995"
TL;DR: In this paper, an alternative formulation of the "perfectly matched layer" mesh truncation scheme is introduced, based on using a layer of diagonally anisotropic material to absorb outgoing waves from the computation domain.
Abstract: An alternative formulation of the "perfectly matched layer" mesh truncation scheme is introduced. The present scheme is based on using a layer of diagonally anisotropic material to absorb outgoing waves from the computation domain. The material properties can be chosen such that the interface between the absorbing material and free space is reflection-less for all frequencies, polarizations, and angles of incidence. This approach does not involve a modification of Maxwell's equations and is easy to implement in codes that allow the use of anisotropic material properties.
1,068 citations
TL;DR: In this article, a method for solving small-strain plasticity problems with plastic flow represented by the collective motion of a large number of discrete dislocations is presented, modelled as line defects in a linear elastic medium.
Abstract: A method for solving small-strain plasticity problems with plastic flow represented by the collective motion of a large number of discrete dislocations is presented. The dislocations are modelled as line defects in a linear elastic medium. At each instant, superposition is used to represent the solution in terms of the infinite-medium solution for the discrete dislocations and a complementary solution that enforces the boundary conditions on the finite body. The complementary solution is nonsingular and is obtained from a finite-element solution of a linear elastic boundary value problem. The lattice resistance to dislocation motion, dislocation nucleation and annihilation are incorporated into the formulation through a set of constitutive rules. Obstacles leading to possible dislocation pile-ups are also accounted for. The deformation history is calculated in a linear incremental manner. Plane-strain boundary value problems are solved for a solid having edge dislocations on parallel slip planes. Monophase and composite materials subject to simple shear parallel to the slip plane are analysed. Typically, a peak in the shear stress versus shear strain curve is found, after which the stress falls to a plateau at which the material deforms steadily. The plateau is associated with the localization of dislocation activity on more or less isolated systems. The results for composite materials are compared with solutions for a phenomenological continuum slip characterization of plastic flow.
901 citations
TL;DR: It is demonstrated that a variety of boundary conditions stipulated on the Radiative Transfer Equation can be implemented in a FEM approach, as well as the specification of a light source by a Neumann condition rather than an isotropic point source.
Abstract: This paper extends our work on applying the Finite Element Method (FEM) to the propagation of light in tissue. We address herein the topics of boundary conditions and source specification for this method. We demonstrate that a variety of boundary conditions stipulated on the Radiative Transfer Equation can be implemented in a FEM approach, as well as the specification of a light source by a Neumann condition rather than an isotropic point source. We compare results for a number of different combinations of boundary and source conditions under FEM, as well as the corresponding cases in a Monte Carlo model.
642 citations
Book•
01 Jan 1995
TL;DR: In this article, the authors describe a variety of methods for the approximate simulation of material surfaces, and provide the first comprehensive treatment of boundary conditions in electromagnetics, including impedance, resistive sheet, conductive sheet and generalised (or higher order) and absorbing (or non-reflecting) boundary conditions.
Abstract: Non-metallic materials and composites are now commonplace in modern vehicle construction, and the need to compute scattering and other electromagnetic phenomena in the presence of material structures has led to the development of new simulation techniques. This book describes a variety of methods for the approximate simulation of material surfaces, and provides the first comprehensive treatment of boundary conditions in electromagnetics. The genesis and properties of impedance, resistive sheet, conductive sheet, generalised (or higher order) and absorbing (or non-reflecting) boundary conditions are discussed. Applications to diffraction by numerous canonical geometries and impedance (coated) structures are presented, and accuracy and uniqueness issues are also addressed, high frequency techniques such as the physical and geometrical theories of diffraction are introduced, and more than130 figures illustrate the results, many of which have not appeared previously in the literature. Written by two of the authorities m the field, this
graduate-level text should be of interest to all scientists and engineers concerned with the analytical and numerical solution of electromagnetic problems.
641 citations
TL;DR: In this article, a nonrelativistic Hamiltonian of the interaction between a moving mirror and radiation pressure was derived directly from the equation of motion of a moving moving mirror, and the wave equation with timevarying boundary conditions.
Abstract: We present a nonrelativistic Hamiltonian of the interaction between a moving mirror and radiation pressure. This Hamiltonian is derived directly from the equation of motion of a moving mirror, and the wave equation with time-varying boundary conditions. We discuss the canonical quantization of both the field and the motion of the mirror.
572 citations
TL;DR: In this article, a comparison between comprehensive linear gyrokinetic calculations employing the ballooning formalism for high-n (toroidal mode number) toroidal instabilities are described.
569 citations
TL;DR: In this paper, a numerical code based on Nwogu's equations is developed, which uses a fourth-order predictor-corrector method to advance in time, and discretizes first-order spatial derivatives to fourthorder accuracy, thus reducing all truncation errors to a level smaller than the dispersive terms.
Abstract: The extended Boussinesq equations derived by Nwogu (1993) significantly improve the linear dispersive properties of long-wave models in intermediate water depths, making it suitable to simulate wave propagation from relatively deep to shallow water. In this study, a numerical code based on Nwogu's equations is developed. The model uses a fourth-order predictor-corrector method to advance in time, and discretizes first-order spatial derivatives to fourth-order accuracy, thus reducing all truncation errors to a level smaller than the dispersive terms retained by the model. The basic numerical scheme and associated boundary conditions are described. The model is applied to several examples of wave propagation in variable depth, and computed solutions are compared with experimental data. These initial results indicate that the model is capable of simulating wave transformation from relatively deep water to shallow water, giving accurate predictions of the height and shape of shoaled waves in both regular and irregular wave experiments.
546 citations
TL;DR: In this paper, a one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion.
Abstract: A one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion. The model is derived from the Stokes equations by use of rational asymptotic expansions and under a slender jet approximation. The equations are solved numerically and the jet radius is found to vanish after a finite time yielding breakup. The slender jet approximation is valid throughout the evolution leading to pinching. The model admits self-similar pinching solutions which yield symmetric shapes at breakup. These solutions are shown to be the ones selected by the initial boundary value problem, for general initial conditions. Further more, the terminal state of the model equation is shown to be identical to that predicted by a theory which looks for singular pinching solutions directly from the Stokes equations without invoking the slender jet approximation throughout the evolution. It is shown quantitatively, therefore, that the one-dimensional model gives a consistent terminal state with the jet shape being locally symmetric at breakup. The asymptotic expansion scheme is also extended to include unsteady and inertial forces in the momentum equations to derive an evolution system modelling the breakup of Navier-Stokes jets. The model is employed in extensive simulations to compute breakup times for different initial conditions; satellite drop formation is also supported by the model and the dependence of satellite drop volumes on initial conditions is studied.
545 citations
TL;DR: In this article, a stress jump condition was developed based on the non-local form of the volume averaged Stokes' equations and the excess stress terms that appeared in the jump condition were represented in a manner that led to a tangential stress boundary condition containing a single adjustable coefficient of order one.
532 citations
TL;DR: Liouville theory is shown to describe the asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant as mentioned in this paper, and the anti-de Sitter boundary conditions implement the constraints that reduce the WZW model to the Liouville model.
Abstract: Liouville theory is shown to describe the asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant. This is because (i) Chern - Simons theory with a gauge group on a spacetime with a cylindrical boundary is equivalent to the non-chiral SL(2,R) WZW model; and (ii) the anti-de Sitter boundary conditions implement the constraints that reduce the WZW model to the Liouville theory.
508 citations
TL;DR: Gash's analytical model of rainfall interception is reformulated, with improved boundary conditions, to give a better description of the evaporation from sparse forest as discussed by the authors, and the model is tested against data from Les Landes Forest collected during HAPEX-MOBILHY.
Book•
01 Jan 1995
TL;DR: In this paper, the hodge decomposition is used for boundary value problems for differential forms, and the boundary value problem can be solved using the Hodge-decomposition.
Abstract: Analysis of differential forms.- The hodge decomposition.- Boundary value problems for differential forms.
TL;DR: In this paper, a surface thermal boundary condition for a world ocean model is proposed based on previous methods which have used bulk formulas to define a model-dependent correction to the air-sea fluxes applied to the model.
TL;DR: In this paper, new collocation methods are given for solving symmetrical boundary-value problems, where orthogonality conditions are used to select the collocation points and the accuracy obtained is comparable to that of least squares or variational methods and the calculations are simpler.
TL;DR: In this paper, the development of a viscous incompressible flow generated from a circular cylinder impulsively started into rectilinear motion is studied computationally, and an adaptative numerical scheme based on vortex methods is used to integrate the vorticity/velocity formulation of the Navier-Stokes equations for a wide range of Reynolds numbers (Re = 40 to 9500).
Abstract: The development of a two-dimensional viscous incompressible flow generated from a circular cylinder impulsively started into rectilinear motion is studied computationally. An adaptative numerical scheme, based on vortex methods, is used to integrate the vorticity/velocity formulation of the Navier–Stokes equations for a wide range of Reynolds numbers (Re = 40 to 9500). A novel technique is implemented to resolve diffusion effects and enforce the no-slip boundary condition. The Biot–Savart law is employed to compute the velocities, thus eliminating the need for imposing the far-field boundary conditions. An efficient fast summation algorithm was implemented that allows a large number of computational elements, thus producing unprecedented high-resolution simulations. Results are compared to those from other theoretical, experimental and computational works and the relation between the unsteady vorticity field and the forces experienced by the body is discussed.
TL;DR: In this paper, a new and efficient algorithm for computing the three-dimensional stress and velocity fields in grounded glaciers including the role of deviatoric stress gradients was proposed, which can be used for a wide rangе of stress-strain-rate relations, as long as strain only depends on deviating and shear stresses and on temperature.
Abstract: A new and efficient algorithm for computing the three-dimensional stress and velocity fields in grounded glaciers includes the role of deviatoric stress gradients. A consistent approximation of first order in the aspect of ratio of the ice mass gives a set of eight field equations for the five stress and three velocity components and the corresponding boundary conditions. A coordinate transformation mapping the local ice thickness on to unity and approximating the derivatives in the horizontal direction by centered finite-differences yields five ordinary differential and three algebraic equations. This allows use of the method of lines, starting the integration with prescribed stress and velocity components at the base, and a simple iteration procedure converges rapidly. The algorithm can be used for a wide rangе of stress-strain-rate relations, as long as strain only depends on deviatoric and shear stresses and on temperature. Sensitivity tests using synthetic and realistic ice geometries show the relevance of normal deviatoric stresses in the solutions for the velocity components even for ice sheets. Stress and velocity fields may deviate substantially from the widely used shallow-ice approximation.
TL;DR: In this paper, a non-slip boundary condition at a wall for the lattice Boltzmann method is presented, where unknown distribution functions at the wall are assumed to be an equilibrium distribution function with a counter slip velocity which is determined so that fluid velocity at the boundary is equal to the wall velocity.
Abstract: A non‐slip boundary condition at a wall for the lattice Boltzmann method is presented. In the present method unknown distribution functions at the wall are assumed to be an equilibrium distribution function with a counter slip velocity which is determined so that fluid velocity at the wall is equal to the wall velocity. Poiseuille flow and Couette flow are calculated with the nine‐velocity model to demonstrate the accuracy of the present boundary condition.
TL;DR: In this article, a method for computing rigorous upper bounds under plane strain conditions is described, based on a linear three-noded triangular element, which has six unknown nodal velocities and a fixed number of unknown multiplier rates, and uses the kinematic theorem to define a kinematically admissible velocity field as the solution of a linear programming problem.
TL;DR: In this article, the use of a numerical time-domain simulation based on the finite-difference timedomain approximation for studying low and middle-frequency room acoustic problems is described, and an interesting approach lies in using the FDTD simulation to adapt a digital filter to represent the acoustical transfer function from source to observer.
Abstract: This paper illustrates the use of a numerical time‐domain simulation based on the finite‐difference time‐domain (FDTD) approximation for studying low‐ and middle‐frequency room acoustic problems. As a direct time‐domain simulation, suitable for large modeling regions, the technique seems a good ‘‘brute force’’ approach for solving room acoustic problems. Some attention is paid in this paper to a few of the key problems involved in applying FDTD: frequency‐dependent boundary conditions, non‐Cartesian grids, and numerical error. Possible applications are illustrated with an example. An interesting approach lies in using the FDTD simulation to adapt a digital filter to represent the acoustical transfer function from source to observer, as accurately as possible. The approximate digital filter can be used for auralization experiments.
TL;DR: In this paper, a hydrodynamic boundary condition is developed to replace the heuristic bounce-back boundary condition used in the majority of lattice Boltzmann simulations, which is applied to the two-dimensional, steady flow of an incompressible fluid between two parallel plates.
Abstract: A hydrodynamic boundary condition is developed to replace the heuristic bounce‐back boundary condition used in the majority of lattice Boltzmann simulations. This boundary condition is applied to the two‐dimensional, steady flow of an incompressible fluid between two parallel plates. Poiseuille flow with stationary plates, and a constant pressure gradient is simulated to machine accuracy over the full range of relaxation times and pressure gradients. A second problem involves a moving upper plate and the injection of fluid normal to the plates. The bounce‐back boundary condition is shown to be an inferior approach for simulating stationary walls, because it actually mimics boundaries that move with a speed that depends on the relaxation time. When using accurate hydrodynamic boundary conditions, the lattice Boltzmann method is shown to exhibit second‐order accuracy.
TL;DR: In this article, similar solutions of the laminar boundary-layer equations describing heat and flow in a quiescent fluid driven by a stretched surface subject to suction or injection are obtained.
01 Jan 1995
TL;DR: In this article, the boundary function method has been applied in the theory of semiconductor devices, and a mathematical model of combustion process in the case of autocatalytic reaction has been proposed.
Abstract: 1. Basic Ideas Regular and singular perturbations Asymptotic approximations Asymptotic and convergent series Examples of asymptotic expansions for solutions of regularly and singularly perturbed problems 2. Singularly perturbed ordinary differential equations Initial value problem The critical case Boundary value problems Spike-type solutions and other contrast (dissipative) structures 3. Singularly perturbed partial differential equations The method of Vishik-Lyusternik Corner boundary functions The smoothing procedure Systems of equations in critical cases Periodic solutions Hyperbolic systems 4. Applied problems Mathematical model of combustion process in the case of autocatalytic reaction Heat conduction in thin Bodies Application of the boundary function method in the theory of semiconductor devices Relaxation waves in the FitzHugh-Nagumo system On some other applied problems Index.
TL;DR: In this paper, a first-principles model of anomalous thermal transport based on numerical simulations is presented, with stringent comparisons to experimental data from the Tokamak Fusion Test Reactor (TFTR).
Abstract: A first‐principles model of anomalous thermal transport based on numerical simulations is presented, with stringent comparisons to experimental data from the Tokamak Fusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)]. This model is based on nonlinear gyrofluid simulations, which predict the fluctuation and thermal transport characteristics of toroidal ion‐temperature‐gradient‐driven (ITG) turbulence, and on comprehensive linear gyrokinetic ballooning calculations, which provide very accurate growth rates, critical temperature gradients, and a quasilinear estimate of χe/χi. The model is derived solely from the simulation results. More than 70 TFTR low confinement (L‐mode) discharges have been simulated with quantitative success. Typically, the ion and electron temperature profiles are predicted within the error bars, and the global energy confinement time within ±10%. The measured temperatures at r/a≂0.8 are used as a boundary condition to predict the temperature profiles in the main confinement ...
TL;DR: In this article, the stabilization of finite element methods in which essential boundary conditions are approximated by Babuska's method of Lagrange multipliers is discussed and there is a close connection with this technique and a classical method by Nitsche.
TL;DR: Liouville theory is shown to describe the asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant as mentioned in this paper, and the anti-de Sitter boundary conditions implement the constraints that reduce the WZW model to the Liouville model.
Abstract: Liouville theory is shown to describe the asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant. This is because (i) Chern-Simons theory with a gauge group $SL(2,R) \times SL(2,R)$ on a space-time with a cylindrical boundary is equivalent to the non-chiral $SL(2,R)$ WZW model; and (ii) the anti-de Sitter boundary conditions implement the constraints that reduce the WZW model to the Liouville theory.
TL;DR: In this article, an exact polynomial expansion of the operator [E−(H+Γ)−1, Γ being a simple complex optical potential, was shown to converge uniformly in the real energy domain.
Abstract: The new recently introduced [J. Chem. Phys 102, 7390 (1995)] empirical recursion formula for the scattering solution is here proved to yield an exact polynomial expansion of the operator [E−(H+Γ)]−1, Γ being a simple complex optical potential. The expansion is energy separable and converges uniformly in the real energy domain. The scaling of the Hamiltonian is trivial and does not involve complex analysis. Formal use of the energy‐to‐time Fourier transform of the ABC (absorbing boundary conditions) Green’s function leads to a recursion polynomial expansion of the ABC time evolution operator that is global in time. Results at any energy and any time can be accumulated simultaneously from a single iterative procedure; no actual Fourier transform is needed since the expansion coefficients are known analytically. The approach can be also used to obtain a perturbation series for the Green’s function. The new iterative methods should be of a great use in the area of the reactive scattering calculations and o...
TL;DR: In this paper, the boundary conditions for reactive flows described by Navier-Stokes equations are discussed. And a formulation based on one-dimensional characteristic waves relations at the boundaries, previously developed by Poinsot and Lele for perfect gases with constant homogeneous thermodynamic properties, is rewritten and extended in order to be used in the case of gases described with realistic thermodynamic and reactive models.
TL;DR: In this article, numerical techniques developed to investigate viscoplastic Stokes flows within a model of lithospheric deformation are discussed, in particular, the techniques are related to a subduction model of compressional orogens.
Abstract: SUMMARY
This paper presents and analyses numerical techniques developed to investigate viscoplastic Stokes flows within a model of lithospheric deformation. In particular, the techniques are related to a subduction model of compressional orogens. The driving mechanism in the model corresponds to the near-rigid convergence and subduction of one mantle lithosphere beneath another in plane strain and this boundary condition forces flow in an overlying viscoplastic model crust. The numerical techniques use the arbitrary Eulerian-Lagrangian formulation in which flows with free surfaces and large deformation are computed on an evolving Eulerian finite-element grid that conforms to the material domain. A regridding algorithm allows the associated Lagrangian motion and fields to be followed, and, in addition, coupled back to the Eulerian calculation of the flow. Mass-flux boundary conditions are used so that the effects of erosion and deposition by surface processes, and mass loss by subduction can be included in the model calculation. The evolving model crustal layer is flexurally compensated using a general elastic beam formulation. The applicability of the numerical techniques to problems ranging from accretionary wedges to crustal and lithospheric scale deformation is discussed. Simple flows, a linear viscous subduction model, a whirl flow, and a quasi-convection model are used to show that the mass conservation, regridding and surface tracking errors are small. The broader applicability of the modelling techniques is reviewed.
TL;DR: In this article, the exact nonreflecting boundary conditions at artificial boundaries for the numerical solution of the Helmholtz equation and the time dependent wave equation in unbounded domains were developed.